OPRE 6302. OM : Economic Order Quantity
Statement of Exercises
1. [Deducing Demand] Cindy and Mindy were in the same student group while studying for their MBA at UTD. They graduated together but started working as inventory managers in diﬀerent but competing retailers selling air conditioners in Dallas. While in school, they learned only the economic order quantity model for ﬁnding the optimal order sizes. Now they are both purchasing air conditioners from Trane to sell at their stores. Cindy knows that the order setup cost with Trane is $200 and the annual inventory holding cost is $400. Cindy expects that Mindy has the same cost ﬁgures. Cindy has accidentally learned that Mindy is ordering 10 air conditions every time she orders. Show how Cindy can use this information to deduce the demand Mindy faces. Explain why would competitors way want to know each other’s demand. 2. [Spring Water] The demand for spring water at the Plano WalMart is 600 litres per week. The setup cost for placing an order to replenish inventory is $25. The order is delivered by the supplier which charges WalMart $0.10/liter for the cost of transportation from the Ozark mountains to Plano. This transportation cost increases the cost of water to $1.25/liter. The water loses its freshness while stored at the Plano WalMart. To account for this, the WalMart charges an annual holding cost of $2.6/liter. Determine how often the WalMart should order for water and what size each order should be. 3. [Shoe Assembly] A shoe assembly plant buys leather tops and soles from its suppliers. The leather tops have no color on them when bought. The assembly plant ﬁrst dies the leather with colors like black, beige, brown and cream. Then it sews the colored leather tops to the soles. Finally leather tops are polished with an agent that depends on the color of the shoe. Basically there are three operations in the shoe plant: Coloring, Sewing and Polishing. The activity times and set up times for these operations are given in minutes as follows: Operation Activity time Set up time Coloring 0.25 30 Sewing 0.20 20 Polishing 0.15 45
Soles and the leather top-sole assemblies are processed in batches in all operations. The batch sizes are kept the same at all operations. Before a batch goes through an operation, the shoe plant must set up the machines for that operation. a) How many leather tops can be colored in an hour with a batch size of 40? b) Explain why sewing cannot be the bottleneck operation under any batch size. c) For which batch sizes is coloring the bottleneck operation? Here your answer can be an interval of batch sizes rather than a single number because there are many batch sizes which make coloring the bottleneck. 4. [EPROM] A local company produces a programmable EPROM (erasable programmable read-only memory) for several industrial clients. They have experienced a relatively ﬂat demand of 2500 units per year for the product. The EPROM is produced at a rate of 10000 units per year. The accounting department has estimated that it costs $50 to initiate a production run, each unit costs the company 1
$2 to manufacture, and the cost of holding is base on a 30% annual interest rate. Determine the optimal size of a production run, the length of each production run, and the average annual cost of holding and setup. What is the maximum level of on-hand inventory of the EPROMs? 5. Textbook 5.4.
A NSWER for Exercise 1: Since Cindy knows that Mindy learned only the EOQ model during her MBA, Cindy safely assumes that Mindy uses the EOQ formula which yields R= Q2 h 102 ∗ 400 = = 100/year. 2K 2 ∗ 200
Competitors can use each other’s demand information while formulating sales strategies such as price discounts, sales campaigns. It also helps a retailer, while negotiating with a supplier, to know whether that retailer is selling signiﬁcantly more than the others. The retailers which sell signiﬁcantly more are...
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