ESI6323 Models for Supply Chain Management 2021 Summer Homework 5 – Cycle Inventory Management in a Supply Chain Homework Questions Question 1 Gator Automobiles (GA) has its engine assembly plant in Atlanta and its automobile assembly plant in Houston. Engines are transported between the two plants using trucks, with each trip costing $1,000. The automobile plant assembles and sells 150,000 automobiles per year. Each engine costs $500; GA incurs an annual inventory carrying rate of 20 percent per year. a. How many engines should GA load on each truck? (5 pts.) b. What is the annual inventory holding cost? (5 pts.) c. What is the average annual cost associated with this policy? (5 pts.) Question 2 A steel rolling mill can produce I-beams at the rate of 30 tons per week. Customer demand for the beams is 6 tons per week. To produce I-beams, the mill must go through a setup that requires changing to the appropriate rolling patterns. Each setup costs the mill $15,000 in labor and lost production. I-beams cost the mill $3,000 per ton and the mill has a holding cost of 20 percent. Assume the mill operates 52 weeks per year. a. b. c. d. What is the optimal production batch size for I-beams? (5 pts.) What is the annual setup cost of the optimal policy? (5 pts.) What is the annual inventory holding cost? (5 pts.) The mill would like to produce I-beams in batches of 50 tons. For what setup cost would this batch size be optimal? (5 pts.) 1 ESI6323 Models for Supply Chain Management 2021 Summer Question 3 Gator Mobile (GM) sells four models of cell phones, Gator21 Mini, Gator21, Gator21 Pro, and Gator21 ProMax. Demands and costs for independent ordering are shown in the table below. Gator21 Gator21 Gator21 Pro Gator21 Mini ProMax Annual demand rate 40,000 50,000 30,000 10,000 Order cost $3,000 $3,000 $3,000 $3,000 Product-specific order cost $1,000 $1,300 $1,600 $2,000 Unit cost $400 $400 $400 $400 Annual inventory carrying rate 0.3 0.3 0.3 0.3 A fixed order cost of $3,000 is incurred each time an order is placed. For each model ordered and delivered with the same order, an additional fixed cost is incurred for receiving and storage. Evaluate the lot sizes that GM should order and the annual cost of such a policy. The store manager may consider the following approaches to the multiple products ordering decision: • Each model is to be ordered individually, the order cost as well as the product-specific order cost are incurred for each model. • All models are to be ordered jointly in each order and the order cost is incurred for the batch of products. What policy should the manager take to minimize the average annual cost? (30 pts.) Question 4 Demand for Bluetooth headphones at Gator Electronic (GE) is 5,000 per month. Holding cost is 25 percent and the company incurs a fixed cost of $500 for each order placed. a. The supplier offers an all unit quantity discount with a price of $200 per headphone for all orders under 1,000, a price of $195 for all orders of 1,000 or more but under 2,000 and a price of $190 for all orders of 2,000 or more. How many headphones should GE order per replenishment? (15 pts.) b. The supplier offers a marginal unit quantity discount with a price of $200 per headphone for all orders under 1,000, a price of $195 for all orders of 1,000 or more but under 2,000 and a price of $190 for all orders of 2,000 or more. How many headphones should GE order per replenishment? (20 pts.) 2
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