Homework 2
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School
Oklahoma State University *
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Course
4623
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
2
Uploaded by ProfessorGiraffe4040
Homework 2
1. There are 6 independent regional markets, each with average weekly demand of 200 units and standard deviation of 40. Please compare the total safety stock level for each of the following four systems: decentralized, centralized, cross-docking, and a multi-echelon system with an additional layer of central distribution center between the factory and the regional warehouses (please refer to the slides of Multi-echelon Inventory System for the four systems). The review period is 1 week at each facility. The service level of each warehouse is 95%. The lead time from the manufacture to the regional warehouses is 11 weeks for the decentralized and the centralized systems. The lead time from the manufacturer to the cross-docking site or the
central distribution center is 8 weeks, and from them to the regional warehouses is 3 weeks. *Students in 5763 please also compare the total average inventory level.
2. The demand distribution for one of the snow jack designs is as follows: Demand (
D)
8,000
10,000
12,000
14,000
16,000
18,000
Probability
0.11
0.11
0.28
0.22
0.18
0.1
For the buy-back contract
discussed in the class, the parameters are as follows:
Retail Price
$125
received by the retailer
Salvage Price
$20
received by the manufacturer
Variable Production Cost
$35
paid by the manufacturer
Fixed Production Cost
$100,000
Paid by the manufacturer
For the revenue sharing contract
discussed in the class, the parameters are as follows:
Retail Price
$125
shared between the manufacturer and the retailer
Salvage Value
$20
shared between the manufacturer and the retailer
Variable Production Cost
$35
paid by the manufacturer
Fixed Production Cost
$100,000
paid by the manufacturer
1)
Use the scenario approach to find the optimal order quantity and expected profit for the retailer under a wholesale-price only contract. W= $80, P= $125, S=$20, fixed set-up cost F = $100,000. This problem is the same as the example discussed in the class. Please calculate the retailer’s and the manufacturer’s profits with the above parameters and compare with the answers in the slides, and see if the manufacture salvage the buy-back items or not for the answers in the slides. The purpose is to verify you set up the spread sheets correctly.
2)
Find the optimal order quantity for the retailer under the following two new buy-back contracts separately: (1) w=$71 and b=$50; (2) w=$89 and b=$75. Calculate the expected profits for the retailer, the manufacturer, and the whole supply chain under each contract.
3)
Find the optimal order quantity for the retailer under the following two new revenue sharing contracts separately: (1) w=24 and f
=0.4; (2) w=21 and f
=0.6. The revenue sharing rate, f
, is the
proportion paid to the manufacturer. Calculate the expected profits for the retailer, the manufacturer, and the whole supply chain under each contract.
4)
* Find the underage cost, the overage cost, and the optimal order quantity under each scenario in the above questions.
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