Homework 3 Solution

 

Question 1

All these contracts are appropriate to increase the likelihood that the retailer purchases a higher number of items from the supplier and hence ultimately sells more to the customer. Without the contract, the risk to the retailer is high if bought items remain unsold – with the contract this risk is shared with the suppliers. On the other hand, because of the uncertainty in the demand, the probability of selling more also increases.

 

Question 3

The studios benefited because they got a percentage of the revenue from renting additional DVDs. The cost structure for the studios is such that typically the cost for manufacturing an incremental unit is low – therefore, the studios benefited by actually increasing their margins on these additional DVDs which would have been non-existent if the contract was not in place.

 

Question 4

Generally speaking, there is a lag between development of algorithms in the operations management literature and their adoption in business.  There are several reasons for this:

 

  1. Practitioners are not familiar with the literature.

 

  1. It is hard to convince the industry that analytical models are useful.  There is resistance to change.

 

  1. Possible gaps between theory and practice.

 

  1. There are practical problems in implementation.  For instance, without the development of information technology, it would have been hard for the movie studios to track end-customer demand and the revenue received by Blockbuster.

 

Also, in this particular case, the increasingly lucrative movie rental business due to advances in home theater systems, and increased competition from media distribution over the Internet may have forced Blockbuster and the movie studios to re-consider and improve their business models.

 

 

Question 6

Changing the values in the Inventory.xls spreadsheet based on the input data for the question, the answers are as follows:

a.             For the buy-back contract, the order quantity is 16000 units. At this point, retailer profit is $420,500 and manufacturer profit is $241,500 for a total supply chain profit of $662,000.

b.            With a revenue sharing contract, the optimal order quantity is also 16000 units. In this case the retailer profit is only $118,500 while the manufacturer has a much larger profit at $543,500.

 

 

Question 9

a)         Critical fraction = (50-20)/(50-10) = 75%

System optimal production quantity = 2500

b)         i.          Critical fraction = (50-40)/(50-10) = 25%

Distributor order = 2200

Distributor’s expected profit = $21,440

Manufacturer’s expected profit = $22,000

ii.         Reservation price = $5

Execution price = $30

Distributor order = 2500

Distributor’s expected profit = $34,120

Manufacturer’s expected profit = $34,120

c)         i.          Critical fraction = (40-20)/(40-10) = 2/3

Manufacturer production = 2400

Manufacturer’s expected profit = $45,120

Distributor’s expected profit = $23,040

ii.         Cost sharing = $3.3875

Wholesale price = $36.45

Critical fraction = (36.45-(20-3.3875))/(36.45-10)=3/4

Manufacturer production level = 2500

Manufacturer’s expected profit = $45,123

Distributor’s expected profit = $23,117