Question

Suppose that a two-level supply chain consisting of a consumer electronics manufacturer and a retailer are in the business of selling noise cancelling headphones. These headphones are in high demand now, especially, since a lot of people plan to fly to their vacation destinations during the summer. As you may agree, noise cancelling headphones are a blessing on long-haul flights.

For the manufacturer, noise cancelling headphones is a high margin product. However, given the randomness in demand it is not obvious how much the retailer should order. Assume that the retailer orders once before the summer begins. Once an order is placed, the retailer does not have a second opportunity to update its order size.

Suppose that the retail price of the headphones is $350 and it costs the manufacturer $250 to produce each unit. The retailer’s belief about demand can be approximated by a normal distribution with mean 10,000 and standard deviation 2100. The wholesale price agreement between the manufacturer and the retailer is $275 per unit. Any headphones not sold at the end of the season are salvaged at $240 per unit.

What is the retailer’s order size that maximizes his expected profit? What is the first-best order quantity for the supply chain?                                    [10 points]

Suppose that the sequence of events in the above are altered. The manufacturer suggests that instead of the retailer placing an order for the summer, it may be better off if the manufacturer were to produce first. The manufacturer would then place the entire inventory of headphones produced on the retailer’s shelf. The retailer still makes the profit margin of on each unit of headphone sold. The leftover inventory at the end of summer is the manufacturer’s responsibility (i.e., salvaged at the above mentioned price). In exchange, the manufacturer asks the retailer for its private demand information. How should the retailer respond to the manufacturer’s proposal? Are there any concerns for the manufacturer in implementing this new strategy?                                                             [10 points]

You are hired as an inventory manager by the manufacturer. After going through the history of demand realizations and inventory decisions, you think the above situation can be improved for both players in the supply chain. Specifically you suggest the supply chain implement a revenue sharing contract. Recall that the revenue sharing contract specifies the wholesale price and the share of the retailer revenues that will be passed on to the manufacturer. To make the deal fair for the retailer, you suggest that the retailer keep 50% of the total revenues. What should be the optimal Why might your employer (the manufacturer) object to your proposal?       [5 points]

Suppose that the manufacturer rejected your proposal of the revenue sharing contract. You are back at square one. However, this time around you want to try the returns contract. In this returns contract the manufacturer determines the wholesale price and the price at which the manufacturer will buy back any inventory leftover with the retailer at the end of the summer. Learning from your previous mistake you fix the wholesale price like in the original wholesale agreement. What should be the price that will coordinate the supply chain?                               [5 points]

Answer 1

For retailer

Underage cost, Cu = Retail price - wholesale price = 350 - 275 = $ 75

Overage cost, Co = wholesale price - salvage value = 275 - 240 = $ 35

Critical fractile = Cu/(Cu+Co) = 75/(75+35) = 0.682

z = NORMSINV(0.682) = 0.4728

Retailer's order size = mean demand + z * Std dev of demand = 10000 + 0.4728*2100 = 10993

For Supply chain

Underage cost, Cu = Retail price - manufacturing cost = 350 - 250 = $ 100

Overage cost, Co = manufacturing cost - salvage value = 250 - 240 = $ 10

Critical fractile = Cu/(Cu+Co) = 100/(100+10) = 0.9091

z = NORMSINV(0.9091) = 1.3352

Retailer's order size = mean demand + z * Std dev of demand = 10000 + 1.3352*2100 = 12804