Ie460, Fall 2009 Homework 2

IE460, Fall 2009

October 7, 2009 HOMEWORK 2

This homework assignment is due October 16th , 2009 by 5:00 p.m. No late submissions will be accepted. Question 1 A retailer purchases three different items (A, B and C) from the same distributor. Annual demand values for these three products are 10000, 8000 and 5000 units, respectively. The wholesale prices per unit of each product are 400 TL, 500 TL and 100 TL. The retailer pays 3000 TL as a fixed replenishment cost. There is also a product-specific cost of replenishment, which is incurred whenever that type of product is included in an order. These costs are 500 TL for A, 700 TL for B and 2500 TL for C. The inventory holding cost percentage is 0.2, independent of the product type. • Assume that the retailer makes independent replenishment decisions for the three items. Compute the optimal order quantity, replenishment cycle length and average annual costs (including set-up and inventory holding) for each product type resulting from this policy. • How would the order quantity, replenishment cycle length for each product, and the total average annual costs over all product types change under complete aggregation? • Assume that the retailer decides to use a tailored aggregation policy. He/she makes replenishment decisions for items A and B jointly, but item C separately. Compute the replenishment cycle lengths and the total average annual costs resulting from this policy. • Compare your results in the second and third parts of this question.

Is a complete

aggregation or a tailored aggregation better? Can you generalize your results? Explain the reasons. Question 2 A retailer uses capacitated trucks in inbound transportation. Each truck has a capacity of carrying 100 units and a cost of $20. The retailer faces 10000 units of demand annually. The inventory holding cost per unit per year is $5. Assume that there is ample number of trucks available for use, however, the retailer has a warehouse space of storing at most 380 units. Apart from the truck costs, there is also a fixed replenishment cost amounting to $30. • Plot the average annual total costs of the retailer with respect to his/her replenishment order quantity. • Compute analytically the replenishment quantity of the retailer that minimizes his/her average annual costs. Show all your work.