Consider a supply chain composed of a manufacturer that produces a product and a retailer that sells this product to consumers. The manufacturer operates on a make-to-order basis, while the retailer operates on a procure-to-stack basis. First, the retailer determines their order quantity from the manufacturer. Next, the manufacturer produces the retailer's order quantity and delivers it to the retailer. Finally, consumer demand is realized according to the following distribution:

Probability   Demand
0.15          900
0.12          1000
0.13          1100
0.14          1200
0.14          1300
0.16          1400
0.16          1500

The manufacturer's unit cost of production is 80, and the salvage value for the product is 560 per unit.

(a) Find the retailer's optimal order quantity. Then, calculate each firm's expected profits if the retailer orders this quantity.

(b) Find the system-optimal (i.e., supply-chain optimal) production quantity and calculate the resulting expected system-wide (i.e., supply chain) profit if the retailer orders this quantity.

(c) Assume now that the manufacturer will pay the retailer 560. Find the retailer's optimal order quantity and calculate each firm's expected profit if the retailer uses this order quantity.

(d) Compare the total supply chain profits underparts (a) and (c). How do you explain the difference?