Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. Its trucking company charges Prefab $400 per shipment, independent of the quantity purchased. The manufacturer offers an all unit quantity discount with a price of $1 per square foot for orders under 20,000 square feet, $0.98 per square foot for orders between 20,000 square feet and 39,999 square feet, and $0.96 per square foot for orders greater than or equal to 40,000 square feet. Prefab incurs a holding cost of 20 percent. What is the optimal lot size for Prefab? What is the annual cost of such a policy? What is the cycle inventory of plywood at Prefab? How does it compare with the cycle inventory if the manufacturer does not offer a quantity discount but sells all plywood at $0.96 per square foot?

Input Annual demand for Ford spare parts, D1 Annual demand for GM parts, D2 Cost per Ford part, C1 Cost per GM part, C2 Holding cost, h (enter as %) Fixed cost per shipment, S Ford and GM Ship Separately Optimal order size for Ford Optimal order frequency for Ford Cycle inventory of Ford Annual holding cost for Ford Annualshipping cost for Ford Optimal order size for GM Optimal order frequency for GM Cycle inventory for GM Annual holding cost for GM Annual shipping cost for GM Two Products Are Shipped Jointly Fixed cost per truck for joint shipment, S Optimal order frequency , n* Order size for Ford Cycle inventory for Ford Annual holding cost for Ford Order size for GM Cycle inventory for GM Annual holding cost for GM Annual combined shipping cost Total annual cost Annual savings through aggregation Should Ford and GM accept the 3rd party's proposal? How should they divide the fixed cost per truck among themselves? Answer:

All Unit Discount Fixed cost per order = per order Monthly demand = sq. feet Holding percentage = % Pricing: Min Qty Max Qty Price per sq. ft. 0 19,999 20,000 40,000 40,000 Range i Q Adjust to q Total Cost 0 1 2 Highlight optimal quantity in above table with different color Without Quantity Discount Price per sq ft Q Total Cost

Input Data - Part a) Retailer Annual Demand Order cost per lot Unit cost Holding cost Crunchy Order cost per lot Unit cost Holding cost (enter as %) Retailer Orders Independently Economic Quantity Ordered by Retailer Retailer ordering cost Retailer holding cost Retailer total cost Crunchy delivery cost Crunchy holding cost Crunchy total cost Total cost across both parties Orders Optimize Joint Costs - Part b) Quantity that minimizes total cost Retailer ordering cost Retailer holding cost Retailer total cost Crunchy delivery cost Crunchy holding cost Crunchy total cost Total cost across both parties

We start with the optimal scenario where the retailer tries to maximize his profits and Orange theirs. Each prices to maximize their profits. Retailer Retail price p Demand Profit Orange Company Wholesale price Cost Profit We now consider the case where Orange offers a $40 discount relative to their price in Cell B8 and see how the retailer adjusts retail price to maximize profits. Retailer Retail price p Demand Profit Discount passed along by retailer Orange Company Discount Wholesale price after discount Cost Profit