Consider a two-stage supply chain (A supplies B that supplies customer demand). Customer demand is uniformly distributed between 500 and 1000. The cost to make a unit at A is $100. They sell the item to B for $150 who sells to a customer for $200. The transportation cost between A to B is $2 per unit, and the material handling cost at B is

$1 per unit. Newsvendor assumptions hold. If there is any leftover stock anywhere, it has a salvage value of $30. Answer the following:

a. Determine the order quantities and expected profits (for each party) if A and B act independently.

b. Determine the optimal order quantities if the supply chain behaves in a centralized way.

c. See if you can determine a buy-back contract that “coordinates”

the supply chain.

d. See if you can determine a revenue sharing contract that “coordinates”

the supply chain.

e. Compare your solutions to parts

(c) and (d).