A manufacturing firm produces and sells a product to a single independent retailer. The product is sold during a single selling season. The manufacturer has production cost is $6.00 per unit and the retailer sells the product to the consumers at a price of $28.00 per unit. Unsold units at the end of the selling season have a salvage value of $2.00. If the retailer cannot meet the demand during the selling season then she has a goodwill penalty cost of $3.00 and the manufacturer has a goodwill penalty cost of $2.5. To procure the product the retailer has a cost of $1.00 per unit. The retailer places an order with the manufacturer at the start of the selling season and the delivery is instantaneous. The consumer demand X follows a Gamma distribution in the interval (0, ∞) with shape parameter α = 1 and scale parameter β = 100 .

E) The manufacturer now offers a revenue-sharing contract satisfying the equations at the bottom of page 246 in Cachon where
λ = -----
1. Identify the resulting wholesale price as well as the fraction of the revenue which the retailer should keep.
2. Find an optimal order quantity for the retailer using the wholesale price and the fraction of supply chain revenue which the retailer should keep found in question E.1.
3. Construct a diagram showing the individual members profit as well as the supply chain profit as a function of the retailer’s order size.
4. Is the revenue-sharing contract offered by the manufacturer a coordinating contract for the supply chain? Argue why or why not.
5. Given the wholesale price and the share of revenue that the retailer keeps in the revenue sharing contract which were found in E.2, then identify a corresponding buy-back contract. Discuss advantages and disadvantages the buy-back contract compared with the revenue-sharing contract.

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