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Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 67P

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Question

A firm is attempting to minimize its shipping costs. The firm has 3 factories and must supply the needs of its 3 customers without
shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the
capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer
Shipping Costs (5/unit)
Customer 1
Customer 2
Customer 3
13
15
Factory/Capacity
A/170 units
8/170 units
C/160 units
13
14
46.43
7
10
Requirement-250 units
Requirement-83 units
Requirement-167 units
Complete the table below to show the quantity shipped from each factory to each customer. (Leave no cells blank - be certain to
enter "0" wherever required.)
Answer is complete but not entirely correct.
Shipping Costs (S/unit)
Customer
Factory
Customer Customer
Answer is complete but not entirely correct.
Shipping Costs ($/unit)
Customer
Customer
Customer
Factory
1
2
3
A
170 X
83
0
B
170 X
170 X
C
160
0
0
What is the total cost of meeting customer requirements each day?
Total cost

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This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)

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