Problem: Supply Chain Coordination

A supplier manufactures a product at cost m = $50 and sells it to a retailer at wholesale price c = $150. The retailer sells this product to consumers at retail price p = $250. The replenishment lead time for this product is long relative to the selling season, so the retailer only has one opportunity to stock the product. Demand for the product is normally distributed with a mean of 1200 units and a standard deviation of 500 units. Units unsold at the end of the season are salvaged at price v = $20.

a. How many units of the product should the retailer order to maximize its expected profit? What is the associated retailer's expected profit and the supplier's expected profit?

b. How many units of the product should the retailer order to maximize total supply chain expected profit? What is the associated retailer's expected profit and the supplier's expected profit?

c. To motivate the retailer to buy more product, the supplier offers the following deal: the wholesale price is reduced to c = $70, but the retailer must pay the supplier an additional $100 for every unit that it sells. The supplier is also willing to buy back units that the retailer is unable to sell at buyback price b. These units are then salvaged by the supplier. What value of b should the supplier offer to maximize total supply chain expected profit? What is the associated retailer's expected profit and the supplier's expected profit?