外文翻译(英文)

Title: Modelling of transport costs and logistics for on-farm milk segregation in New Zealand dairying

Material Source: Computers and Electronics in Agriculture

Author: A. E. Dooley, Parker, H. T. Blair

Abstract

On-farm milk segregation to keep milk with high value properties separate from bulk milk will affect transport logistics. Separate milk collection, either as independent runs for different milk types,or storage of distinct milk types in the truck and trailer units, may increase the length and number of runs required. Two contrasting regions,with different farm sizes and roading networks were modelled,at two stages of lactation over 20 years. Thirty farms in each region were modelled with 0, 25, 50 and 100% of farms per region changing milk types over a transition period of up to 18 years. Genetic algorithm software was used to search for the order of the farm milk collection pick-ups which gave an optimal, least cost solution for milk collection for each prescribed set of inputs. Milk collection costs within scenario were variable over time depending on the amounts of the different milk types, increasing whenever another run was required, then decreasing over time as the milk load increased. Milk collection cost is small relative to milk income, with the status quo (SQ) cost for milk collection being less than NZ$9.61/kl for the North Island and NZ$13.53/kl for the South Island farm sets. The increased transport costs associated with collecting two milk types ranged from 4.5 to 22.0% more for the different scenarios. The extra cost to an average size North Island farm changing systems (25% farms changing), compared to an equivalent status quo farm, would be between NZ$307 and NZ$1244 per year. Fewer farms changing to differentiated milk production increased the costs per kilolitre of differentiated milk.

Keywords: Milk transport; Scheduling; Milk segregation; Collection costs

1.Introduction

Milk with high value properties can be segregated from bulk milk, both on-farm and between farms, allowing it to be processed into niche products, e.g., milk with particular proteins such as A2 β-casein or B β-lactoglobulin milk, light coloured milk, organic milk or milk with antibiotic properties. On-farm segregation of high value milk has associated effects on the logistics of milk collection. Currently, New Zealand dairy companies deduct about $0.04/l from farmers’ payouts to cover costs associated with the transportation and storage of bulk milk,and the removal of water at the factory. Milk segregated at the farm is likely to increase this cost because of higher transport and milk storage costs. Separate milk collection, either as independent runs for different milk types, or storage of distinct milk types in the truck and trailer units, may increase the length and number of trips required. Extra vats and milk silos may be also required to segregate milk. It follows that products from segregated milk must command either a higher market value or a reduced processing cost, to offset these additional costs.

The software used by dairy and other transport companies to optimise scheduling decisions is commercially sensitive and specific to a compa ny’s particular operation. Furthermore,this software typically relates to the collection of only one milk type.A simulation model for studying transport logistics was, therefore, constructed to quantify these costs and the practicalities of collecting different milks. Increased transport costs associated with milk changing from one type to another were determined by modelling situations where none, 25, 50% and all farms in a collection area changed to another milk type over a 20-year period. Implications for farmers and their milk processor in adopting on-farm milk segregation are discussed.

2. Method

2.1. Problem description

Two contrasting geographic configurations of dairy farms were modelled, at two

stages of lactation (peak and late). The smaller, more concentrated dairy farms were represented by a North Island dairying area and the larger, more dispersed farms were represented by a South Island dairying area. The model was developed using Microsoft Excel spreadsheets, and the Evolver genetic algorithm software to search for the order of the farm milk collection pick-ups which gave an optimal, least cost solution for milk collection for each prescribed set of inputs.

A hypothetical set of 30 farms was defined for each region, based on actual farm milk production data supplied by a New Zealand dairy company. The North Island set of farms represented an area with small herds (average=177cowsperfarm) near the factory, whereas the South Island farms had large herds (average greater than 500 cows, Livestock Improvement Corporation (LIC), 1999) on farms physically further apart. Each farm produced one or two types of milk, henceforth labelled “milk A” and “milk B”. Th e collection of each milk type, on each farm, was defined as a separate stop, giving 60 possible milk collection stops. The number of stops and the milk volumes collected varied over the 20 years according to the number of farms changing from milk A to milk

B milk and the rate of change between milk types within farms. All herds were seasonally calved in the spring.

2.2. Scenarios examined

The model simulated the effect of some farms within a catchment changing from the production, and segregation, of milk A to milk B milk over time on changing milk volumes of the two milk types, milk collection requirements and collection costs. Four scenarios of change in a milk collection area were explored: no farms (status quo (SQ)), 25% (8 farms), 50% (15 farms) and all farms changing to milk B milk (Table 1). For each scenario, farms were randomly allocated to the two groups (changing or not). North and South Island herds (small and large volumes per stop) and either daily or every other day collections were simulated.

The initial percentage of milk B milk on farms involved in a change in milk type ranged from 26 to 47%, with herds randomly allocated to five different gene frequencies associated with the different amounts of milk B. Once 95% or more of the milk from a herd was milk B; it was assumed all milk was milk B, since for practical purposes, it is unlikely a separate stop would be made for 5% of the herd’s production. The time taken for a herd to change from one particular type of milk to another using genetic selection took about 14 years, but this was influenced by the initial number of milk B cows in the herd and associated gene frequency.

Table 1 Transport model scenarios run

To simplify the analyses, it was assumed that all farmers would commit to supplying Milk B milk or not,with in the first 3 years.Farms changing to milk B supply were randomly allocated to an initial year of change at a ratio of 3:4:1 for years 1–3 for the 25 and 50% scenarios. Where all herds in a collection area changed, it was assumed that this was a policy decision and that all farms changed in the first year.

A bridging point en route, at the edge of the collection area closest to the dairy factory was selected. Consequently, only the distances between farms, farms and the bridging point, and the bridging point and the factory, needed to be recorded. Mellalieu and

Hall (1981) adopted a similar approach in modelling a milk transport planning model. The distance between the dairy factory and the bridging point was assumed to be 25 and 85km for the North and South Islands, respectively.

2.3. Milk production volumes

Production for each farm in year 1 was based on actual production data for the farms in the 1997/98 (North Island) and 1998/99 (South Island) lactations. Milk collection was

simulated for the peak supply day for both the North and South Islands, and the first day

when all farms were on every second day pick-up during late lactation for the North Island.

The flatter lactation curve in the South Island compared to the North Island (LIC, 1999)

meant the amount collected on the first day of every second day collection in late lactation

was similar to the daily pick-up during peak lactation, therefore, this scenario was not modelled. These 2 lactation days simulated two points on the seasonal supply milk volume curve from which other transport effects could be interpolated.

The average amount ofmilkfortheherdsinyear1atpeaklactationwas3094l(σ =1544)

per day for the North Island an d 11577 (σ =3629) for the South Island. In late lacta- tion, this value was 1920l (σ =1036) every second day for the North Island. Milk yield per farm was assumed to increase, based on the historic average, by 1.5% per hectare per year (LIC, 1999). The percentage of milk B produced over the 20 years is shown in Table 2.

2.4. Tanker parameters

Tanker capacity was 11,300l for the truck unit and 17,500l for the trailer unit based on approximately 95% loading for actual milk volumes (Spooner, General Manager Trans-

port Operations, New Zealand Dairy Group, Hamilton, 2000, personnel communication).

If only one type of milk could be collected during a run, it was assumed that the full amount (28,800l) could be collected in one unit (truck and trailer combined). Total vol-

umes of milk A and milk B milk to be collected were checked for each stop and if the tanker was empty, the type with the greater volume was allocated first to the larger trailer unit.

While costs can be calculated by separating them into running (per kilometre costs) and hourly costs, the information was not readily available in this format, therefore, a flat rate

per kilometre cost was assumed. Costs were estimated from dairy company information to

be $3.45 and $1.75/km for the North and South Islands, respectively, with the former being

greater due to overheads being spread over the shorter distance travelled.

Table 2 Percentage of the total milk supply that was milk B over the 20 years for different rates of farm adoption

2.5. Milk collection routes

The model inputs required were:

1. A grid with distances between each stop and the factory, and between each of the stops.

2. A table with the amount of milk at each stop on a given day (in either peak or late lactation), for each of the 20 years.

3. The volume of milk that can be carried in the truck and trailer units.

4. Costs per hour and per kilometre, time spent unloading at the factory, time per stop and the average tanker speed. The latter three were used in calculating the time taken per trip.

5. The initial sort order for the stops. To set up a run, the number of stops with milk to be collected was counted. These stops were then sorted into one of 12 predefined orders.

The orders of the milk collection stops used to initialise the GA were derived using a greedy heuristic (Hesse, 1997). Stops with milk to be collected were sorted by visiting the stop nearest the factory, then moving to the next closest stop and so on until all stops had been visited. Six initial sort orders were generated by ordering stops by milk type within farm order and farm within milk type order, in both clockwise and anticlockwise directions.A further six sort orders were generated by running these sort orders through a program that assumed that once a stop was reached that was unable to be collected(e.g.,wrong milk type, too much milk volume) the program continued to check if further stops could be collected rather than stopping the run there. This ensured the tanker was as full as possible before returning to the factory, but increased the distance travelled per run. This procedure was repeated until all milk was collected. Direction travelled had no effect on distance so it was assumed the tanker would travel in the most efficient direction (clockwise or anticlockwise) in terms of loading, i.e., to the furthermost point on the route first to ensure the load is at a minimum for as long as possible. Consequently, loading was not taken into consideration.

The 12 predefined sort orders were used to initialise the GA. The Evolver GA sorted the sequence of the milk collection stops to find the least cost sort order. Milk was collected in sequence of sort order. If the volume of milk at the next stop could not be

accommodated, the tanker returned to the factory. It then returned to the next stop in the sort order to resume milk collection. Evolver default parameters for the order solving method were used for the mutation rate (0.06) and the crossover rate (0.5). Population size was set to 1000 and a random seed was used to generate the sort orders evaluated by Evolver. The Evolver GA was run fives times for each of the 20 years for the North Island, but only three times for the South Island due to the computing time required to derive a solution.

The optimum value found by the genetic algorithm search method may not necessarily be the actual optimum value (Buckles and Petry, 1992). Therefore, a direct comparison between two scenarios in a particular year cannot be made definitively, as the optimum value identified for one scenario may be closer to its actual optimum value than the other. However, if it is assumed that over the 20 years, the average deviation of values from their actual optimum is similar for all scenarios then this search method is likely to be effective in comparing the various scenarios.

The optimum (least cost scenario) for each year was written to a summary output page. Other information included the number of stops and runs, the distance travelled, the time taken,the volumes of milk A and milk B milk, and the order of the stops, highlighting when the tanker returned to the factory.

The time taken to collect and return all the milk to the factory was derived, even though this value was not used directly for calculating milk collection costs. Time taken was estimated to be half an hour for the turn around at the factory and 0.2h (12min) per stop. Average tanker speed was estimated to be 70km/h in the North Island and 80km/h in the South Island. Travelling time was calculated as kilometres travelled divided by speed. The proportional increase in the number of tankers required to collect all the milk was the difference between a scenario and its associated status quo option, assuming all milk must be collected within a set time period, e.g., every 24h during peak lactation.

2.6. Milk collection costing methods

Two milk collection costs were applied to each scenario. First, the average collection cost per kilolitre of milk was calculated for each of the 20 years, i.e., the extra cost associated with transport of differentiated milk was spread across all milk. Second, a “user pays” or marginal cost approach was applied where the extra cost relative to the SQ associated with collecting differentiated milk was assigned to milk B. Thus, extra costs were assigned to those switching to milk B milk. There was considerable variability within years making it difficult to compare between scenarios (Dooley, 2002). Hence, costs were discounted overthe 20 years and a constant SQ cost per kilolitre for the 20 years calculated which gave an equivalent overall cost. This cost was also used for milk A. The remainder of the cost was allocated to milk B and a constant milk B cost per kilolitre was calculated in a similar manner. These methods are described more fully by Dooley (2002). The single value for milk A and milk B transport costs enabled comparability between scenarios. Discounting takes time into account when comparing costs by converting costs for all years to year 1 values.

Dairy companies charge farmers a per litre volume charge which covers volume related costs, including transport. The extra on-farm costs associated with milk collection were calculated for a North Island farm and a South Island farm. Costs were calculated for 25 and 50% of farms changing, with both types of milk able to be collected in a run. Farms were assumed to start differentiating milk in year 1. Peak milk collection costs only were used for the South Island. For the North Island, with a much more pronounced seasonal milk supply curve, the average of the peak and late lactation costs were used. The North Island farm was assumed to produce 574,884 l per lactation in year 1 (the average for the data set), and the South Island 2,097,676l (LIC, 1999).

3. Results and discussion

3.1. Average milk collection cost

3.1.1. Comparison with the SQ (0% of farms changing) ThedifferenceintheaveragemilkcollectioncostsbetweentheSQandthedifferentiated

milk scenarios for all years ranged from 4.48% less to 26.86% more for the differentiated

milk scenario (Table 3). Differences were most variable for the North Island peak lactation

option. The average cost per kilolitre for milk collection in the North Island during peak

lactation for 0, 25, 50 and 100% farms changing is shown in Fig. 1 for every alternate year.

3.1.2. Stage of lactation comparison

Total collection costs are greater at peak than late lactation because of the larger volume

ofmilk;however,costsperkilolitreweregreateratlatethanpeaklactationbecauseoflonger distances travelled to collect an equivalent volume of milk. Average North Island collection

costs per kilolitre over the 20 years were 16.4, 14.7 and 14.1% more in late lactation as

compared to peak lactation for SQ, 25 and 50% of farms changing to milk B production,

respectively.Averagemilkcollectioncostsperyearrangedfrom1to23%moreperkilolitre

in late lactation than peak lactation and this variation could be explained almost entirely

by the number of trips required to collect the milk. Costs were 12–23% more per kilolitre

for late lactation milk where only one less trip was required to collect milk in late lactation

as compared to peak lactation. Once the collection of peak lactation milk became less efficient (two extra trips for peak lactation milk collection) the difference was only 1–2%

more.

Late lactation costs were not calculated for the South Island because production was about half that of peak lactation, therefore, collection costs per kilolitre once all herds were

on every second day collection (185 days after peak lactation) would be similar to peak lactation. In contrast, North Island production was about 31% of peak lactation, once all

farms were on every second day collection (203 days after peak lactation).

Factors other than milk volume relative to peak lactation volumes may influence the change to every second day milk collection. For example, changing to two milk types may mean a farm moves to every second day collection sooner, particularly during the transition years, when the volumes of one or both milk types would be less than for the

SQ situation. Although not investigated, costs per kilolitre may be greater still at the end

of lactation, or prior to all farms going on to every second day collection, as the volume

of milk collected per stop will be lower at these times than for the situation modelled for

late lactation. Modelling the final stages of lactation would be complex as not all farms

switch to every second day collection at once, nor do all herds cease lactation on the same

day.

3.1.3. Variation in average milk collection costs over the years Withineachofthescenarios,milkcollectioncostsvariedovertime(Fig.2).Thecostper kilolitre increased sharply once an extra run was required to collect the milk, then

declined

gradually as the tanker loads approached capacity volumes, thus spreading costs over a

greater volume of milk (Fig. 3). As the number of farms changing to milk B production

increased, the likelihood of having partial loads of one or the other milk types increased,

resulting in greater variation in the collection costs over time.

The number of tanker runs had the greatest impact on milk collection costs because most of the distance travelled was getting to and from the milk collection area, rather than

collectingmilkfromthefarmswithinthearea.Forexample,inthepeaklactationSQscenario for year 1, and assuming a flat per kilometre cost, 91.6 and 86.0% of the collection costs

for the North and South Islands, respectively, were for travelling to and from the collection

area. Thus, the first priority in determining the order of the stops for milk collection is to ensure the loads are as close to capacity as possible. The distance travelled around the

stops within a collection area is of secondary importance. The balance of milk types in the

transition years can affect the number of runs required as is shown by year 16 in Fig.

3. In

this year, milk A and milk B milk volumes are similar and all milk can be carried in four

trips, whereas in years 15 and 17, the slightly greater amount of either milk type means an

extra trip is required with consequent cost increases.

This variation in collection costs affected the difference between the SQ and farms

changing options. Some of the more extreme differences in collection costs between the

SQ and other options occurred in years where the average cost was decreasing for the SQ

option but increasing for the differentiated option. This is illustrated by the North Island

peak lactation costs for years 15 and 16 in the 25% option, 14 and 15 in the 50% option,

and 12–16 in the 100% option. In most of these cases, the cost per kilolitre exceeded the

SQ cost by more than 20% in that year (Table 3).

In general, average costs for milk segregation were greater than the SQ in the middle to

later transition years (Table 3) once most of the milk had changed to milk B. North Island

late lactation results did not show this to the same extent, probably because the number of

trips remained the same (three) for all scenarios over the 20 years. The South Island early

lactation results are not as marked as those for the North Island and in some instances, the

collection of two milk types in the South Island was more efficient than the SQ scenario because the smaller lot sizes allowed the tanker to carry closer to capacity volumes (e.g.,

year 13, for 25% of the farms changing to milk B, fewer trips were required than in the SQ

scenario).

3.2. Technology adoption time frame ThemodelassumedallfarmschangedtomilkBovera20-yearperiodthroughselection,

with a 3-year technology adoption time frame. These assumptions simplify reality.

Farmers

could, for example, adopt a number of policies to move toward producing a different milk

type. As well as changing the herd over time through breeding, they could also buy and sell

cows to accelerate the change to one milk type (reducing or eliminating transition years),

maintain split herds as a policy to spread risk, or adopt a combination of policies. The farmers changing to milk B production are likely to adopt a range of management policies

and this will impact on the rate of technology adoption. Any combination of transitional

managementpoliciesandtechnologyuptakewithina20-yearperiodcanbeexploredwithin the model.

Factors other than farmer policy may affect the amount of milk produced over time and associated transport costs. A dairy company may pay on the level of a component in the milk rather than segregating the milk so that all milk B milk would be collected together from the start (i.e., no transitional years). If there are no transitional years and those farms changing produce all milk B in their first year, then the increased transport

costs are likely to be lower, e.g., similar to the last 2–3 years modelled. Alternatively, where transitional years apply, the initial amount of milk B produced will be depen- dent on the level in the herd, e.g., selection on a qualitative trait with a higher or lower gene frequency. Where there is a higher initial proportion of milk B, a comparison can be

made from the year that starts with that proportion. However, in this situation the first few

years may be inaccurate, as the rate of technology adoption will not have been taken into

consideration.

3.3. Average minimum load size

The average minimum load in the North and South Islands was compared for years 11–20 at peak lactation with 25% of the farms changing to milk B milk. The North Island

average minimum load was less than for the South Island (average minimum load was 54.4% of capacity for the North Island as compared to 71.3% for the South Island). The

small number of farms modelled would have affected these results, particularly in the North Island where the number of runs required was small (3 or 5) relative to the South

Island where 13–18 runs were required. However, the average capacity of the remaining

loads was slightly greater for the North than the South Island, i.e., 94.3 and 92.6% for the North and South Islands, respectively. These results gave an overall average tanker

load of 86.0 and 91.3% of capacity, for the North and South Islands, respectively. The better South Island loading rate reflected the greater number of runs required to col- lect all the milk, with most of the loads at near to full capacity. In practice, a larger number of farms in a collection area would enable tanker capacity to be more fully utilised.

3.4. Farm and herd size

The 30 farms were assumed to remain the same size over the 20 years, whereas current

trendssuggestthatbothfarmsizeandherdsizeareincreasing(LIC,1999).Farmamalgama- tions are, therefore, likely to occur over the 20 years. While this would reduce the number

of stops and increase the amount of milk per stop and farm, the total milk collected from

the geographic area incorporating these 30 farms in the North Island may not differ greatly

from that predicted, assuming the increase in per hectare production (1.5% per annum)

remains similar. Fewer farms would, however, affect the milk collection pattern with pos-

sibly 2–3 farm stops per run in the North Island rather than 5 or 6 as modelled, giving a farm distribution and milk collection cost pattern similar to that of South Island. South

Island milk production within a given area is likely to increase through farm conversions

to dairying (MAF, 2000). This would reduce collection costs per kilolitre slightly because

the tanker will travel shorter distances within a set geographic area to collect a full load of

milk.

3.5. Time taken for milk collection and tanker requirements

Differences among the scenarios were small for the time taken to collect the milk over the last 2–3 years, when all farms produced milk of one type or another (0–5% more time than the SQ). The difference in time taken between the SQ and segregation scenar-

ios tended to increase as the number of farms changing to milk B increased. The overall

average difference in collection times between the SQ and the other scenarios at peak lactation in the North Island for 25, 50 and 100% of farms changing was 12.7, 23.0 and 45.0%, respectively. The greatest difference between the SQ and the other scenar- ios for 25, 50 and 100% of farms changing was 23.2, 38.4 and 65.2%, respectively. In the South Island, the difference in most cases was less than 10% (averages of 4.0 and 7.5%, maximums of 9.5 and 13.3%, respectively, for 25 and 50% of farms changing). As

for costs, a direct time comparison between scenarios within years cannot easily be made

because time taken to collect milk is not solely affected by the number of runs (see Sec-

tion 2). However, while it offers simplicity a flat per kilolitre rate may not fully account

for labour costs or the extra time required for more stops where farms are changing milk

types.

3.6. User pays cost calculation method

Dairy companies are unlikely to pass actual extra costs on to farmers changing milk type policy at rates that vary markedly from year to year. However, the “user pays” method

allowed the likely extra transport costs to be passed on to farmers changing policies to be

determined and this is spread over the 20 years. The overall difference in total collection

costs between the SQ and other policies within scenarios using this pricing method ranged

from 0.8 to 7.0% at a 7% discount rate (Table 4).

The SQ cost per kilolitre for late lactation milk collection was 17.5% more than for peak lactation ($7.56 cf. $8.89 for peak and late lactation, respectively). South Island milk

collection costs were 73.8% more than for the North Island at peak lactation ($7.56/kl cf.

$13.14/kl for the North Island and the South Island, respectively). The actual extra costs

associated with milk B milk collection at peak lactation and late lactation were almost the same in the North Island with 25% of farms changing, i.e., 9.23?7.56=$1.67/kl and 10.57?8.89=$1.68/kl. The difference with 50% of farms changing was less in late lactation than in peak lactation, i.e., $0.87 versus $1.06/kl, respectively. The difference

in costs between the SQ and 50% of farms changing was the same for the North and South Islands ($1.06/kl) at peak lactation. However, the extra costs associated with 25%

of farms changing in the South Island were low ($0.59/kl) at peak lactation. Extra costs of

milk B milk collection are, therefore, not necessarily different between Islands or stage of

lactation.

All farms in the last 2–3 years produced either milk A or milk B milk (Table 2). Costs per kilolitre for the differentiated scenarios were also lower in relation to SQ in these years.

This is particularly noticeable for all three North Island, peak lactation scenarios (Table 3).

Therefore, it may not be appropriate to spread the difference in costs over the entire 20

years at the same rate. Rather, it may be better to spread these costs over fewer years, or

alternatively, once the extra costs have been recouped over the 20 years, to review the extra

transport costs attributable to milk B milk. Also, it can be argued that farms producing two milk types (in transition or as a policy) should pay more in collection costs than those producing only one milk type. Although this would pose practical difficulties, due to

farmers using a range of policies and adoption rates, it would better reflect a “user pa ys”

approach.

3.7. Average milk collection cost: one milk type per run and every second day collection

3.7.1. One milk type collected per run Whereonlyonemilktypewascollectedperrun,collectioncostswerethesameorgreater

than collection of two types per run for all but 1 year, where costs were less. In most years,

the difference between one and two types per run was either nil or very small (Fig. 4). For

example, for the 50% of farms changing scenario, the percentage increase over the SQ was

12.4% with one milk type per run compared to 8.1% for two milk types per run, which

equates to a difference of $0.56/kl or $0.006cents/l.

3.7.2. Milk collected every second day

Every second day milk collection (peak lactation, North Island) was more economical than every day milk collection (Fig. 5). Discounted (7%) total costs for every second day

collection were 8.40 and 4.23% less overall than their daily milk collection counterparts

for 25 and 50% of farms changing, respectively. Only one of the years for 25% of farms

changing, and three of the years for 50% of farms changing, were more costly than their

daily collection equivalent. Furthermore, every second day collection for 25% of farms

changing was 4.41% less than the SQ daily milk collection, while the discounted cost of

every second day collection was almost the same as daily SQ collection (0.31% more).

Milk collection every second day during peak lactation could be used to counter the increased collection costs associated with two milk types. For milk processing purposes, it may also be more convenient to have all the milk of a particular type collected on the same

day.Everyseconddaycollectionduringpeaklactationmay,therefore,beparticularlyuseful