Ie460, Fall 2009

IE460, Fall 2009

November 3, 2009

HOMEWORK 3 This homework assignment is due November 13th , 2009 by 5:00 p.m. No late submissions will be accepted. Question 1 Consider a warehouse-retailer system in which the warehouse orders in bulks and dispatches to the retailer in smaller quantities. The retailer operates in an EOQ setting and orders Qr units in each cycle. The warehouse’s replenishment quantity Qw is given by nQr where n is a positive integer. The retailer incurs a fixed cost of $Kr = 300 at each replenishment and an inventory holding cost of hr = $0.5 per unit per year. The warehouse’s ordering cost per replenishment and inventory holding cost per unit per year are given by Kw = $500 and hw = $0.2, respectively. The retailer faces a demand rate of D = 5000 units per year. • Assume that the retailer makes his/her replenishment decision independently. Compute the optimal order quantities of the retailer and the warehouse. What are the resulting average annual costs for the retailer and the warehouse? • Now, consider a scenario where the parties decide their replenishment quantities jointly. How do the average annual costs for the retailer, the warehouse and the supply chain compare with respect to those in the first part of the question?

Question 2 Assume that the warehouse in Question 1, uses a truck load carrier for inbound replenishment. The truck load carrier has ample number of trucks and charges $40 for each truck whether it is fully or partially loaded. Each truck has a capacity of carrying 50 units. • Write an expression for the warehouse’s average annual costs as a function of Qr and n. • Write an expression for the retailer’s average annual costs as a function of Qr . • Assume that the parties make their replenishment decisions independently. Compute the optimal order quantities of the retailer and the warehouse.