14_USTB OM Homework Assignments北京科技大学运营管理作业答案

USTB

Operations Management

Homework Assignments

By

Dr. Zhu，xiaoning

Student Name: 黄诗蕴

Take-Home Problem Solving and Essay Questions

Problem #1-Decision Science (Module 10 Decision Analysis used)

ABC is planning to publish 2CD titles: Discos in 70’s and Romantic 60’s. It is expected that payoff from 70’s will be $100K if demand is low and $600K if demand is high. It is also expected that payoff from 60’s will be $200K if demand is low and $400K if demand is high.

a)Which title should ABC goes first based on Maximin（中间）, Maximax（第一个）, Minimax

Regret and Laplace（最后）?

b)Give your final recommendation.

(a)

Maximin 如下图

分析：保守型方案，认为两种CD 需求都low ，但是推荐价格高的商品（60s 的CD ）

Maximax 如下图

分析：乐观方案，认为两种商品需求都高。并且推荐价格更高的商品（60s 的CD ）。

Minimax regret and laplace 如下图

分析：悲观的方案，认为两种CD 需求都小，使用Minimax ，得出解决方案为70s 定价为$100K,60s 定价为$200K 。并且推荐价格低的商品（70s ）

（b ）综合分析

Maxmin 策划的分析：保守型方案，认为两种CD 需求都low ，因此得出解决方案为70s 定价为$100K,60s 定价为$200K 。但是推荐价格高的商品（60s 的CD ）。 Maximax 分析：乐观方案，认为两种商品需求都高。因此得出解决方案为70s 定价为$600K,60s 定价为$400K,

并且推荐价格更高的商品（70s 的CD ）。

Minmax 策划的分析：悲观的方案，认为两种CD 需求都小。得出解决方案为70s 定价为$100K,60s 定价为$200K 。并且推荐价格低的商品（70s ）

Problem #2-Waiting Line Model (Module 9 Waiting Lines used)

Assuming 25 customers are arriving as the Poisson probability distribution within one hour and the service rate is two minutes per customer as exponential probability distribution in a one-line facility.

Assuming the waiting cost per time period for each unit is $20 and the service cost per time period for each channel $18.

a)For economic cost analysis, how many channels should company set?

b)Give your reasons.

（a）

实验得，当channel 为3，总费用为$71.11

实验得，当channel 为4，总费用为$88.72

实验得，当channel 为2，总费用为$56.17

实验得，当channel 为1，总费用为$118

综上所述，在channel 为2时，费用最低，为$56.17，之后随着channel 数量增大，费用变高。

Problem #3-Transportation Problem (Module 2 Transportation used)

Arizona Plumbing which makes, among other products, a full line of bathtubs. To be successful, the firm must decide which of its factories should supply which of its warehouses. Relevant data for Arizona Plumbing are presented in the following table shows, for example, that it costs Arizona Plumbing 5$ to ship one bathtub from its Des Moines factory to its Albuquerque warehouse, $4 to Boston, and 3$ to Cleveland. Likewise, we see in the figure that the 300 units required by Arizona Plumbing ’s Albuquerque warehouse might be shipped in various combinations from its Des Moines, Evansville, and Fort Lauderdale factories.

a) Prepare a simple table for shipping routes from origins to destinations. b) Find the minimal total shipping cost.

（a ）

(b)

最小费用为$3900

Problem #4-Invenroty Management (Module 8 Inventory used)

Green Tea AAA Inc. has a near constant demands on propane of 3000 liters per month with unit price of $1.00; the firm ’s cost of capital is 10% and other annual holding cost is 5%; the ordering cost is $10 flat each time. The firm is operating 360 days year and it takes 4 working days for propane delivery.

a)How much to order each time?

b)When to order (while inventory is fallen to what level…)?

（a）

Order point is 400, number of order is2190.89, price of order is $2190.89.

存货达到400开始订货，一年花费$328.32

Problem #5-Invenroty Management with Quantity Discount (Module 8 Inventory used) Johnson Clothing Inc. has the related inventory data shown below: Its annual demand is 2000 units with the annual inventory holding cost of 20% and the ordering cost of $20 per order. The firm is operating 250 days per year and it takes 5 working days for propane delivery.

Order size Discount Unit cost

0 - 99 0% $ 10.00

100 - 299 1% $ 9.90

300 - 999 2% $ 9.80

1000 and over 3% $9.70

a)What is the best-ordered unit?

b)When to order (while inventory is fallen to what level…)?

a) the best-ordered unit is 300.00

b) 存货低于record point （40.00）时候开始订货。