A newsvendor who chooses information effort
A Newsvendor Who Chooses Informational Effort
Thomas Marschak
Walter A.Haas School of Business,University of California,Berkeley,California94720,USA,marschak@https://www.360docs.net/doc/9114104357.html,
J.George Shanthikumar
Krannert School of Management,Purdue University,West Lafayette,Indiana47907,USA,jshanthi@https://www.360docs.net/doc/9114104357.html,
Junjie Zhou
School of International Business Administration,Shanghai University of Finance and Economics,Shanghai,20043,China
zhoujj03001@https://www.360docs.net/doc/9114104357.html,
W e study a newsvendor who can acquire the services of a forecaster,or,more generally,an information gatherer(IG) to improve his information about demand.When the IG’s effort increases,does the average ex ante order quantity rise or fall?Do average ex post sales rise or fall?Improvements in information technology and in the services offered by forecasters provide motivation for the study of these questions.Much depends on our model of the IG and his efforts.We study an IG who sends a signal to a classic single-period newsvendor.The signal de?nes the newsvendor’s posterior probability distribution on the possible demands and the newsvendor uses that posterior to calculate the optimal order. Each of the possible posteriors is a scale/location transform of the same base distribution.When the IG works harder,the average scale parameter drops.Higher IG effort is always useful to the newsvendor.We show that there is a critical value of order cost.For costs on one side of this value more IG effort leads to a higher average ex ante order and for costs on the other side to a lower average order.But for all costs,more IG effort leads to higher average ex post sales.We obtain analogous results for a“regret-averse”newsvendor who suffers a penalty that is a nonlinear function of the discrepancy between quantity ordered and true demand.
Key words:newsvendor;inventory management;information gathering;demand forecasting
History:Received:October2012;Accepted:January2014by Jayashankar Swaminathan,after2revisions.
1.Introduction
A growing demand-forecasting“industry”(whose current players include Oracle Retail Demand Fore-casting,Sylvon,Direct Tech,Demand World)offer individually designed demand forecasts to retailers and inventory managers.Continual improvement in the quality of forecasts is claimed.The technology for assembling datasets on which forecasts can be based (scanner data,survey data)steadily improves.In this paper,we study the effects of more and better demand information on the behavior of inventory managers.
Speci?cally,we consider a model in which the inventory manager is a classic newsvendor whose demand changes at regular intervals and is indepen-dent of previous demands.The newsvendor uses his information about forthcoming demand to place an order with a manufacturer.Every unit ordered has the same cost and every unit sold has the same price. The newsvendor’s information about forthcoming demand is supplied by an Information gatherer(IG). After exerting effort,the IG sends one of several
possible signals to the newsvendor.The signal deter-mines a posterior demand distribution and the news-vendor uses that distribution to calculate that period’s optimal order.Without the IG,the newsvendor would use a prior distribution.When the IG exerts more effort in his study of future demand,the poster-ior distributions become,on the average,more useful to the newsvendor.
Our central questions are the following:Does more effort on the part of the IG increase or decrease the newsvendor’s average ex ante order,when we average over all of the IG’s possible signals?Does it increase or decrease the newsvendor’s average ex post sales?
Our paper provides a new approach to a puzzle considered in a number of earlier papers:are invento-ries and information substitutes?When information about demand improves do inventories shrink?In our approach,inventory size is measured by the newsvendor’s average order and better information means higher IG effort.We study a model of the IG in which effort has a natural de?nition.
Consider a speci?c example,where the role of “newsvendor”is played by an NGO(nongovernmental 110
Vol.24,No.1,January2015,pp.110–133DOI10.1111/poms.12208 ISSN1059-1478|EISSN1937-5956|15|2401|0110?2014Production and Operations Management Society
organization).The NGO orders medicines for a partic-ular disease and ships them to countries where the disease is endemic.Each dose of medicine cures the disease and costs c.Each cured person has value v>c.The NGO procures the services of an IG,an expert on the disease,whose effort(research budget) can be varied.The IG provides one of several possible signals,where each signal de?nes a posterior distribu-tion on forthcoming demand(number of diseased persons).The NGO uses that posterior to choose an expected cost-minimizing order,where cost is the sum of overage and underage costs.The NGO has to tell its suppliers,who must plan ahead,what its aver-age order will be,and also wants to announce to the world the average number of cured persons.So,the NGO wants to know the average,over all the IG’s sig-nals,of the ex ante expected cost-minimizing order,as well as the average,over all signals,of the ex post deliveries(“sales”).
We shall avoid the ambitious question of how much IG effort the newsvendor should buy from a member of the forecasting“industry.”That would require us to specify a price for each of an IG’s possible efforts and to balance the cost of more IG effort against its bene?ts to the newsvendor.It is natural,in our view, to defer the more ambitious investigation until we have studied a variety of IG models and we know more,for each of the models,about the direction in which the ex ante and ex post quantities move when IG effort increases.
There are a number of ways to model an IG and his efforts and we shall have to choose one of them.The IG might partition the possible demands,reporting to the newsvendor the set of the partitioning in which the current demand lies.Higher IG effort might yield a re?nement of the partitioning that the IG obtains for a lower effort.Alternatively,the possible partition-ings might not be successive re?nements.Instead—assuming that the possible demands are the points of an interval—the sets of a partitioning might be subin-tervals having equal prior probability,where the number of such subintervals grows when IG effort increases.In another model,the IG samples from the population of potential demanders,each of whom,let us say,demands either one unit or two units in the next period.The IG then reports the sampling results to the newsvendor.Higher IG effort means a larger sample.In yet another model,the IG issues a point-valued forecast of the demand and higher effort means that the forecast’s average-squared error is reduced.Each model of the IG presents its own chal-lenges when we study the effect of more IG effort on the newsvendor’s average ex ante order quantity and on average ex post sales.
We shall identify a special property of the newsven-dor’s payoff function:it is shift-invariant and satis?es a homogeneity condition.We choose a model of the IG which turns out to articulate well with that special property,so that sharp results can be obtained.In our model,the IG is a scale/location transformer.He has a base distribution on the possible demands and a collection Y of possible signals.For a given value of true demand,there is a probability distribution on Y. After devoting effort to the study of forthcoming demand,the IG obtains a signal,say y,and conveys that signal to the newsvendor.The signal y de?nes a pair(a(y),b(y)),where a(y)is a location parameter and b(y)>0is a scale parameter.The location/scale pair (a(y),b(y))de?nes a transform of the IG’s base distri-bution and that transform becomes the newsvendor’s posterior.The newsvendor uses the posterior to calcu-late the optimal order quantity.The variance of the transformed distribution is increasing in b(y).So it is natural to de?ne the IG’s effort in terms of average scale reduction and to say that the IG works harder when the average value of b(y),over all the IG’s signals y,drops. We?rst consider a classic newsvendor,who sells at a price of one,obtains no salvage value from unsold stock,and has an order cost of c per unit,where 0 mineD;qTàcq j y ,where D denotes realized demand.We shall obtain results that hold no matter what the IG’s base distribution may be and no matter what his collection of possible location/scale pairs may be.Here are our results for the classic newsvendor: [1]When the IG works harder,the newsvendor bene?ts.His average pro?t(weakly)rises. [2]There is a critical value of the cost c.If cost exceeds the critical value then the newsven- dor’s average ex ante order rises whenever the IG works harder;if cost is less than the critical value then the average order drops whenever the IG works harder.If cost equals the critical value,the average order stays the same when- ever the IG works harder. [3]Whenever the IG works harder,the average of the classic newsvendor’s ex post sales goes up or stays the same,whatever c may be. Note that we could,if we wish,avoid the term “works harder,”which refers to the effort that the IG chooses.In view of statement[1],we could use instead the term“whenever the newsvendor bene-?ts,”which refers to the outcome of the effort choice. But we?nd it instructive to identify a plausible IG-effort measure(average scale reduction in our loca-tion/scale model of the IG)and to interpret our results as telling us the effect of more IG effort on average newsvendor order quantity and average sales.Observe that[2]implies Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society111 [20]For any?xed c,the effect of more IG effort on the average ex ante order is monotonic: either more effort increases the average order (or leaves it unchanged),or more effort decreases the average order(or leaves it unchanged). After studying the classic newsvendor,we turn to a “generalized”newsvendor,who suffers a penalty that depends,nonlinearly and asymmetrically,on the gap between the order quantity chosen and the quantity that turns out to be ideal.Such a newsvendor is shown to be“regret-averse.”For the generalized newsvendor,we obtain counterparts of the preceding results. What about an IG who is not our scale/location transformer?There may be other IGs for whom we again get the results just listed when we study the effect of more IG effort on the newsvendor’s average orders.But there are certainly IGs for whom the above results are sharply violated. Consider the following simple example.Demand is 0,1or2with respective prior probabilities0.1,0.1, 0.8,so expected demand is1.7.The IG has three effort levels. ?At the lowest effort,the IG provides no new information and the newsvendor’s posterior probabilities are the same as the priors.?At the intermediate effort level,the IG sends the newsvendor one of two signals denoted y1 and y2.Signal y1tells the newsvendor that demand is0with probability1and1with probability1 2.Signal y2tells the newsvendor that demand is certainly2.The signal probabil- ities are0.2for y1and0.8for y2. ?At the highest effort level,the IG provides the newsvendor with perfect information about demand. For a given value of c in(0,1),it is straightforward to show that expected newsvendor pro?t rises when we go from lowest IG effort to intermediate effort and from intermediate effort to highest effort,and to cal-culate,for each effort level,the newsvendor’s average optimal ex ante order quantity and average ex post sales.(For intermediate effort,we average over the two possible signals).Figure1shows the relation between the cost c and the average order quantity for each of the three effort levels. Notice that the?gure differs from our result[20]. For a?xed value of c in(0.5,0.8],the average order quantity drops when the IG goes from lowest effort to intermediate effort,but rises when the IG goes from intermediate effort to highest effort.That means that [2]is also violated:there is no critical value of cost such that for all costs on one side,the average order rises whenever the IG works harder and for all costs on the other side,the average order falls whenever the IG works harder.When we turn to our scale/loca-tion IG,we will obtain two?gures(Figures3and5 below)which again show the relation between c and average order quantity.They will obey statements[2] and[20]and will contrast sharply with Figure1(Fig-ure3will portray a uniform-distribution example and Figure5will portray a normal-distribution example). As for average ex post sales,we?nd,in our three-demand example,that statement[3]is also violated: for0.5 1.1.A Remark on the Blackwell IG One might conjecture that results about the effect of more IG effort on the newsvendor’s average orders are easily obtained if we let our IG?t the assumptions of the celebrated papers by Blackwell on comparisons of experiments.(See Blackwell,(1951,1953);detailed treatments are found in Marschak and Miyasawa (1968),in Chapter1of Marschak and Radner(1972), and in Marschak et al.(2013).)The Blackwell theo-rems have played a large role in the economics of information.Consider an IG whose signals are received by an action-taker.The action-taker responds to a signal by choosing an action which maximizes expected payoff for the posterior implied by the sig-nal.Now consider two of the IG’s effort levels and suppose that whatever the action-taker’s payoff function may be,and whatever the prior may be,the action-taker bene?ts(weakly)when the IG switches from the lower effort to the higher effort:after the switch,the best expected payoff,averaged over the IG’s signals, rises or stays the same.Let us call such an IG a Black-well IG with respect to the two efforts.One example of a Blackwell IG is an IG who partitions the states of the world and tells the action-taker the set in which the Figure1Average Order:The Three-Demand Example Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 112Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society true state lies.The IG’s second effort re?nes the?rst effort’s partitioning.That re?nement cannot harm the action-taker,no matter what the payoff function and the prior may be.In a second example,the states are the proportion of persons that are of the?rst type in a two-type population,and the action-taker’s payoff depends on the action he chooses and on the true pro-portion of type-1persons.(We suggested such an example above for the case where the action-taker is a newsvendor with two types of demanders.)The Blackwell IG samples the population,learns each sampled person’s true type,and reports the result to the action-taker.A larger sample—i.e.,more IG effort —can never hurt the action-taker,no matter what the payoff function and the prior may be. The comparison-of-experiments literature shows (among many other results)that an IG is a Blackwell IG with respect to the two efforts if and only if the fol-lowing holds:for any convex function/on the possi-ble posteriors,the expected value of/,over the IG’s signals,is at least as high for the larger effort as for the smaller effort.If the action-taker is our newsven-dor,and if his best order quantity were a convex(con-cave)function of the posterior,then we could immediately conclude that his average order cannot drop(cannot rise)when the Blackwell IG makes an effort switch that bene?ts the newsvendor.Unfortu-nately,the required convexity(concavity)does not,in general,hold.Moreover,our scale/location IG,for whom effort is de?ned by the average of the scale parameters,is not,in general,a Blackwell IG with respect to the two efforts.For some scale/location IGs,we can?nd a prior and a payoff function such that lower average scale implies a lower average value of the action-taker’s best expected payoff,and another prior and payoff function such that lower average scale implies a higher average value of the action-taker’s best expected payoff.In summary,the Blackwell theorems do not provide a shortcut in our investigation. 1.2.Some Related Literature We shall discuss four groups of papers. First,many papers have studied the effect of changes in the distribution of demand on an inven-tory manager’s pro?t and order size,but are not directly concerned with the improvement of demand information.An early paper in this group is Gerchak and Mossman(1992),where demand(at a?xed price) is a weighted sum of a?xed component and a ran-dom component.Higher uncertainty means that more weight is given to the latter.The effect of more uncer-tainty on the pro?t and order size for a single-period newsvendor is studied.Ridder et al.(1998)study a single-period newsvendor and compare the inventory cost under two demand distributions that are ordered according to various forms of n-th order stochastic dominance.They show that under second-order sto-chastic dominance,lower demand variance always implies lower cost.But they give conditions for third-or higher-order stochastic dominance under which inventory cost can be lower while the variance is higher.Papers by Song and Zipkin(1993),Song (1994),and Song et al.(2010)have an analogous agenda in a dynamic inventory setting.They trace the effect of variability in lead time(time until the ordered inventory is delivered)on inventory cost.In Agrawal and Seshadri(2000),Li and Atkins(2005), and Xu et al.(2010)both price and quantity are cho-sen,the effect of price on demand is random,and the variability of that effect in?uences the inventory man-ager’s pro?t and order size. In a second group of papers,the inventory man-ager’s information about future demand can be improved by advance ordering.If a buyer commits to an order to be delivered at a future date,that removes the uncertainty about that buyer’s future demand. Moreover,the advance order may provide clues as to the future demand of those buyers who do not order in advance.An early paper in this group is Buzacott and Shanthikumar(1994),which investigates the value of better forecasts obtained by advance demand information in production/inventory systems.It is shown that the improved forecast serves as a substi-tute for safety stock.Another early paper is Hariharan and Zipkin(1995).They study a dynamic inventory system where customers randomly arrive and each places an order for delivery at a later time.A delivery later than the time the customer selected may occur. The main conclusion is that when an optimal base-stock policy is followed,an increase in average demand lead time(the length of time the customer agrees to wait)has the same effect on system perfor-mance as a drop in average supply lead time(the time between receipt of the order by the supplier and its delivery). Another early contribution to the advance demand information literature is Gallego and€Ozer(2001). They?nd optimal state-dependent policies for sto-chastic inventory systems,where the state re?ects the current advance demand information.The bene?ts of advance demand information are investigated in fur-ther detail in€Ozer(2003).In Lu et al.(2003)a similar agenda is pursued(in the paper’s section6)for the more complex setting of a multicomponent assemble-to-order system.It is now found that knowing demand in advance is more useful(there are fewer late deliveries)than reducing the supply lead time for the components.Papers by€Ozer and Wei(2004)and by Karaesmen et al.(2004)study capacitated produc-tion systems and?nd that advance demand informa-tion can be a substitute for both capacity and Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society113 inventory.Other papers reaching similar conclusions include Gayon et al.(2009)and Karaesmen et al. (2002).Song and Zipkin(2012)also obtain similar results for a model in which demand is driven by underlying random variables like weather or the behavior of competitors,and advance information about those variables is revealed by advance orders. Later papers(Boyaci and€Ozer2010,Prasad et al. 2011)extend the problem to include the inducement of advance demand by appropriate pricing policies.If discounts are used,the cost of the discount has to be balanced against the value of the improved demand information. A third group of papers consider the sharing of demand information.In Lee et al.(2000)a retailer’s demands follow a process known to the retailer.In each period,the retailer has an inventory,observes current demand,and orders from the manufacturer an amount that permits the retailer to meet current demand and replenish inventory.The manufacturer, in turn,anticipates the retailer’s orders,maintains his own inventory,and places his own replenish-ment orders with a supplier.The paper studies the bene?ts of information sharing by comparing the case where the manufacturer does not know the retailer’s demand process and the case where he does(sharing).The comparison is made with respect to the manufacturer’s expected cost and expected inventory.It is found,under general conditions,that both of these are lower under sharing.A similar con-clusion is reached in Cachon and Fisher(2000), where there are several retailers and they face a sta-tionary demand process.The manufacturer either knows the retailers’orders or knows both their orders and their inventory positions as well(shar-ing).In Gaur et al.(2005)the problem posed in Lee, Song,and Tang is revisited for the case where retailer demand follows an autoregressive moving average process.It is found that whenever the manu-facturer bene?ts from sharing,the manufacturer’s average safety stock declines.Many papers focus on strategic aspects of information sharing.They study a game played by various members of a supply chain.The players may be a manufacturer and retail-ers,as in Zhang(2002)and Li and Zhang(2008).In an equilibrium of the game,the retailers may choose to convey private information about demand and inventory positions to the manufacturer,who uses it in choosing a price.These papers do not directly address the effect of sharing on inventory size,i.e., the average inventory size when sharing occurs at the game’s equilibrium and the size when it does not. Finally,there are papers which do not fall easily into the three preceding groups but nevertheless investigate,in various other ways,the effect of improved information about demand on pro?t and on inventory size.An early paper is Milgrom and Roberts(1988),in which a producer chooses a col-lection of varieties of its product and each customer demands one variety.The producer can stock a quantity of each variety,or he can survey(at a cost) a fraction of customers,obtaining perfect informa-tion for each surveyed customer.It is found that the producer does one or the other,but not both. Another early paper is Dudley and Lasserre(1989). Here demand is determined by a stochastic process and a forecast of next period’s demand is based on observed demand in a past period.If the past per-iod is more recent,the forecast costs more but it is more reliable.A producer chooses his forecast expenditure and responds to the forecast by choos-ing inventory size.It is found that when there is a drop in the cost of a forecast(for every given past period),then the average inventory size drops.Ca-chon and Fisher(1997),a paper based on observed practice,studies an inventory management system in which each retailer’s daily demands are used to make an exponential-smoothing forecast of future demand.A simple but practical reorder rule uses the forecasts.Simulations suggest that the forecasts reduce excess inventories.Bergen and Iyer(1997) consider the improvement in demand forecasts when we shorten the time between(1)the retailer’s placement of an order and(2)production and deliv-ery of the order by the manufacturer.Final demand becomes known very shortly after(2)occurs.Hence, the time between(1)and the realization of demand is reduced.Forthcoming demand is better estimated when it is just a short time away.So there is a tradeoff between the extra cost of rapid production and delivery on the one hand and improved inven-tory decisions due to better forecasts on the other. The paper studies the preferred tradeoff from the viewpoint of the manufacturer and that of the retai-ler.Among other results,one?nds that shortening the lead time reduces the retailer’s average order. That occurs as well in a later paper by Lau and Lau (2002),where some of the assumptions in Bergen and Iyer are relaxed.Gurnani and Tang(1999) study a retailer who can place an order with a sup-plier at one of two time points.Both points occur before demand is https://www.360docs.net/doc/9114104357.html,rmation about the forthcoming demand is summarized by a one-dimensional signal.As time passes,more becomes known about the forthcoming demand,so the corre-lation between the signal and the true demand is higher at the later point than at the earlier one. However,unit cost is random(as well as demand) and its average is higher for orders placed later. Under certain conditions on the random cost,it is found that when the retailer behaves optimally,his Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 114Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society average early order drops when the correlation increases.There is a similar result in Choi et al. (2003),where a related two-time point model with Bayesian updating is studied. Toktay and Wein(2001)study a production man-ager who obtains demand forecasts and chooses a production plan that meets demand while minimiz-ing expected inventory costs.Demand follows a sta-tionary stochastic process.The forecaster may specify the process incorrectly.The effect of improved fore-cast quality is studied.Under certain conditions, higher quality leads to smaller inventories.In Jain and Moinzadeh(2005)there is uncertainty about the manufacturer’s available supply and better informa-tion about the supply allows the retailer to have a smaller safety stock. Iyer et al.(2007)consider a retailer,a manufacturer, and an information system which provides signals about demand.Demand has two possible values and there are two signals.The information system’s reli-ability is measured by a number in[0,1],namely the probability of high demand given the signal called “high,”which is assumed to equal the probability of low demand given the signal called“low.”“More information”means a higher value of that number.If ?rst-best decisions are made,more information leads to lower excess stock. Bensoussan et al.(2009)is a recent paper which explicitly addresses the question whether demand information is a substitute for inventory size,and ?nds that this is indeed the case.There is a single decision-maker,an“Inventory Manager,”who con-fronts a(?nite)sequence of demands and chooses an order in each period as a function of what he knows about the demand history thus far.The most recently known demand may be some periods earlier.The delay can be reduced.The manager’s cost in each per-iod depends on the period’s starting inventory and on the new order.Unmet demand is backlogged and ful?lled in the next period.Each period’s order maxi-mizes discounted future cost.For a given delay,the dynamic-programming solution is characterized. Shorter delays indeed lead to smaller average inven-tories. On the other hand,Anand(2009)presents an inno-vative in?nite-period model in which the conclusion is quite different.A producer and an inventory man-ager seek to maximize discounted expected pro?t.In each period,the inventory manager observes a signal about the forthcoming demand.A myopic policy, which is shown to be optimal,determines the current period’s production quantity,the manager’s current order,and the amount the manager ships to demand-ers.The manager’s shipment is the smaller of his cur-rent inventory and a“ship-up-to”threshold.The threshold depends on the current signal.The signal is supplied by what we have called,in the preceding discussion,a Blackwell IG.It is found that if the ship-up-to threshold is concave in the signal(which?ts a variety of examples),then we have“complements”rather than“substitutes”:an increase in the Blackwell IG’s effort leads to higher average inventories. The path we follow here appears to be new:choose a model of an IG,de?ne effort as a function of the IG’s signal set,and investigate the effect of higher effort on the newsvendor’s average orders and average ex post sales in a single-period setting. 1.3.Plan of the Rest of the Paper In section2,we formally describe our IG,who per-forms a scale/location transform of a base distribu-tion.We discuss two examples of such an IG in detail:a normal-distribution example and a uni-form-distribution example.We brie?y sketch two other examples:a triangular-distribution example and a?nite example.Section3identi?es a key property of the newsvendor payoff function:it is shift-invariant and homogeneous of degree one.Sec-tion3then presents two-key lemmata which exploit that key property as well as the scale/location prop-erty of our IG.Section4presents two propositions about the usefulness of more IG effort for the classic newsvendor and the effect of more effort on the average ex ante order and the average ex post sales. In section5we consider a generalized“regret-averse”newsvendor and we obtain two proposi-tions that are the analogs of the propositions in sec-tion4.Section6provides some concluding remarks and points to a large unexplored terrain for future research. 2.The IG Who Transforms a Base Distribution and Sends a Signal to the Newsvendor The true demands lie in a set D R.Once true demand has been chosen by“Nature,”the IG observes a signal y which is conveyed to the newsven-dor.Our IG/newsvendor model has the following elements: ?The newsvendor and the IG know the joint distribution of the pair(D,y),The marginal distribution of D is the prior on D.?For a given y,the joint distribution determines the posterior CDF on the true demands;once he receives the signal y,the newsvendor uses that posterior to calculate his order.?For every y,the posterior CDF has the follow- ing property in our model:it is a scale/loca- tion transform of a?xed base CDF,denoted B, which has mean zero.The location parameter Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society115 is denoted a(y).The scale parameter is positive and is denoted b(y).The posterior CDF(a transform of B)is denoted T a(y),b(y). Let z denote the base random variable.Since its mean is zero,the mean of the transformed variable D=a(y)+b(y)z is a(y).The variance of D is(b(y))2 times the variance of the base random variable.Note that the base CDF B and the transformed CDF T a(y),b(y)—which is the newsvendor’s posterior—obey the fol-lowing: T aeyT;beyTeDT?B DàaeyT beyT : That fact will be used in several of our proofs.The IG has a collection of possible signals.Each signal identi?es a location/scale pair and hence a posterior CDF.We shall call the collection of posterior CDFs a structure.We will want to compare alternative struc-tures.To do so,we use an index g.A value of g identi?es a particular structure.For that structure, the set of possible signals is denoted Y g.For each signal y in Y g,the location/scale pair is denoted(a (y,g),b(y,g))and the corresponding transform of the base B is T a(y,g),b(y,g).That transform is the newsven-dor’s posterior CDF.It is helpful to use an abbrevi-ated symbol for the newsvendor’s CDF,namely F g y. Thus, F g y?T aey;gT;bey;gT: For a given g,we shall call the pair I g?h Y g;f F g y g y2Y g i the information structure identi?ed by g. The symbol E F y will denote expectation under the CDF F y,and the symbol E y2Y will denotes expecta-tion with respect to signals in the set Y.We shall say that the family of structures{I g}has the average-scale-reduction order or,for brevity,the scale-reduction order,if E y2Y g0bey;g0T\E y2Y g bey;gTwhenever g0[g: If a family of structures has the scale-reduction order,then it is reasonable to take g as an IG-effort index:a higher value of g means a drop in the aver-age,over all signals,of the transformed distribu-tion’s standard deviation. We shall show that scale reduction is useful to the newsvendor:it increases the average,over all sig-nals,of his highest attainable expected pro?t given the signal.So for a family that has the scale-reduc-tion order,the?rst of two structures is more useful than the second if and only if the?rst requires more IG effort.That is our statement[1]in the Introduc-tion.Moreover,we shall?nd,as in statements[2] and[3],that scale reduction(more effort)always leads to higher average ex post sales,but for certain values of the cost c it leads to a higher average ex ante order,and for other values to a lower average order. Note that the example in the Introduction,where demand D takes just three values,does not have the location/scale property.Consider the two signals in the intermediate effort structure.For the?rst signal, the posterior assigns positive probability to the?rst two demands only.For the second signal,the poster-ior assigns positive probability to the third demand only.There does not exist a base distribution B on the three demands such that each of the two posteriors is a scale/location transform of B. 2.1.First Example:The IG Has a Uniform Base Distribution and Partitions a Uniformly Distributed Set of True Demands Suppose that the set of possible true demands is D??0;1 and the prior is the uniform distribution on[0,1].Let the IG’s base distribution B be the uniform distribution onà1 2 ;1 2 ?? .For the information structure I g,there are n g possible signals and the signal set is Y g?f y1egT;y2egT;...;y n g egTg.The typical signal y2Y g de?nes the location parameter a(y,g)and the scale parameter b(y,g).These,in turn, de?ne a transform of B.The transform is the newsvendor’s posterior CDF given the signal y.The posterior is uniform on the interval h aey;gTàbey;gT 2 ; aey;gTtbey;gT i &?0;1 .The width of the interval equals b(y,g).The probability of the signal y equals that width divided by the width of D??0;1 ,i.e.,it equals b(y,g).So the average scale parameter for the structure I g is E y2Y g bey;gT? X n g i?1 b y iegT;g !2 : The IG’s structure family{I g}has the scale-reduc-tion order(i.e.,E y2Y g0beyT\E y2Y g beyTwhenever g0>g) if X n g i?1 b y iegT;g !2 is strictly decreasing in g: That is the case,in particular,if the IG always parti-tions[0,1]into equal intervals and there are more of them when g rises,i.e.,b y iegTT;g eT?1 n g for all i, where n g is strictly increasing in g.Higher g then Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 116Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society means that,on the average,the posterior distribu-tion has narrower support. To illustrate further,let the IG’s family of possible structures contain just two structures,I g and I g 0.The structure I g partitions [0,1]into just two intervals,0;15??and 1 5;1à?.The structure has two signals.Signal y 1(g )—or y 1,for brevity —identi?es the location/scale pair ea ey 1;g T;b ey 1;g TT?110;15àáand signal y 2 identi?es the pair ea ey 2;g T;b ey 2;g TT?35;45àá .The ?rst pair tells the newsvendor that demand is uniformly distributed on a ey 1;g Tàb ey 1;g T 2;a ey 1;g Ttb ey 1 ;g T 2h i ? 0;15?? .The second pair tells him that demand is uni-formly distributed on a ey 2;g Tàb ey 2;g T 2 ;a ey 2;g Tth b ey 2;g T2 ?15;1??.The two signal probabilities are the two subinterval widths 15;4 5,and the average scale parameter is 15àá2t45àá2?1725.Structure I g 0,on the other hand,partitions [0,1]into the three intervals 0;14??;14;34à?;34;1à?.It has three signals.They identify,respectively,the loca-tion/scale pairs 18;1 4àá;12;12àá;and 78;14àá,and those pairs tell the newsvendor,respectively,that demand is uniformly distributed on 0;14??,on 14;34??,and on 34;1?? .The three signal probabilities are the three subinterval widths 1;1;1 ,and the average scale parameter is 14àá2t12àá2t14àá2?38.That is smaller than 1725,so the IG’s effort increases when he goes from structure I g to structure I g 0.We shall return to the two structures I g ;I g 0below,when we illustrate our general Propositions. 2.2.Second Example:Demand is Normally Distributed and the IG Observes Demand Plus a Normally Distributed Noise In the next example,the set D of demands is the real line.The prior is normal with mean l and variance 1f ,where f >0.The IG observes demand plus a normally distributed noise.For a given true demand D ,we have the following for the signal y :y ?D t ; is normally distributed with mean zero and variance 1 g : The random pair (D ,y )has a bivariate normal dis-tribution.Each of its two means equals l .The two variances are 1f and 1f t1g .The covariance equals 1 f .We ?nd that the conditional distribution of D given a sig-nal y is normal with mean a ey ;g T? g y tfl g tf and standard deviation b ey ;g T? ??????????? 1g tf s :We can now describe the IG’s procedure as a scale/location transformation,where the above g is the IG’s index.The base distribution is the standard normal N e0;1T.The IG’s set of possible indices g is the posi-tive real line.For every g ,the signal set Y g is the real line.When the newsvendor receives the signal y 2Y g ,he replaces the prior with the posterior F g y ,namely the normal CDF with mean a (y ,g )and variance (b (y ,g ))2.Since the term y does not enter the expression for b (y ,g ),it is automatically the case that if g 0 >g then we have E y 2Y g 0b ey ;g 0T?????????????1g 0tf s \ ??????????? 1 g tf s ?E y 2Y g b ey ;g T:So the family of structures I g has the scale-reduction order.When the IG switches from g to g 0 >g ,he works harder.The average standard deviation of noise is reduced.For a given con?dence level,the average width of a con?dence interval around the mean for the posterior obtained in I g 0(averaging over the signals in Y g 0 )is less than the average width for the posterior obtained in I g (averaging over the signals in Y g ).2.3.Other Examples:Triangular and Finite Consider the case where the prior distribution of demand is symmetric and triangular with support [0,1].Let the IG’s base density function be symmetric and triangular with support à12;1 2??.In a location/scale transform of the base density,where the loca-tion/scale parameter pair is (a ,b ),we shift the apex of the base triangle to the right by the distance a (i.e.,we add a to the mean),and we multiply the width of the base support by b .We then have another symmetric triangular density function,where the coordinates of the apex are a ;2àá,the mean is a ,and the support is a àb 2;a tb 2 ?? ?0;1 .That transformed density function is the newsvendor’s posterior density func-tion when the signal he receives identi?es the pair (a ,b ).Now consider an IG with two structures.In each structure,a signal identi?es a location/scale pair.Effort is higher in the second structure if the average scale parameter,over all the signals,is lower.In the ?rst structure,the IG has three signals,with probabilities 14;12;1 4àá.For the ?rst signal, ea ;b T?14;12àá ,so the posterior density function is symmetric and triangular with mean 14and support 0;12?? .For the second and third signals,the (a ,b )pairs are 12;12àáand 34;12àá.Those de?ne posterior symmetric Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 117 triangles with supports 14;34?? and 12;1??.The average-scale parameter is 12.In the second structure,the IG has ?ve signals,with probabilities 116;18;116;12;14àá .The (a ,b )pairs are 18;14àá;14;14àá;38;14àá;e12;12T,and 34;12àá. The average scale parameter is now 14á1 16t14á18t14á116t12á12t12á14?7 16,so the second structure indeed requires more effort than the ?rst. For a simple ?nite example,let the possible demands be D *,D *+L ,D *+2L ,D *+3L ,D *+4L ,D *+5L ,where L >0.In the prior distri-bution,each of these has probability 16.Let the base variable take just three values,namely à1,0,1,each with probability 13.Note that the mean of the base distribution is zero and that the three mass points of the support {à1,0,1}are evenly spaced with a gap of one between the successive points.In an (a ,b )location/scale transform of the base distri-bution,we again have three evenly spaced mass points in the support.The new mean is a plus the base distribution’s mean,i.e.,it is a +0=a .The gap between the successive mass points is now b times the base distribution’s gap,i.e.,it is b á1=b .Now consider an IG with three structures.The ?rst struc-ture has two signals,each with probability 12.The ?rst signal tells the newsvendor that the support of the demand distribution is {D *,D *+2L ,D *+4L },where the three probabilities are equal.The poster-ior is then an (a ,b )transform of the base,where (a ,b )=(D *+2L ,2L ).The second signal tells the newsvendor that the support is {D *+L ,D *+3L ,D *+5L }(with equal probabilities).This time (a ,b )=(D *+3L ,2L ).The second structure also has two signals,each with probability 12.The ?rst signal tells the newsvendor that the support is {D *,D *+L ,D *+2L }(with equal probabilities),so (a ,b )=(D *+L ,L ).The second signal tells the newsvendor that the support is {D *+3L ,D *+4L ,D *+5L }(with equal probabilities),so (a ,b )=(D * +4L ,L ).Finally,the third structure has four signals,each with probability 14.The ?rst two signals provide the same information as the two sig-nals of the ?rst structure and they have the same (a ,b )pairs as the ?rst structure’s signals.The last two signals provide the same information as the two signals of the second structure and they have the same (a ,b )pairs as the second structure’s sig-nals.Average scale is 2L for the ?rst structure,L for the second structure,and 32L for the third structure.So effort rises when the IG goes from the ?rst structure to the third and then from the third to the second. We now prove general propositions about the effects of more IG effort (lower average scale)on the newsvendor.The propositions apply,in particular,to the four examples just discussed. 3.A Property of the Newsvendor’s Payoff Function and Two Key Lemmata The newsvendor’s payoff function u eq ;D T?min eD ;q Tàcq has the following property: There exists a number c such that for any a and any b [0;we have u eq ;D T?ca tb áu q àa b ;D àa b for all q ;D : 8><>:e1T So the function u is shift-invariant and homoge-neous of degree one.The role of c is played by 1àc . To obtain results about the effect of a change in our IG’s structure on the newsvendor’s order quantities we need two key lemmata.Lemma A exploits the shift invariance and homogeneity of the newsvendor’s payoff function.Those properties articulate well with the scale/location property of our IG’s family of structures.That allows us to obtain a key linear relation between the average best quantity if demand had the base distribution and the average best quantity when demand has the transformed distribution.Lemma B obtains a similar relation between the base distribution’s highest attainable expected pro?t and the highest attainable expected pro?t for the transformed dis-tribution. The proof of each lemma,and the proofs of each of the subsequent propositions,are found in the Appen-dix. L EMMA A.Let u =min (q,D )àcq be the newsvendor’s payoff function.Consider an IG who has a base CDF B with mean zero.The IG’s signal determines a location parameter a and a scale parameter b >0.They de?ne a transformed CDF T ab .Let q B denote the smallest maximizer of E B u (q,D )and let q ab denote the smallest maximizer of E T ab u eq ;D T.Let u B denote E B u (q B ,D )and let u T ab denote E T ab u eq ab ;D T.Then q ab ?a tb áq B : eA1T and u T ab ?c a tbu B ;where c ?1àc : eA2TWhen there are several maximizers of E B u (q ,D ),the proof requires us to identify one of them.Our proof uses the smallest maximizer. Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 118 Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society To state the second lemma,we let U (g )denote the average,over all the signals in Y g ,of the newsven-dor’s expected value of the pro?t u when he responds to each signal by maximizing expected pro?t under the posterior (the transformed distribution)that the signal identi?es.The symbols q B ,u B ,as well as sym-bols of the form q ab ,all have the same meaning as in Lemma A.Each signal y in Y g identi?es a location parameter a (y ,g )and a scale parameter b (y ,g ).We let ^q eg Tdenote the average,over all the signals in Y g ,of the newsvendor’s smallest maximizing quantity.Thus, ^q eg T E y 2Y g q a ey ;g T;b ey ;g T; U eg T E y 2Y g eu q a ey ;g T;b ey ;g T;D àáá: We let V (g )denote the average of the scale parame-ter,over all the signals in Y g .So V eg T E y 2Y g b ey ;g T: A structure family {I g }has the scale-reduction order if V (g 0) For every pair (g 0,g ),we have ^q eg 0Tà^q eg T?q B áeV eg 0TàV eg TTeB1TU eg 0TàU eg T?u B áeV eg 0TàV eg TT: eB2T Note that Equations (B1)and (B2)concern,respec-tively,the change in expected order quantity and the change in expected pro?t when we move from one structure to another.We ?nd that the ?rst change equals a constant times the change in average scale,and the second change equals another constant times the change in average scale.The ?rst constant is the base distribution’s average order and the second con-stant is the base distribution’s average pro?t. 4.Two Propositions About the Change in the Classic Newsvendor’s Order Quantity When the IG Switches From One Structure to Another In the ?rst of the two propositions which now follow,we consider the classic newsvendor’s ex ante order quantity.Recall that an IG has a collection of possible signals,each identifying a posterior.We have called the collection a structure .We now consider a switch from one structure to another.We ?nd that a switch in the IG’s structure is useful to the newsvendor —it increases the average pro?t U —if and only if the switch also reduces V ,the average scale parameter.We also ?nd a critical value of the cost c .On one side of the critical value,a useful switch increases the average order.On the other side,such a switch decreases the average order. P ROPOSITION 1.Consider a classic newsvendor whose pro?t is min (q,D )àcq,with 0 [1]V(g 0) [2]If 1àc ^q eg 0T[^q eg T. [3]If 1àc >B(0),then U(g 0)>U(g )if and only if ^q eg 0T\^q eg T. [4]If 1àc =B(0),then ^q eg 0T?^q eg T.To interpret the number B (0),recall that the base CDF B has mean zero.If the base CDF has a symmet-ric density function,then B e0T?12.That is the case in the uniform example in section 2.1and the normal example in section 2.2.So in those examples,the criti-cal value of c is 12.Note that for the normal-distribu-tion case there is a direct way of seeing the criticality of c ?12.The direct argument uses the fact that when demand is normal,the optimal order equals mean demand plus standard deviation times the order that is optimal when mean is zero and standard deviation is one.Proposition 1uses a more general argument to obtain the criticality of c ?12,and that argument cov-ers the normal case,the uniform case,and the triangu-lar case discussed in 2.3.It turns out that in all these cases the criticality of c ?1is explained by the fact that every posterior is a scale/location transform of a common distribution.In Proposition 3,we will obtain a generalization of the criticality of c ?12for a gener-alized newsvendor.There,however,we see no direct path leading to that generalized conclusion in the nor-mal-distribution case. 4.1.Illustrating Proposition 1in a Uniform-Distribution Example Consider the uniform-distribution example in section 2.1above.Demand is distributed uniformly on [0,1]and that is the newsvendor’s prior.Consider the two structures,I g and I g 0.In I g ,the IG partitions [0,1]into n subintervals having probabilities (widths)p 1,...,p n ,where P n 1?1p i ?1.The newsvendor learns the subin-terval that contains the current demand.It is straight-forward to show that average profit over all subintervals ? c áec à1T2áX n i ?1 ep i T2t1 2:e2T In I g 0the IG partitions [0,1]into k subintervals having probabilities (widths)r 1,...,r k ,where Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 119 P k 1?1r i ?1.For I g ,the average scale parameter is P n i ?1ep i T2and for I g 0,it is P k i ?1er i T2 .The structure I g 0requires more scale-reduction effort than I g if X k 1?1 er i T2\X n 1?1 ep i T2:Suppose,in particular,that I g and I g 0are the two speci?c structures presented in section 2.1above.In I g there are two subintervals,0;1 5??and 15;1à?.In the higher effort structure I g 0,there are three subintervals 0;1??;1;3à?;3;1à?.In Figure 2,we illustrate state-ment [1]of the Proposition by using statement (6)and graphing the average pro?ts U (g )and U (g 0)for all val-ues of the unit cost c .The ?gure has two additional average pro?t graphs.One concerns perfect informa-tion,where the newsvendor knows demand exactly and his order always matches demand.The other con-cerns the no-information case,where the newsvendor only knows that demand is uniform on [0,1]. Next,we illustrate statements [2]–[4]of the Proposi-tion,using the same speci?c structures I g and I g 0as in Figure 2.Figure 3shows the relation between the unit cost c and the average orders (over all signals),^q eg T and ^q eg 0 T.When I g has n subintervals with probabili-ties (widths)p 1,...,p n ,it is straightforward to estab-lish that ^q eg T?12àc áX n i ?1ep i T2t1 2: e3TUsing Equation (3),we calculate average order for the structures I g ;I g 0of Figure 2.For each structure,we graph average order as a function of c in Figure 3.The ?gure again has two further average pro?t graphs.One concerns perfect information,where average order is 12,the mean of the true demands.The other concerns the no-information case,where the newsvendor always orders 1àc ,since that quantity meets the critical-fractile condition (at that quantity,cumulative density equals 1àc ).At c ?12,both the average order for I g and the average order for I g 0,equal 12.So at c ?12,the I g graph,and the I g 0graph intersect the perfect-information graph,the no-information graph,and each other. A partial intuition for Figure 3is provided by noting that for extremely small c ,the order is very large for every signal,and the average order (over all signals)is large as well,while for c close to one,the average order is small.So it is plausible that improved infor-mation lowers average order when c is small but raises it when c is close to one.Proposition 1supplements that intuition and covers intermediate values of c .4.2.Illustrating Proposition 1in a Normal-Distribution Example Now consider the normal-distribution example in sec-tion 2.2.Demand is distributed normally with mean l and variance 1f ;that is the newsvendor’s prior.The newsvendor receives a signal from a scale/location IG whose base CDF is the standard normal,which we denote N .When the IG has the structure I g ,then the signal y 2Y g tells the newsvendor that F g y ,the pos-terior CDF on the demands,is the transform of the base distribution given by the location parameter a (y ,g )and the scale parameter b (y ,g ).So F g y is normal with mean a ey ;g T?g y tfl g tf and standard deviation b ey ;g T???????1 g tf q .The average of the posterior mean a (y ,g ),over all signals y ,equals l ,the mean of the prior. For a ?xed unit cost c ,consider the newsvendor’s order,under the structure I g ,given the signal y 2Y g .The order equals the mean of F g y plus N à1 e1àc Ttimes the standard deviation of F g y ,i.e.,the order equals g y tfl tN à1 e1àc Tá??????????? 1s :Figure 2 Average Pro?t:Uniform Example Figure 3Average Order:Uniform Example Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 120 Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society For the structure I g 0,the newsvendor’s optimal order given the signal y 2Y g 0 is g 0 y tfl g 0tf tN à1 e1àc Tá ???????????? 1g 0tf s :In Figure 4,the counterpart of the uniform-distribu-tion Figure 2,we again illustrate statement [1]of the Proposition.To distinguish the structures portrayed from those of Figure 2,we label them ~I g and ~I g 0,with respective signal sets ~Y g ;~Y g 0 .For every c ,the ?gure shows average pro?t (over all signals)for the two structures and also shows average pro?t for the per-fect-information case and the no-information case.The ?gure is drawn for the case l ?4;f ?14;g ?7 36 ;g 0?2: To illustrate statements [2]–[4],we continue to study this case and we calculate the average orders, ^q eg Tand ^q eg 0T.Each of the signal sets ~Y g ;~Y g 0is the real line.For ~I g and ~I g 0,the signals are normally distributed with mean l and with variance 1f t1g and 1f t1 g 0,respectively.The average order quantities over all sig-nals are ^q eg T?l tN à1 e1àc Tá ??????????? 1g tf s ;^q eg 0T?l tN à1 e1àc Tá???????????? 1g 0tf s : We compute ^q eg Tand ^q eg 0Tfor every c .The graphs are shown in Figure 5,the counterpart of the uni-form-distribution Figure 3.As before,the ?gure also depicts perfect information and no information.Under perfect information,the order equals true demand,so for every c ,the average order is l .If there is no information,then for a given c ,the order is the quantity meeting the critical-fractile condition for the newsvendor’s prior CDF (the normal CDF with mean l and variance 1f ),i.e.,it is the quantity for which the mass to the left equals 1àc .At c ?12,the critical-fractile quantity equals l ,and that is also the average perfect-information quantity. Figures 2and 4share a key property:regardless of unit cost,the higher effort structure yields higher average pro?t (over all signals).Figures 3and 5share a second key property:there is a critical value of c such that the high-effort average order (over all sig-nals)is less than the low-effort average order for costs below the critical value but is greater for costs above it.Both properties would also be exhibited in a pair of ?gures that we omit here.They concern the triangular example in section 2.3.On the other hand,in the three-demand example of the Introduction,where (as we saw)the scale/location property fails,both of the key properties are violated.For average order,we have Figure 1,which stands in sharp contrast to Fig-ures 3and 5.We obtain Figures 2–5by direct compu-tation.For the uniform-distribution ?gures (Figures 2and 3),we use the formulae given in Equations (2)and (3).Another direct computation yields the omit-ted ?gures concerning the triangular case.If we had only the ?gures,we would be puzzled by their sharing of the key properties.The puzzle is resolved by Prop-osition 1,where a unifying argument covers the uni-form-distribution example,the normal-distribution example,the triangular example,and others.The common thread is that every newsvendor posterior can be interpreted as the scale/location transform of a ?xed base distribution.As we have seen,that fact turns out to articulate well with the key property of the newsvendor’s payoff function —the function is shift-invariant and satis?es a homogeneity condition.The three-demand example of the Introduction lacks the scale/location property and it lacks the key prop-erties of Proposition 1as well. Figure 5Average Order:Normal Example Figure 4Average Pro?t:Normal Example Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 121 The next proposition concerns the classic newsven-dor’s average ex post sales.This time there is no criti-cal value of c .Consider a switch in IG structure which is useful to the newsvendor and hence (as statement [1]of Proposition 1showed),reduces the average-scale parameter.Whatever c may be,the switch increases the average,over all signals,of ex post sales. In stating the proposition,we let ^S eg Tdenote the average ex post quantity,over all the signals in Y g ,when the newsvendor responds to each signal with an optimal order.Thus, ^S eg T E y 2Y g E T a ey ;g T;b ey ;g T min q a ey ;g T;b ey ;g T;D àá :P ROPOSITION 2.Let the assumptions of Proposition 1 hold.Then, U eg 0T[U eg Tif and only if ^S eg 0T[^S eg T:4.3.Illustrating Proposition 2in a Uniform-Distribution example Another straightforward argument shows that if [0,1]is partitioned into n subintervals with widths p 1,...,p n ,then average expost sales over all subintervals ?12à12c 2áX n i ?1 ep i T2:e4T Using Equation (4),we calculate average ex post sales for the same two structures I g and I g 0that are used in Figures 2and 3.Figure 6then graphs aver-age ex post sales as a function of c for each structure.Once again,there are also graphs for perfect infor-mation and for no information. 4.4.Illustrating Proposition 2in a Normal-Distribution Example A somewhat cumbersome calculation (using the for-mula for the mean of a left-tail-truncated normal dis-tribution)shows that for our normal-distribution example average expost sales ?l t ?????????? 1 g tf s á Z min x ;N à1e1àc T á1??????2p p e àx 2=2dx ! :e5T Note that Z min x ;N à1 e1àc T á1??????2p p e àx 2=2dx \Z x á1??????2p p e àx 2=2 dx ?0 : So average ex post sales rise when g rises.That is seen in Figure 7,where we again use l ?4;f ?14;g ?736;g 0 ?2.Again,the ?gure has two additional graphs,for the perfect-information case and the no-information case. As before,we can study ex post sales directly for the uniform-distribution example (using Equation (4))and for the normal-distribution example (using Equa-tion (5)).But Proposition 2again provides a unifying argument that covers both examples and explains why Figures 6and 7share a key property that is lack-ing in the three-demand example of the Introduction.In that example,as we saw,the IG does not perform a scale/location transform.Higher IG effort yields Figure 7 Average Ex Post Sales:Normal Example Figure 6Average Ex Post Sales:Uniform Example Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 122 Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society higher average pro?t,but for some values of c ,aver-age ex post sales fall when effort increases.Proposition 2tells us that this cannot happen when the IG is a scale/location transformer.Then higher effort yields higher average pro?t and for every c ,average ex post sales rise when effort increases. 5.A Generalization:A Newsvendor Who is “Regret-Averse” 5.1.A Class of Quantity-Choosers That Includes a Regret-Averse Newsvendor Consider next a new version of the newsvendor.To introduce the new version,we ?rst recall that the clas-sic newsvendor’s task can be stated in an alternative way:he seeks to minimize c áeq àD Ttte1àc TáeD àq Tt; where J +is the standard shorthand for max(0,J ).It must be the case that one of the two summed terms equals zero.The ?rst term is the unsold-inventory (overage)penalty and the second term is the unful-?lled-demand (underage)penalty.We can rewrite the whole expression as c á?eq àD Ttt 1àc c áeD àq Tt :Thus —since c >0—the classic newsvendor seeks to maximize the following payoff function: u eq ;h T?àj q àh j r for q !h àK áj q àh j r for q \h ,& e6Twhere h =D ,K ?1àc c àár and r =1.Now suppose that when the newsvendor’s quan-tity deviates from the quantity that turns out to be ideal —namely the quantity that equals realized demand —then the penalty suffered is no longer lin-ear in the absolute size of the deviation.Instead,the penalty is given in the above payoff function u ,where h again equals D ,K again equals 1àc c àár ,but r is now greater than one .Such a newsvendor is our generalized newsvendor. It will be useful to let the state variable in the func-tion u continue to be the above general variable h and to study a quantity-chooser whose payoff function u is de?ned by Equation (6),where K is an arbitrary positive number.The state h chosen by Nature is the quantity that turns out to be ideal,and u describes the penalties suffered by a quantity-chooser when the quantity he chooses departs from the ideal.Our main interest is the case where h =D ,the quantity-chooser is our generalized newsvendor,and K ?1àc àár .But the Proposition which follows is stated for a general quantity-chooser. We note that the generalized newsvendor described by the above u is regret-averse .Consider regret in a general setting.Given a payoff function,the regret associated with a state and an action taken before that state becomes known is the amount by which the payoff actually earned falls short of what could have been earned had the state been known before the action had to be chosen.An early and widely cited discussion of regret appears in Bell (1983).In our setting,continue to assume that price is one and cost is c with 0 q eq ;D T?c ámax eq àD ;0Tte1àc Támax eD àq ;0T:Note that either the ?rst or the second of the two summed terms must equal zero.The ?rst term of q is the regret experienced when demand becomes known and turns out to be less than or equal to the order quantity q .The second term is the regret expe-rienced when demand turns out to be greater than or equal to q .Regret is zero when demand turns out to match q .But since one of the two terms in q has to equal zero,we have,for any r >1and for the payoff function u in (+)(with K ?1àc c àár ): ?q eq ;D T r ?c r á?eq àD Tt r te1àc Tr á?eD àq Tt r ?àc r áu eq ;D T: Thus,maximizing the expected value of u (and hence the expected value of c r áu )is equivalent to minimizing the expected value of the r th power of regret.A decision-maker who minimizes the expected value of regret raised to the power r ,where r >1,is said to be regret-averse . Various departures from the classic risk-neutral newsvendor have been explored.The expected-util-ity-maximizing risk-averse newsvendor is discussed in Agrawal and Seshadri (2000);Eeckhoudt et al.(1995);Lau (1980);and Choi and Ruszczynski (2008).The newsvendor who minimizes maximum regret is discussed in Perakis and Roels (2008).Thus far,how-ever,the regret-averse newsvendor has not appeared on the scene.Papers by experimentalists,like Schweitzer and Cachon (2000)and Ho et al.(2010),report that some subjects ?nd avoiding unsold stock to be more important than avoiding unful?lled demand.The regret-averse newsvendor would seem to be a prom-ising model in studying the way the strength of this bias changes when there is a change in c or in infor-mation about demand.Moreover,a recent paper by Hayashi (2008)provides axioms that justify regret aversion. Note next that the payoff function in Equation (6)satis?es a condition which generalizes the shift Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 123 invariance and homogeneity condition in Equation (1)above.A payoff function u (q ,h )satis?es the general-ized condition if: There exists a function f such that for any a and any b [0;we have eyTf eb T[0and u eq ;h T?f eb Táu q àa b ;h àa b for all q ;h : 8 >>><>>>: e10T For the case where f is the identity,condition (10)becomes condition (1),where the “c ”of condition (1)is zero. Our general payoff function u in (6)obeys condition (10 )with f (b )=b r .To see this,?rst consider pairs (q ,h ) such that q ≥h .Then for b >0,we have q àa b !h àa b and hence u eq ;h T?àj q àh j r ?b r áq àa b àh àa b r ?b r áu q àa b ;h àa b :For pairs (q ,h )such that q b \h àa b and hence u eq ;h T?àK áj q àh j r ?b r áàK áq àa b àh àa áb r !?b r áu q àa b ;h àa b :We now have a general proposition about a quan-tity-chooser.In particular,the quantity-chooser may be our generalized newsvendor.Then,the proposi-tion becomes a counterpart of our classic newsvendor Proposition 1.Its proof uses an extended version of Lemmas A and B as well as the fact that the payoff function satis?es Equation (10).The proposition again considers a switch from one IG structure to another.We require,however,that when the switch occurs,the average (over all signals)of the scale parameter b moves in the same direction as the average of b r .If that is so,then we again ?nd that the new structure is more useful for the quantity-chooser than the old one if and only if the average scale parameter drops after the switch. In addition,the proposition ?nds that there is a crit-ical value of the penalty parameter K .On one side of that value,a useful switch increases the quantity-chooser’s average ex ante quantity.On the other side,such a switch decreases the average quantity.Finally,we ?nd that if the base CDF B has a density function that is symmetric around zero (or if r =2)then the critical value of K is one.If the quantity-chooser is our regret-averse newsvendor,then K ?1àc c àár .Hence,K =1is equivalent to c ?12.So for the symmetric case,we have generalized newsvendor counterparts of the classic newsvendor statements [2]and [3]of Proposition 1. In stating the proposition,we again use the symbols ^q eáT,U (á),V (á).In de?ning those symbols (just before Lemma B),we used the quantity q a (y ,g ),b (y ,g ),the small-est maximizer of E T a ey ;g T;b ey ;g Tu eq ;D T.Our new de?nitions of ^q eáT,U (á),V (á)again use the quantity q a (y ,g ),b (y ,g ),in exactly the same way as before,but that quantity is now the smallest maximizer of E T a ey ;g T;b ey ;g Tu eq ;h T,where u (q ,h )is the payoff function in (+).We also use a new symbol,namely V r (g ).That denotes the average,over all the signals in Y g ,of the r th power of the scale parameter b (y ,g ). P ROPOSITION 3.Consider a quantity-chooser whose pay-off function is the function de?ned in Equation (6),namely u eq ;h T?àj q àh j r for q !h àK áj q àh j r for q \h ,& e6Twhere h is a state variable,r >1and K >0.Consider an IG who obtains scale/location transforms of a base CDF B which has mean zero,is not a one-point distribution,and has a density that is positive at every point of its support.Every signal y in the IG’s signal set Y g de?nes the pos-terior CDF used by the quantity-chooser,namely the transform F g y ?T a ey ;g T;b ey ;g T.Let I g ?h Y g ;f F g y g y 2Y g i and I g 0?h Y g 0 ;f F g 0y g y 2Y g 0i be two of the IG’s structures.Sup-pose that when the IG switches from I g to I g 0;then V and V r move in the same direction.e?T Then [1]V(g 0) U eg 0T[U eg Tif and only if ^q eg 0T[^q eg T:[3]If K U eg 0T[U eg Tif and only if ^q eg 0T\^q eg T:[4]If r =2,then statements [2]and [3]hold for K *=1. Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 124 Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society [5]If B is symmetric around zero —i.e.,for any z we have B(àz)=1àB(z)—then statements [2]and [3]hold for K *=1.Note that if the quantity-chooser is our generalized newsvendor —so K ?1àc c àár —and if r ?2and B is not symmetric around zero,then [2],[3]are state-ments about a critical value of c and that critical value is not 12.The inequalities K >K *,K are equiva-lent,respectively,to the inequalities c \1K ?eT 1=r t1 ;c [ 1 K ?eT1=r t1 .To interpret condition (*),which concerns the IG,?rst consider the IG in the normal-distribution exam-ple in 2.2above.Recall that b ey ;g T???????1 g tf q .The signal y does not enter that expression,so condition (*)is automatically met.Next,consider the IG in the uni-form-distribution example in section 2.1.The set of possible demands is [0,1].Suppose that the signal set Y g partitions [0,1]into g equal subintervals.We may let Y g be the ?rst g positive integers.The signal y =i tells the newsvendor that the true D is uniformly distributed on a ei ;g Tà b ei ;g T2;a ei ;g Ttb ei ;g T2h i ,where a ei ;g T? 2i à1 2g and b ei ;g T?1g .Thus, V eg T?E i 2Y g b ei ;g T?1 g ;V r eg T?E i 2Y g b ei ;g TeTr ? 1 g r :So when the index g changes,V and V r indeed move in the same direction. Suppose,on the other hand,that the IG does not partition D ??0;1 into equal subintervals.Rather there is a ?xed integer m >0such that for every g the signal set Y g de?nes a partitioning of [0,1]having m subintervals whose widths need not be equal.The m -subinterval partitioning changes when g changes.For a given g ,V (g )is the average of the m subinterval widths,while V r (g )is the average of the m widths,each raised to the power r .Without further restrictions we cannot claim that V and V r move in the same direction when g changes. It is easily veri?ed,however,that we can make that claim (for any r >1)if m =2,i.e.,every signal set Y g partitions [0,1]into just two subintervals. For any ?xed m ,moreover,we can claim that V and V r move in the same direction if the IG’s information structures I g obey the following condition: Suppose g 0>g ;w 0?ew 01;:::;w 0m Tis the vector of subinterval widths for Y g 0 ;and w =(w 1,...,w m )is the vector of subinterval widths for Y g .Then w 0majorizes w —i.e.,the largest component of w 0is not lower than the largest component of w , the sum of the two largest is not lower,the sum of the three largest is not lower,and so on.It is shown in the Appendix that this claim is correct. 5.2.An Ex Post Proposition For the Generalized Newsvendor Let our quantity-chooser again be our generalized regret-averse newsvendor.We can repeat a key step in the proof of Proposition 3to obtain an analog of our Proposition 2,which concerned ex post sales for a classic newsvendor.Suppose the IG moves from one information structure to another and the second is more useful to the newsvendor than the ?rst.(That is equivalent,as [1]of Proposition 3told us,to the state-ment that the IG’s average scale parameter drops).Then we ?nd,just as in Proposition 2,that for all val-ues of the cost c (with 0 To state this ?nal proposition,we need to reinter-pret the symbol ^S eg T E y 2Y g E T a ey ;g T;b ey ;g Tmin q a ey ;g T;b ey ;g T;D àá :The quantity q a (y ,g ),b (y ,g )is now the smallest maxi-mizer of E T a ey ;g T;b ey ;g Tu eq ;D T,where u (q ,D )is the payoff function in Equation (6)(with h =D ). P ROPOSITION 4.Consider again the generalized newsven-dor whose payoff function given in Equation (6),i.e.,it is u eq ;D T?àj q àD j r for q !D àK áj q àD j r for q \D ,& where K ?1àc c àár and r >1.Consider an IG who obtains scale/location transforms of a base CDF B which has mean zero and a density that is positive at every point of its support.Every signal y in the IG’s signal set Y g de?nes the posterior used by the newsvendor, namely F g y ?T a ey ;g T;b ey ;g T.Let I g ?h Y g ;f F g y g y 2Y g i and I g 0?h Y g 0 ;f F g 0 y g y 2Y g 0i be two of the IG’s structures.Then U eg 0T[U eg Tif and only if ^S eg 0T[^S eg T:6.Concluding Remarks We have considered a newsvendor who obtains the services of an IG.The IG expends effort and sends to the newsvendor a signal that provides information about the unknown true demand.A joint distribution Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 125 on the possible signal/demand pairs is known to the IG and the newsvendor.The IG’s signal de?nes a pos-terior and the newsvendor uses that posterior to choose an order quantity.We studied the effect of more IG effort on the average ex ante order and the average ex post sales. We developed a model of the IG for which(1) there is a critical value of the classic newsvendor’s unit cost,where on one side more effort leads to a higher average ex ante order and on the other side to a lower one;and(2)regardless of cost,more IG effort always leads to higher average ex post sales. Moreover,(1)and(2)continue to hold when we replace the classic newsvendor with a generalized (regret-averse)newsvendor.In our model,each of the posteriors which the newsvendor obtains from the IG is a scale/location transform of a?xed base distribution,and more effort means a drop in the average scale parameter. More remains to be learned about scale/location IGs.In the Introduction,we considered a three-demand example where the posteriors implied by the IG’s signals were not transforms of a common base distribution.But,as we saw in the very simple ?nite example in2.3,we can also construct?nite examples where the scale/location property holds. The effect of more IG effort on the newsvendor can be studied in more general?nite cases.When we turn to IGs who are not scale/location transformers, there is even more to be learned.It is reasonable to con?ne attention to models in which higher IG effort is useful to the newsvendor.Even then,there are IG models for which statements(1)and(2)no longer hold. Rapid improvements in the technology of informa-tion gathering in general,and demand forecasting in particular,provide a stimulus for further research.As surveying of consumers gets cheaper,it becomes par-ticularly interesting to study the case where the IG is the sampler brie?y discussed in the Introduction He samples the demanders and determines how much each demander in the sample is willing to pay for a given amount.As sample size grows,do average order and average sales rise or fall? Empirical studies of real IGs and their efforts remain quite scarce.That may be because theory has been scarce as well.Without theory,empiricists may not know what hypotheses to test and what datasets to assemble.If theorists show that for a particular model of an IG more effort induces infor-mation users to move their choices in a certain direction(induces newsvendors to increase their orders,for example),then that tells the empiricist that it would be useful to see whether real IGs?t that particular model and whether real users’choices indeed move in the direction that the theory predicts.In another paper(Marschak et al.2013), we study a variety of IGs who are not scale/loca-tion transformers and a variety of“Producers,”who use the IG’s signals and are not newsvendors.For each IG/Producer pair,we ask the same question that we have asked in the present paper:does more IG effort raise or lower the average quantity chosen by the Producer? It is not only the model of the IG that can be varied but the model of the newsvendor as well.For exam-ple,the newsvendor might choose both price and quantity,as in Agrawal and Seshadri(2000).There is a randomly shifting demand curve which determines realized demand for a given price,and an IG can be asked to study the shifts.If the newsvendor’s chosen quantity is less than realized demand,then he can buy more at a?xed“emergency”price;if it is more, he receives a salvage value for the unsold quantity.In another variation,we can continue to let quantity be the only choice variable,with selling price?xed and quantity demanded uncertain,but we can try to gen-eralize to a newsvendor who is risk-averse rather than regret-averse. We have not asked how much IG effort the news-vendor ought to buy if he has to pay for it.We have also avoided incentive-oriented models where the IG chooses how hard to work,bears the cost,and receives a reward from the newsvendor.In our view, those hard questions are important,but it is appropri-ate to defer them until we better understand,for a variety of IG models,the effect of more effort on the quantities we have studied. Acknowledgments We are grateful to a Senior Editor and three referees for comments and suggestions that substantially improved the paper. Appendix P ROOF OF L EMMA A.First note that for any function g,a change-of-variables argument yields E B geatbrT?E T ab gerT:eiT Now?x q,let D play the role of“r,”and let u(q,á) play the role of“g(á).”Using Equation(i),we obtain E T ab ueq;DT?E B ueq;atbDT: But since u has the property(1)(de?ned in section 3),we have E B ueq;atbDT?c atbáE B u qàa b ;D ; Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 126Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society where c =1àc .Thus, E T ab u eq ;h T?c a tb áE B u q àa b ;D :eii T Since b >0,Equation (ii)implies that a quantity q which maximizes E B u q àa b ;D àáalso maximizes E T ab u eq ;D T.Hence u T ab ?max q E T ab u eq ;D T?c a tb ámax q E B u q àa b ;D :eiii TBut for ?xed (a ,b ), the set of possible values of q àa b equals the set of possible values of q :eiv T (Both sets consist of all the reals).Thus we have max q E B u q àa b ;D ?max eq àa T=b E B u q àa b ;D ?max q E B u eq ;D T?u B : So,using (iii), u T ab ?c a tb áu B ; i.e.,Equation (A2)holds. Next,note that since q ab is a value of the variable q which maximizes the term on the left of the equal-ity in Equation (ii),the quantity q ab àa b maximizes the entire term on the right of the equality in Equation (ii)and therefore (since b >0)it maximizes E B u q àa b ;h àáas well.So we obtain,using Equation (iv), E B u q ab àa b ;D !E B u q ;D eTfor all q 2R :Since q B is the smallest maximizer of E B u (q ,D ),we have q B q ab àa b :ev T Now apply (ii)to obtain E T ab u ea tbq B ;D T?c a tb áE B u eq T ;D T: evi T Since E B u (q B ,D )≥E B u (q ,D )for all q 2R ,(vi) implies that E T ab u ea tbq B ;D T!E T ab u eq ;D Tfor all q 2R :Since q ab is the smallest maximizer of E T ab u eq ;D T,we have q ab a tbq B : Since (v)implies q ab ≥a +bq B ,we conclude that q ab ?a tbq B ; i.e.,Equation (A1)holds. h P ROOF OF L EMMA B.First,recall that for a given sig-nal y ,the CDF T a (y ,g ),b (y ,g )is the (posterior)CDF of the random variable D ,and that D is a transform of the base random variable z .Speci?cally,for a given signal y ,we have D ?a ey ;g Ttb ey ;g Táz ; where b (y ,g )>0.Since the mean of the base ran-dom variable is zero,the transformed random vari-able D has (posterior)mean E T a ey ;g T;b ey ;g TD ?a ey ;g T: ei T Next,we use the following general fact,which holds for any IG: The expectation,over all the IG’s signals,of the posterior mean given the signal equals the prior mean,i.e.,if Y is the set of possible signals,we have E y 2Y eE F y D T? D ;where D is the mean of the prior CDF and F y is the posterior given the signal y : 8 >>>>>><>>>>>>: e#T Applying (#),we obtain E y 2Y g E T a ey ;g T;b ey ;g TD ? D :eii T Using (i)and (ii),we obtain E y 2Y g a ey ;g T? D :eiii T Equation (A1)of Lemma A implies,for every (y ,g ), q a ey ;g T;b ey ;g T?a ey ;g Ttb ey ;g Táq B : Hence,taking expectations over the signals y 2Y g ,and using (iii),we obtain ^q eg T? D tq B áV eg T:eiv T Moreover (i),(ii),and (A2)of Lemma A imply U eg T?c D tu B áV eg T:ev TStatement (iv)implies Equation (B1)and statement (v)implies Equation (B2).h Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management 24(1),pp.110–133,?2014Production and Operations Management Society 127 P ROVING P ROPOSITION1.In proving Proposition1,we will need the following Lemma. L EMMA C.Suppose the IG is a scale/location transformer with a family of structures I g?h Y g;f F g y g y2Y g i. Then the following statements hold If u B\0then Veg0T\VegTif and only if Ueg0T[UegT: eC1TIf q B\0;then Veg0T\VegTif and only if^qeg0T[^qegT: eC2TIf q B[0;then Veg0T\VegTif and only if^qeg0T\^qegT: eC3TIf u B q B[0then Ueg0T[UegTif and only if^qeg0T[^qegT: eC4TIf u B q B\0then Ueg0T[UegTif and only if^qeg0T\^qegT: eC5T If u B?0and q B?0;then UegTis the same for all g: eC6T If u B?0and q B?0;then^qegTis the same for all g: eC7TIf u B?0and q B ?0;then^qegTis the same for all g and so is UegT: eC8TP ROOF. (C1)follows from Equation(B2)of Lemma B. (C2)and(C3)follow from Equation(B1)of Lemma B. (C4)–(C8)follow from Equations(B1)and(B2)of Lemma B. P ROOF OF P ROPOSITION 1.By assumption,the base CDF B has an everywhere positive density function, which we shall denote g,That implies that Bà1(1àc) is the unique maximizer of E B[min(q,h)àcq]. Step1 In this Step,we show that u B<0. Since q B maximizes E B(min(q,D)àcq)it satis?es B(q B)=1àc.We have u B? Z1 à1 ?mineq B;zTàcq B gezTdz ? Z q B à1 zgezTdzt Z1 q B q B gezTdzàcq B ? Z q B à1 zgezTdztq Báe1àBeq BTTàcq B ? Z q B à1 zgezTdz: (To obtain the?nal equality,we use the fact that B (q B)=1àc).If q B≤0,then at every z in[à∞,q B]we have zg(z)≤0.The set{z:zg(z)<0}has positive probability. So if q B≤0,then u B? Z q B à1 zgezTdz\ Z q B à1 0dz?0: Suppose,on the other hand,that q B>0.Then u B? Z q B à1 zgezTdz? Z1 à1 zgezTdzà Z1 q B zgezTdz: The second integral equals zero since the CDF B has zero mean.The third integral is positive since for every z in[q T,∞]the integrand is positive. Thus,whatever the sign of q B,we have u B<0 Step2 Since u B<0,we immediately obtain statement[1] of the Proposition from(C1)of Lemma C. Step3 In this Step,we show[2],[3],[4]. If1àc If1àc>B(0)then q B>0.Since u B<0,we have u Báq B If1àc=B(0)then q B=0.Since u B<0,we use (C7)of Lemma C to obtain statement[4]. That concludes the proof.h P ROOF OF P ROPOSITION2.Recall that q B and q ab were introduced in Lemma A to denote the newsvendor’s smallest optimal ex ante order under the CDF B and the CDF T ab,respectively.Analogously,let S B and S ab denote,respectively,the average ex post sales under the CDF B and the CDF T ab when the ex ante quantities are q B and q ab,i.e., S B?E B mineq B;DT;S ab?E T ab mineq ab;DT: Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort 128Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society From Lemma A we know that q ab?atbq B: So we have: S ab?Z mineatbq B;DTdB Dàa b ?Z mineatbq B;atbzTdBezT ?Z ?atb mineq B;zT dBezT ?atbS B It follows that ^SegT?E y2Y g ?aey;gTtbey;gTáS B : Since,as noted in the proof of Lemma B, E y2Y g aey;gT? D,we obtain ^SegT? DtVegTáS B: Then(C1)of Lemma C tells us that we indeed have Ueg0T[UegT()^Seg0T[^SegT if S B<0.But that is the case,since S B?Z1 1 mineq B;zTdBezT\ Z1 1 zdBezT?0: That concludes the proof.h P ROVING P ROPOSITION 3.Extended versions of Lemma A and Lemma B. We?rst need extended versions of Lemma A and Lemma B.They exploit the fact that Proposition3’s payoff function obeys condition(10). L EMMA A0.Let R be the set of possible values of an action-chooser’s quantity q.Let the action-chooser’s payoff function u(q,h)satisfy Equation(6)in the statement of Proposition3.Consider an IG who has a base CDF B on R with mean zero.The IG determines a location parameter a and a scale parameter b>0,which de?ne the posterior CDF T ab.Let q B denote the smallest maximizer of E B u(q,h) and let q ab denote the smallest maximizer of E T ab ueq;hT.Let u B denote E B u(q B,h)and let u T ab denote E T ab ueq ab;hT.Then q ab?atbáq B:eA10Tand for any function f satisfyingeyTine11T;we have u T ab ?febTáu B: eA20TP ROOF.For a function f satisfying(?)in(11),we have E B ueq;atb hT?febTáE B u qàa b ;h :eiTThus E T ab ueq;hT?febTáE B u qàa b ;h :eiiT We repeat the argument in the?rst paragraph of the proof of Lemma A to obtain u T ab ?max q E T ab ueq;hT?febTámax q E B u qàa ;h :eiiiT Since f(b)>0,we then have(A20).We now repeat the remaining part of the proof of Lemma A,replac-ing(vi)of that proof with E T ab ueatbq B;hT?febTáE B ueq B;hT: That establishes(A10). To state Lemma B0,we need a new symbol.Given a function f:R!R and the IG index g,de?ne V fegT?E y2Y g febey;gTT: We again consider a payoff function u(q,h)satisfying Equation(6)in the statement of Proposition3.The Lemma concerns V f and the functions^q,U,where ^qegT?E y2Y g q aey;gT;bey;gT;UegT?E y2Y g ueq aey;gT;bey;gT;hT; and,as before,q a(y,g),b(y,g)is the smallest maximizer of E T aey;gT;bey;gT ueq;hT.The symbols q B,u B have the same meaning as in Lemma A0. L EMMA B0.Let f be a function satisfying(?)in our pay-off-function property(10).For every pair(g0,g),the fol-lowing hold: ^qeg0Tà^qegT?q BáeV feg0TàV fegTTeB10TUeg0TàUegT?u BáeVeg0TàVegTT:eB20T P ROOF.The proof again obtains the statements(i)–(iv)in the proof of Lemma B(with h replacing D). Again,(iv)implies(B10).Moreover,(i),(ii),and(A20) imply(B20). The following additional Lemma will be used in proving Proposition3. L EMMA D.Suppose that the support of the base CDF B is the interval[v,w],where v Marschak,Shanthikumar,and Zhou:A Newsvendor Who Chooses Informational Effort Production and Operations Management24(1),pp.110–133,?2014Production and Operations Management Society129 疾病名：高脂血症 英文名：hyperlipoidemia 缩写：HL 别名：hyperlipemia；高脂血；血脂过多 ICD号：E78.5 分类：代谢科 概述：血脂是血浆中的中性脂肪(三酰甘油和胆固醇)和类脂(磷脂、糖脂、固醇、类固醇)的总称，广泛存在于人体中，它们是生命细胞基础代谢的必须物质。血脂中的主要成分是三酰甘油和胆固醇，其中三酰甘油参与人体内能量代谢，而胆固醇主要用于合成细胞浆膜、类固醇激素和胆汁酸。 脂质是体内的一种重要组成成分，广泛存在于各种膜的结构中。脂质为疏水性的分子，不溶或微溶于水，其在维持细胞的完整性方面具有非常重要的作用，并可使血浆中的物质通过直接弥散或经载体进入细胞内。同时，脂质是体内能量贮存的主要形式，也是肾上腺和性腺类固醇激素以及胆酸合成的前体物质。此外，脂质还是血液中许多可溶性复合物运输的载体。 脂质分为：脂肪酸(FA)、三酰甘油(TG)、胆固醇(Ch)和磷脂(PL)。其中三酰甘油和磷脂为复合脂质。血浆中的胆固醇又分游离胆固醇(FC)和胆固醇脂(CE)两种，二者统称为血浆总胆固醇(TC)。 高脂血症(hyperlipoidemia)是指血脂水平过高，可直接引起一些严重危害人体健康的疾病，如动脉粥样硬化、冠心病、胰腺炎等。 流行病学：血脂水平与遗传和饮食习惯密切相关，因此不同种族人群和饮食情况下的血脂水平存在一定的差异。例如：西方男性的平均胆固醇水平为5.4mmol/L，而日本男性相对较低，仅为4.3mmol/L。我国人群的胆固醇水平亦低于欧美人群，平均为3.8～5.14mmol/L。 我国正常人的各种血脂水平(表1)。 体内的血脂水平随着年龄增长逐渐升高。儿童的血脂水平低于成人，其高脂血症的标准为：胆固醇＞5.2mmol/L(200mg/dl)，三酰甘油＞1.6mmol/L(140mg/dl)。此外，血脂亦受性别和生理状态的影响。女性从青春期起直至绝经期，其三酰甘油和胆固醇水平均低于男性，而HDL水平高于同龄男性。 1.高胆固醇血症 高胆固醇血症的原因包括基础值偏高、高胆固醇和高饱和脂肪酸摄入、热量过多、年龄及女性更年期的影响、遗传基因的异常、多基因缺陷与环境因素的相互作用。 (1)基础血浆低密度脂蛋白-胆固醇(LDL-C)水平高：与各种属的动物相比，人类的基础LDL-C水平较高，可能与人体内胆固醇转化为胆汁酸延缓，肝内胆固醇含量升高，抑制LDL受体活性有关。这种较高的基础LDL-C是人类临界高胆固醇血症的主要原因之一。 (2)饮食中胆固醇含量高：胆固醇摄入量从200mg/d增加到400mg/d，血胆固醇可升高0.13mmol/L(5mg/dl)，其机制可能与肝脏胆固醇含量增加，LDL受体合成减少有关。临床研究表明，在健康青年人中，每天饮食中胆固醇摄入量增加100mg，女性血胆固醇水平上升较男性明显。 (3)饮食中饱和脂肪酸含量高：每人每天摄入饱和脂肪酸理想的量应为每天总热卡的7%，若饱和脂肪酸摄入量占每天总热卡的14%，可致血胆固醇增高大约0.52mmol/L (20mg/dl)，其中主要是LDL-C。研究表明，饱和脂肪酸可抑制LDL受体的活性。虽然确切的机制尚不清楚，但可能与下列5方面有关：①抑制胆固醇酯在肝内合成；②促进无活性的非酯化胆固醇转入活性池；③促进调节性氧化类固醇的形成；④降低细胞表面LDL受体活性；⑤降低LDL与LDL受体的亲和性。 (4)体重增加：研究表明，体重增加可使血浆胆固醇升高，肥胖是血浆胆固醇升高的一个重要原因，因为肥胖促进肝脏输出含载脂蛋白B的脂蛋白，继而使LDL生成增 微生物制药的一般工艺流程 微生物制药技术 工业微生物技术是可持续发展的一个重要支撑，是解决资源危机、生态环境危机和改造传统产业的根本技术依托。工业微生物的发展使现代生物技术渗透到包括医药、农业、能源、化工、环保等几乎所有的工业领域，并扮演着重要角色。欧美日等国已不同程度地制定了今后几十年内用生物过程取代化学过程的战略计划，可以看出工业微生物技术在未来社会发展过程中重要地位。 微生物制药技术是工业微生物技术的最主要组成部分。微生物药物的利用是从人们熟知的抗生素开始的，抗生素一般定义为：是一种在低浓度下有选择地抑制或影响其他生物机能的微生物产物及其衍生物。(有人曾建议将动植物来源的具有同样生理活性的这类物质如鱼素、蒜素、黄连素等也归于抗生素的范畴，但多数学者认为传统概念的抗生素仍应只限于微生物的次级代谢产物。)近年来，由于基础生命科学的发展和各种新的生物技术的应用，报道的微生物产生的除了抗感染、抗肿瘤以外的其他生物活性物质日益增多，如特异性的酶抑制剂、免疫调节剂、受体拮抗剂和抗氧化剂等，其活性已超出了抑制某些微生物生命活动的范围。但这些物质均为微生物次级代谢产物，其在生物合成机制、筛选研究程序及生产工艺等方面和抗生素都有共同的特 点，但把它们通称为抗生素显然是不恰当的，于是不少学者就把微生物产生的这些具有生理活性（或称药理活性）的次级代谢产物统称为微生物药物。微生物药物的生产技术就是微生物制药技术。可以认为包括五个方面的内容： 第一方面菌种的获得 根据资料直接向有科研单位、高等院校、工厂或菌种保藏部门索取或购买；从大自然中分离筛选新的微生物菌种。 分离思路新菌种的分离是要从混杂的各类微生物中依照生产的要求、菌种的特性，采用各种筛选方法，快速、准确地把所需要的菌种挑选出来。实验室或生产用菌种若不慎污染了杂菌，也必须重新进行分离纯化。具体分离操作从以下几个方面展开。 定方案：首先要查阅资料，了解所需菌种的生长培养特性。 采样：有针对性地采集样品。 增殖：人为地通过控制养分或培条件，使所需菌种增殖培养后，在数量上占优势。 如何区分定语从句、宾语从句和状语从句？（附习题）| 虫虫讲英语 2018-12-02 14:52 「虫虫讲英语」老少咸宜的英语学习号——有时候，语法换一种方式讲，就听懂了。 如何区分定语从句、宾语从句和状语从句，是学生最常问我的问题之一。今天，我们通过青铜、白银、黄金、王者四级难度的例句，一起研究下怎样一眼辨别英语3大从句。 01 概念 3大从句的区别均在于前面两个字：定语、宾语和状语： 知道了这几个概念，这三种从句就很好理解了： >> 定语从句：作定语的从句，做adj.修饰先行词； 在这里，dog “狗子” 是先行词，即“走在定语从句前面的名词”；定语从句 that shits a lot 其中的 that，指 代了前面的 dog，告诉我们这是一条怎样的狗子：拉很多的狗子。 >> 宾语从句：作宾语的从句，放在动词或介词后面； 第一句，宾语从句为普通的陈述句，放在 think 这个动作后面，由连接词 that 引导。 第二句，宾语从句已经改成陈述句语序，原来人讲的话则是一般疑问句Do you let it go “你丫放不放手” ？该从句放在 depend on 的介词 on 后面，一般疑问句由 whether/ if 引导。 >> 状语从句：作状语的从句，给主句增加信息量。 状语从句，是3大从句中比较好记的一种：有个完整的主句，从句是提供更多信息的，比如上述例句告诉我们他为什么养狗。只要熟悉九大状语从句的引导词（← 戳可查看），几乎一眼就能辨别出状语从句。 02 当堂练习 现在，我们一起看几个句子找找感觉。请判断下列句子是定语从句，宾语从句还是状语从句？ >> 青铜 1. If it is fine tomorrow, I will visit you. 2. I helped an old man who lost his way. 从句小结 从句总述： 从句有主语从句、表语从句、宾语从句、同位语从句、定语从句和状语从句6类。 由于主语从句、表语从句、宾语从句及同位语从句在句子的功用相当于名词，故而这4种从句又通称名词性从句。 1.主语从句（Subject Clause）：用作主语的从句叫主语从句。引导主语从句的关联词有从属连词、疑问代词、疑问副词、缩合连接代词、缩合连接副词等。 2.表语从句（Predicative Clause）：用作表语的从句叫表语从句。引导表语从句的关联词与引导主语从句的关联词大都一样。 3.宾语从句（Object Clause）：在句子中起宾语作用的从句叫做宾语从句.宾语从句分为三类:动词的宾语从句,介词的宾语从句和形容词的宾语从句. 4. 同位语从句（Appositive Clause）：在复合句中用作同位语的从句叫同位语从句。它一般跟在某些名词后面，用以说明该名词表示的具体内容。其关联词多为that。 状语从句还可以分为条件状语从句、原因状语从句、方位状语从句和时间状语从句等。 宾语从句 学习宾语从句要抓住三要素：时态、语序、连接词。 一：时态和语序 1·主句用一般现在时，从句可用任意时态。 2·主句用过去时，从句用过去某个时态。 3·主句用过去时，从句是真理时，只用一般现在时。 语序：宾语从句只能用陈述句语序，坚决不能用疑问句语序。 二：连接词 ①从属连词 连接宾语从句的从属连词主要有that，if，whether. that引导表示陈述句的宾语从句,而if和whether引导表示“是否”的宾语从句. 例句： He told that he would go to the college the next year 他告诉我他下一年上大学. I don’t know if there will be a bus any more. 我不知道是否还会有公交车. ②连接代词 连接代词主要有who, whom ,whose ,what ,whoever ,whomever ,whosever, whatever, whichever等. 连接代词一般指疑问,但what, whatever除了指疑问外,也可以指陈述. 例句： Do you know who has won Red Alert game 你知道谁赢了这一局红警游戏吗 ③连接副词 连接副词主要有when,where,why,how,whenever,wherever,however等. 例句： He didn’t tell me when we should meet again. 他没有告诉我什么时候我们能再见面. 宾语从句： 在句子中起宾语作用的从句叫做宾语从句。通俗的说就是一个句子做另一个句子的宾语. 主要跟在及物动词和介词之后。一般由“引导词＋主语＋谓语＋其它”构成，其语序是陈述句语序。 如何判断： 1．可以从整个句式看,宾语从句只能放在主句谓语动词之后。 2．从引导词看。if充当宾语从句的连接词时，相当于whether，词义为“是否”，when充当宾语从句的连接词时，意为“什么时候”。 3．从时态看。if和when作连接词时，引导宾语从句要注意：从句的谓语动词的时态应根据主句的时态作相应的变化。 所以宾语从句的三大要素：时态语序引导词 前世今生： I know you . you are right.→I know you are right. /I know that you are right. ?引导词 ?that (后面是陈述句) I believe that you are an honest boy. ?what which who I don’t know what they are going to d o. what are they going to do？ whose whom Tell me whose PSP it is.（whose PSP is it？）where when Can you tell me where he lives? where does he live? Why how I know why he was late. (why was he late？) （特殊疑问句） ?if / whether（一般疑问句/是否）I want to know if Miss Gao is back. 高脂蛋白血症的分型 WHO Ⅰ型：高乳糜微粒血症，血清外观有“奶油”样顶层，下层澄清，血清三酰甘油含量显著增加，胆固醇正常或轻度增加，电泳有深染的乳糜微粒带，超速离心乳糜微粒增加与VLDL带分离不清，TC／TG比率＜0.1仅见于I型有诊断价值。 Ⅱ型：高β脂蛋白血症，Ⅱa型血清外观澄清，胆固醇含量增加，三酰甘油含量正常，TC／TG比率＞1.5，电泳β带深染，甚至看不到前β带，超离心LDL含量增加，VLDL和HDL含量正常，Ⅱb型血清外观澄清或轻混，血清胆固醇和三酰甘油含量均增加，TC／TG比率可变、电泳β和前β带均深染，超离心LDL和VLDL均增加。 Ⅲ型：异常β脂蛋白血症或称“漂浮β或阔β”型高脂蛋白血症。血清外观混浊，常具有一模糊的乳糜微粒“奶油”样顶层，血清三酰甘油和胆固醇均增高，琼脂糖或醋酸纤维素薄脂电泳见一条自β位置扩展到前β位置的“阔β"带，这是因为在VLDL部分存在异常的LDL，聚丙烯酰胺凝胶电泳则不见β带，而仅见阔前β带。血浆在盐密度为1.006超离心后的上清液部分作醋酸纤维素薄膜电泳，显示β迁移脂蛋白有肯定性诊断价值，因为正常血浆在此密度下超离心，其上清部分仅存在前β迁移脂蛋白。 Ⅳ型：高前β脂蛋白血症，血清外观澄清或完全混浊，主要视三酰甘油含量而定，无“奶油”样顶层，血清胆固醇正常或增高，三酰甘油增高，前β带深染，超离心VLDL增高，LDL正常。 Ⅴ型：高前β脂蛋白血症及乳糜微粒血症。血清外观有“奶油”样顶层，下层混浊，血清胆固醇和三酰甘油均增加，电泳前β带深染且拖尾至原点，原点出现深染乳糜微粒带超离心乳糜微粒存在，VLDL增加。 Ⅱb型和Ⅳ型有时不易确定，应用下列公式可资鉴别： LDL－C=TC－(TG/5＋HDL－C) 当LDL－C＞130mg／dl(过高界限)时为Ⅱb型，否则为Ⅳ型。 定语从句 定语从句是在主从复合句中修饰某个名词或代词句子，它在句中作定语。被修饰的名词或代词叫先行词，连接先行词和定语从句的词叫引导词(也叫关系词)。如 I know the girl who is sitting under the tree. 我认识那个正坐在树下的女孩。 ↓ ↘引导词↓ 先行词从句 (定语从句) This is the most interesting book that he has ever read. 这是他所读过的书中最有趣的一本。 ↓ ↘引导词↓ 先行词从句 (定语从句) · 考点1：先行词是人时引导词的选用 (1). 先行词是人，引导词后紧跟动词时用who或that. 如： Here comes the man who (that)wants to see you. 想见你的那个人来了。 (先行词是the man, 引导词后紧跟动词wants, 故引导词用who / that) (2). 先行词是人，引导词后紧跟的不是动词时要用who, whom, that. 如： This is the person whom (who, that)you are looking for. 这正是你要找的人。 (先行词是the person, 引导词后紧跟的是you, 不是动词, 故引导词可用who / whom / that) ） 考点2：先行词是物时引导词的选用 (1).先行词是物时，一般情况下引导词可以用which或that. 如： Mary like music that (which) is quiet and gentle.玛丽喜欢安静柔和的音乐。 (先行词是music, 引导词可用which / that) The film which(that) we saw last night was very interesting.我们昨晚看的电影非常有趣。 (先行词是film, 引导词可用which / that) ` (2).以下情况，引导词只能用that, 不能用which. 复合句 【语法要点】 复合句是由一个主句加一个或几个从句所构成的句子。从句只用作句子的一个成分，不能独立。根据从句在句子中的作用，可分为名词性从句、定语从句和状语从句三类。 （一）名词性从句 名词性从句包括主语从句、表语从句、宾语从句、同位语从句。其关联词有连接词that、if、whether；疑问代词who、what、which和疑问副词when、where、how、why等。 1.名词性从句句法结构： 从 属 连 词that whether 主 语 从 句 That he will come is certain.（that不可省） Whether she is coming or not doesn’t matter too much. （不能用if） 宾 语 从 句 I think（that）he will be all right in a few days. I went in and asked if（=whether）they had a cheap suit. I wonder whether（不能用if）it is true or not. 表 语 从 句 The fact is（that）I have never been there. The question is whether（不能用if）it is worth doing. 同 位 语 从 句 The fact that she had not said anything surprised all of us. They asked me the question whether the work was worth doing. 连接代词 that who whom whose which 主 语 从 句 Who will help him is not known. What he said is very important. Which side will win is not clear. 宾 语 从 句 （1）作及物动词的宾语。例如： I really don’t know what he is doing. Do you know who/whom they are waiting for? He asked whose dictionary it was. He can’t tell which method they will use for the experiment. （2）作介词的宾语。例如： Pay attention to what the teacher said. I wondered to whom he had given the letter. 表 语 从 句 That is what he is worried about. The question is who will come here. The question is which team will win the match. 1976年WHO建议将高脂血症分为六型： (1)Ⅰ型高脂蛋白血症：主要是血浆中乳糜微粒浓度增加所致。将血浆至于4℃冰箱中过夜，见血浆外观顶层呈“奶油样”，下层澄清。测定血脂主要为甘油三酯升高，胆固醇水平正常或轻度增加，此型在临床上较为罕见。 (2)Ⅱ型高脂蛋白血症，又分为Ⅱa型和Ⅱb型。 ①Ⅱa型高脂蛋白血症：血浆中LDL水平单纯性增加。血浆外观澄清或轻微混浊。测定血脂只有单纯性胆固醇水平升高，而甘油三酯水平则正常，此型临床常见。 ②Ⅱb型高脂蛋白血症：血浆中VLDL和LDL水平增加。血浆外观澄清或轻微混浊。测定血脂见胆固醇和甘油三酯均增加。此型临床相当常见。 (3)Ⅲ型高脂蛋白血症：又称为异常β-脂蛋白血症，主要是血浆中乳糜微粒残粒和VLDL残粒水平增加，其血浆外观混浊，常可见一模糊的“奶油样”顶层。血浆中胆固醇和甘油三酯浓度均明显增加，且两者升高的程度（以mg/dL为单位）大致相当。此型在临床上很少见。 (4)Ⅳ型高脂蛋白血症：血浆VLDL增加，血浆外观可以澄清也可以混浊，主要视血浆甘油三酯升高的程度而定，一般无“奶油样”顶层，血浆甘油三酯明显升高，胆固醇水平可正常或偏高。 (5)Ⅴ型高脂蛋白血症：血浆中乳糜微粒和VLDL水平均升高，血浆外观有“奶油样”顶层，下层混浊，血浆甘油三酯和胆固醇均升高，以甘油三酯升高为主。 高脂血症的分类 血脂主要是指血清中的胆固醇和甘油三酯。无论是胆固醇含量增高，还是甘油三酯的含量增高，或是两者皆增高，统称为高脂血症。 1、根据血清总胆固醇、甘油三酯和高密度脂蛋白-胆固醇的测定结果，高脂血症分为以下四种类型： （1）高胆固醇血症：血清总胆固醇含量增高，超过5.72毫摩尔/升，而甘油三酯含量正常，即甘油三酯<1.70毫摩尔/升。 （2）高甘油三酯血症：约占20%血清甘油三酯含量增高，超过1.70毫摩尔/升，而总胆固醇含量正常，即总胆固醇<5.72毫摩尔/升。 （3）混合型高脂血症：血清总胆固醇和甘油三酯含量均增高，即总胆固醇超过5.72毫摩尔/升，甘油三酯超过1．70毫摩尔/升。 （4）低高密度脂蛋白血症：血清高密度脂蛋白-胆固醇（HDL-胆固醇）含量降低，<0.9毫摩尔/升。 2、根据病因，高脂血症的分类有： （1）原发性高脂血症：包括家族性高甘油三酯血症，家族性Ⅲ型高脂蛋白血症，家族性高胆固醇血症；家族性脂蛋白酶缺乏症；多脂蛋白型高 微生物制药技术介绍 工业微生物技术是可持续发展的一个重要支撑，是解决资源危机、生态环境危机和改造传统产业的根本技术依托。工业微生物的发展使现代生物技术渗透到包括医药、农业、能源、化工、环保等几乎所有的工业领域，并扮演着重要角色。欧美日等国已不同程度地制定了今后几十年内用生物过程取代化学过程的战略计划，可以看出工业微生物技术在未来社会发展过程中重要地位。 微生物制药技术是工业微生物技术的最主要组成部分。微生物药物的利用是从人们熟知的抗生素开始的，抗生素一般定义为：是一种在低浓度下有选择地抑制或影响其他生物机能的微生物产物及其 衍生物。(有人曾建议将动植物的具有同样生理活性的这类物质如鱼素、蒜素、黄连素等也归于抗生素的范畴，但多数学者认为传统概念的抗生素仍应只限于微生物的次级代谢产物。)近年来，由于基础生命科学的发展和各种新的生物技术的应用，报道的微生物产生的除了抗感染、抗肿瘤以外的其他生物活性物质日益增多，如特异性的酶抑制剂、免疫调节剂、受体拮抗剂和抗氧化剂等，其活性已超出了抑制某些微生物生命活动的范围。但这些物质均为微生物次级代谢产物，其在生物合成机制、筛选研究程序及生产工艺等方面和抗生素都有共同的特点，但把它们通称为抗生素显然是不恰当的，于是不少学者就把微生物产生的这些具有生理活性（或称药理活性）的次级代谢产物统称为微生物药物。微生物药物的生产技术就是微生物制药技术。可以认为包括五个方面的内容： 根据资料直接向有科研单位、高等院校、工厂或菌种保藏部门索取或购买；从大自然中分离筛选新的微生物菌种。 分离思路新菌种的分离是要从混杂的各类微生物中依照生产的要求、菌种的特性，采用各种筛选方法， 快速、准确地把所需要的菌种挑选出来。实验室或生产用菌种若不慎污染了杂菌，也必须重新进行分离纯化。具体分离操作从以下几个方面展开。 定方案：首先要查阅资料，了解所需菌种的生长培养特性。 采样：有针对性地采集样品。 增殖：人为地通过控制养分或培条件，使所需菌种增殖培养后，在数量上占优势。 分离：利用分离技术得到纯种。 发酵性能测定：进行生产性能测定。这些特性包括形态、培养特征、营养要求、生理生化特性、发酵周期、产品品种和产量、耐受最高温度、生长和发酵最适温度、最适pH值、提取工艺等。 工业上生产用菌株都是经过选育过的。工业菌种的育种是运用遗传学原理和技术对某个用于特定生物技术目的的菌株进行的多方位的改造。通过改造，可使现存的优良性状强化，或去除不良性质或增加新的性状。 工业菌种育种的方法：诱变、基因转移、基因重组。 宾语从句和定语从句讲解 （一）that 引导的宾语从句 宾语从句的引导连词有that, who, whose, what, which, 副词when, where, how, why, whether, if 可以跟that 从句做宾语的动词有：say, think ,wish, hope, wonder, know, suppose, see, believe, agree. 1、在学习宾语从句的时候要知道宾语从句的构成 I heard that he would come here later on. 主语谓语动词引导词一个句子作宾语 2、要注意在宾语从句中主句与从句的时态要呼应 （a）当主句用一般现在时，从句要根据实际情况，选择时态 例如：I believe（that）you did your best for that. I believe（that）you will do your best for that. (b) 当主句的时态用一般过去时，从句要用相应的过去时态（过去时代包括，过去进行时，一般过去时，过去将来时，过去完成时等过去时态） 例如：I hear he will come here later on . I heard he would come here later on. I can’t tell him that his mother died. (c)当主句的时态用的是过去时态，但是从句的内容是对客观事情的叙述，从句依然用一般现在时态。 例如：My teacher said that the earth goes around the sun. That 引导的定语从句和that 引导的宾语从句的区别 定语从句在句中作主句的定语，修饰前面的名词或代词。被修饰的词叫先行词，引导定语从句的词叫关系代词。我们今天要学习的时由关系代词that来引导的定语从句 一，that在定语从句中既可指代人也可指代物。先行词是人或者物时，可以用that 来引导 如：Have you seen the woman that is wearing red coat 状语从句练习 ( ) 1. I won't believe you___ I have seen it with my own eyes. A. before B. until C. after D. when ( )2.He ___ home ___ she was satisfied ___ his answer yesterday. A.didn't go; until; with B.wasn't go; after; to C. doesn't go; before; with D. didn't go; until; to ( )3. He ___ back until the work ___ done. A. isn't; will be B. isn't; is C. won't be; will be D. won't be; is ( ) 4. They didn't start the work ___ their teacher came back. A. until B. while C. as soon as D. if ( )5. Tom will call me as soon as he ___ Shanghai. A. arrives B. will reach C.arrives in D.get to ( )6. I'm sure he'll come to see me before he ___ Beijing. A. will leave B. is leaving C. leave D. leaves ( )7. Tom has got a watch. He ___ it for two years. It _______ by his father. A. has bought; was bought B. has got; is bought , C. was bought; has bought . D. has had; was bought "' ( )8. When he got to the station, the train ___. A. left B. had left C. leaves D. has left ( ) 9. The boy told his father what he ___ in the street. A. saw B. have seen C. had seen D. see ( ) 10. We ___ TV when the telephone ____. A.watched; was ringing B. were watching; rang C. watch; rings D. are watching; rang ( ) 11. I ___ you for a long time. Where ___ you ___? A. didn't see; did; go B. didn't see; have; gone C. haven't seen; have; been D. haven't seen; have; gone ( ) 12. Tom___ China for 3 years. A. has been B. has been in C. has been to D. has been at ( ) 13. -Hello! May I speak to Bob? -Sorry, but he ___ for a month. A. had been away B. was left C. left D. has been away 1976年WHO!议将高脂血症分为六型： (1) I型高脂蛋白血症：主要是血浆中乳糜微粒浓度增加所致。将血浆至于4C 冰箱中过夜，见血浆外观顶层呈“奶油样”，下层澄清。测定血脂主要为甘油三酯升高，胆固醇水平正常或轻度增加，此型在临床上较为罕 见。 (2) U型高脂蛋白血症，又分为Ua 型和Ub型。 ①Ua型高脂蛋白血症：血浆中LDL水平单纯性增加。血浆外观澄清或轻微混浊。测定血脂只有单纯性胆固醇水平升高，而甘油三酯水平则正常， 此型临床常见。 ②Ub型高脂蛋白血症：血浆中VLDL和LDL水平增加。血浆外观澄清或轻微混浊。测定血脂见胆固醇和甘油三酯均增加。此型临床相当常见。 (3) 川型高脂蛋白血症：又称为异常B -脂蛋白血症，主要是血浆中乳糜微粒残粒和VLDL残粒水平增加，其血浆外观混浊，常可见一模糊的“奶油样”顶层。血浆中胆固醇和甘油三酯浓度均明显增加，且两者升高的程 度(以mg/dL为单位)大致相当。此型在临床上很少见。 ⑷W型高脂蛋白血症：血浆VLDL增加，血浆外观可以澄清也可以混浊，主要视血浆甘油三酯升高的程度而定，一般无“奶油样”顶层，血浆甘油三酯明显升高，胆固醇水平可正常或偏高。 (5) V型高脂蛋白血症：血浆中乳糜微粒和VLDL水平均升高，血浆外观有“奶油样”顶层，下层混浊，血浆甘油三酯和胆固醇均升高，以甘油三酯升咼为主。 高脂血症的分类 血脂主要是指血清中的胆固醇和甘油三酯。无论是胆固醇含量增高，还是甘油三酯的含量增高，或是两者皆增高，统称为高脂血症。 1、根据血清总胆固醇、甘油三酯和高密度脂蛋白-胆固醇的测定结果，高脂血症分为以下四种类型： (1)高胆固醇血症：血清总胆固醇含量增高，超过 5.72毫摩尔/ 升, 而甘油三酯含量正常，即甘油三酯<1.70毫摩尔/升。 (2)高甘油三酯血症：约占20%血清甘油三酯含量增高，超过1.70毫摩尔/升，而总胆固醇含量正常，即总胆固醇<5.72毫摩尔/升。 (3)混合型高脂血症：血清总胆固醇和甘油三酯含量均增高，即总胆固醇超过5.72毫摩尔/升，甘油三酯超过 1 . 70毫摩尔/升。 (4)低高密度脂蛋白血症：血清高密度脂蛋白-胆固醇(HDL-胆固醇) 含量降低，<0.9毫摩尔/升。 2、根据病因，高脂血症的分类有： (1)原发性高脂血症：包括家族性高甘油三酯血症，家族性川型高脂 微生物制药的研究进展 姓名：李青嵘 班级：生工102 学号：1014200044 摘要 本文通过对历史文献的检索，从微生物生产维生素，微生物生产多价不饱和脂肪酸，微生物生产抗生素，微生物生产抗癌物质，微生物生产医用酶制剂等五个方面综述了微生物制药的研究进展。 关键词：微生物，制药，发酵工程 1.前言 随着生物技术的迅猛发展，在医药领域的许多方面取得了巨大的进展.，其中采用微生物制药，具有生产工艺简单，生产成本低廉，产品产量高，产品纯度高，可大规模工业化生产等优势，同样得到了巨大的发展。从传统工艺，如利用发酵工程生产抗生素、酶制剂以及B-胡萝卜素等；到现今的利用转基因技术生产干扰素、胰岛素、生长因子等几十种新药和疫苗。本文着重综述了微生物的发酵工程在医药研究和生产中应用的最近进展，主要包括生产维生素、多价不饱和脂肪酸、抗生素、抗癌物质医用酶制剂等五个方面。 2.研究内容 2.1.微生物生产维生素 维生素是六大生命要素之一, 为整个生命活动所必需。β-胡萝卜素、VC、VE是目前应用最为广泛，效果最为显著的三种维生素，它们的作用分别是：β-胡萝卜素是强力抗氧化剂, 有抑制癌细胞增殖和提高机体免疫力等作用。V C 和V E 均是抗氧化剂, 前者可阻止、破坏自由基形成，还具有激活免疫系统细胞的活力，刺激机体产生干扰素以抵御外来侵染因子。至于VE可产生抗体，增强机体免疫力。目前，上述的“三素”以实现了微生物工业化生产。 目前，β-胡萝卜素主要是由三孢布拉霉菌生产，在1998年，陈涛等[1]已经针对三孢布拉霉菌的特点，优化发酵工艺，在3M3的发酵罐中发酵120h，生产的β-胡萝卜素产量已达到1146.5mg/L。虽然，传统的工艺生产β-胡萝卜素的产量高，生产周期比较短，但是传统的工艺复杂，成本过高，不利于大规模工业化生产。故,目前许多课题组专注于开发新的生产β-胡萝卜素的菌种或改进传统工艺。据近年所发表的期刊文献，目前，采用红酵母发酵生产β-胡萝卜素是一种工艺简单，成本低廉的方法，虽然在产量方面较传统方法的低很多，但是该方法仍具有很大的发展潜力。何海燕等[2]采用粘红酵母R3-35摇瓶发酵84h，生产的β-胡萝 阶段测试一 1、She tried hard ___________ she failed. 2、Be quick, _________he’ll be angry. 3、You may _________ do it yourself _______ leave it to me. 4、He could read English ________Japanese well. 5、He didn’t know anything about that ________ he couldn’t tell you. 6、________ you ________ he was here yesterday. They were at the cinema. 7、You can _______eat it at home ________ in the open air. Either is OK. 8、Use your head, _______ you’ll have a way. 9、She’s _______ our teacher _______ our friend. 10、Write to me soon, _______I’ll know a lot about you. 单项选择 1. I asked him _________dog it was. A. whose B. which C. who's D. where 2. They go to concerts of modem music_________ they really like it. A. because B. if C. though D. after 3. Find out_________ they are going this evening and ask_________ may join them. A. whether, that B. where, whether 2018年九年级英语专项练习—定语从句和宾语从句 Name__________ Grade__________第一部分单项选择。（本题共45小题，每题1分，计45分） 从每小题所给的A、 B、 C、D四个选项中选出可以填入空白处的最佳答案。 ( )1.— kind of tea would you like —I love tea has a fruity taste. A. Which;what B. What; which C. Whose; that D. What; who ( )2.—Excuse me, how long will it take me to get to the post office —Well, it depends on . A. how you will get there B. when you will get there C. where you will get D. how will you get there ( )3.—Excuse me. Could you please tell me ______ —Sure. Go along this street and turn left. It’s on your right. A. when I can get to the bookstore B. when can I get to the bookstore C. how I can get to the bookstore D. how can I get to the bookstore ( )4.—Why are you so worried —I’ve lost the watch ______ my dad bought me on my birthday. A. what B. who C. whose D. which ( )5. She often parks her car near the house _____she can easily get to. A. where B. who C. which D. what ( )6. Could you please tell ______ A. how can I make the machine work B. how I can make the machine work C. how I can make the machine to work D. how can I make the machine to work ( )7.—What did the manager ask you after the meeting —She asked me__________. A. what I do for the project last week B. if can I finish the work on time C. how did I deal with the problem D. why I was late for the meeting 高脂血症健康指导 1、定义 血脂代谢发生紊乱；脂肪代谢或转运异常；血浆中一种或几种脂质浓度，包括血浆TC及TG水平过高或血浆HDL水平过低；人体血浆中TC、TG和各种脂蛋白含量高于同龄正常值者均称高脂血症。高TC血症和高TG血症均属于高脂血症，既可表现为单纯高TC血症或单纯高TG血症，也可表现为高TC合并高TG混合型高脂血症。 2、症状 高脂血症的临床表现主要包括两大方面: ?脂质在真皮内沉积所引起的黄色瘤； ?脂质在血管内皮沉积所引起的动脉粥样硬化, 产生冠心病和周围血管病等。 由于高脂血症时黄色瘤的发生率并不十分高, 动脉粥样硬化的发生和发展则需要相当长的时间, 所以多数高脂血症患者并无任何症状和异常体征发现。 而患者的高脂血症则常常是在进行血液生化检验(测定血胆固醇和甘油三酯)时被发现的。 3、病因 低密度脂蛋白受体亦称为Apo B、E受体，是一种细胞表面糖蛋白，以肝细胞含量最多。低密度脂蛋白受体基因位于人类第19号染色体，家族性高胆固醇血症发病的原因是低密度脂蛋白受体基因的自然突变，包括缺失、插入、无义突变和错义突变。已发现数十种低密度脂蛋白受体基因突变，可分为五大类。 ?Ⅰ类突变：其特点是突变基因不产生可测定的低密度脂蛋白受体，细胞膜上 无低密度脂蛋白受体存在，是最常见的突变类型。 ?Ⅱ类突变：其特点是突变基因合成的低密度脂蛋白受体在细胞内成熟和运输 障碍，细胞膜上低密度脂蛋白受体明显减少，也较常见。 ?Ⅲ类突变：其特点是突变基因合成的低密度脂蛋白受体可到细胞表面，但不 能与配体结合。 ?Ⅳ类突变：此类突变是成熟的低密度脂蛋白受体到达细胞表面后虽能结合低 密度脂蛋白，但不能出现内移。 ?Ⅴ类突变：其特点是低密度脂蛋白受体的合成、与低密度脂蛋白的结合以及 其后的内移均正常，但受体不能再循环到细胞膜上。 不同种族，低密度脂蛋白受体突变的发生有差异，例如French-Canadians的杂合子家族性高胆固醇血症中，受体基因缺失所致的突变占60%。低密度脂蛋白受体的缺陷最突出的异常是低密度脂蛋白从血浆中分解减慢。在低密度脂蛋白受体正常时，部分中间密度脂蛋白可直接被肝脏低密度脂蛋白受体摄取而分解，而在家族性高胆固醇血症，低密度脂蛋白不能被分解，造成更多的中间密度脂蛋白转化为低密度脂蛋白，使低密度脂蛋白产生增加。 4、风险因素 高脂血症的风险因素包括： ?遗传因素原发性系由于脂质和脂蛋白代谢先天性缺陷引起。 ?某些疾病继发性者主要继发于某种疾病，如糖尿病、肝脏疾病、肾脏疾病、 甲状腺疾病等， ?生活方式以及饮酒、肥胖、饮食与生活方式等环境因素的影响。 长期高脂血症易导致动脉硬化加速，如果长期动脉硬化不但会使硬化的血管变得脆弱，发生破裂，而且还会发生脑梗寒或心梗等。 5、诊断手段 高脂血症相关的检查项目： ?测定血脂谱全套包括空腹TC、TG、LDL-C、HDL-C。 ?判断血浆中有无乳糜微粒存在可采用简易的方法，即把血浆放置4℃冰箱 重点、难点 1. 含有if引导的条件状语从句的复合句中主从句的时态。 2. If引导的宾语从句与条件状语从句的区别。 考情分析 通常在单项选择、完形填空或补全、完成句子等题型中考查，分值约3—4分。 知能提升 （一）知识讲解 【认知讲解】 I. if引导的宾语从句 if 引导宾语从句时，意思为：是否，从句的时态通常要和主句保持一致。 【例句】 I want to know if he lives there. 我想知道他是否住在那儿。 He asked me if I could help him. 他问我是否能帮他。 【考查点】if、whether引导的宾语从句的区别 1. if或whether引导宾语从句时，作“是否”讲，常放在动词ask、see、say、know和find out等后面。一般情况下，两者常可换用，在口语中多用if。 【例句】 Nobody knows whether / if it will rain tomorrow. 没有人知道明天是否下雨。 Lucy asked whether / if they had a cotton sweater. 露西问他们是否有棉制的毛衣。 2. if或whether引导宾语从句时，要注意三个方面，即连词、语序和时态。 if或whether既不能和that 或其他连词（副词）同时使用，也不能省略。 【例句】 我不知道他今天是否会来。 [误] I don’t know that if(whether) he will come here today. [正] I don’t know if(whether) he will come here today. 他走过来看看猫是否出了毛病。 [误] He came to see what if (whether) there was anything wrong with his cat . [正] He came to see if (whether) there was anything wrong with his cat . if或whether引导宾语从句时，虽具有疑问的意义，但其从句应用陈述句的语序。 【例句】 Did you know the way to the hospital The old woman asked me. The old woman asked me if / whether I knew the way to the hospital. 老妇人问我是否知道去医院的路。 if或whether引导的宾语从句应和主句的时态保持一致。即主句为一般现在时，从句用任一种时态；主句为一般过去时，从句则用过去时中的任一种时态。 【例句】 I don’t know if (whether) he has come here. 我不知道他是否来过这儿。高脂血症
微生物制药的一般工艺流程
如何区分定语从句、宾语从句和状语从句
从句归纳区分定语从句、宾语从句、同位语从句
三大从句之宾语从句教学提纲
高脂蛋白血症的分型
初中定语从句和宾语从句
英语三大从句精编版
高脂血症的分型和分类
微生物制药技术介绍
宾语从句和定语从句讲解
(完整版)状语从句和宾语从句练习
高脂血症的分型和分类
(完整版)微生物与制药综述
状语从句和宾语从句测试题(一)
2018年九年级英语专项练习—定语从句和宾语从句
高脂血症健康指导
If引导的两种从句(宾语从句和条件状语从句)