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Assignment #3 Winter 2010

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Management Sciences
MSCI 432
Binyamin Mantin

MSCI 432/633: Production and Service Operations Management, Winter 2010 MSCI 432.001/633: Assignment # 3; MSCI 432.002: Assignment # 2 Due by Thursday, March 11, 2010 in class, individual submissions Note there are 6 questions in this assignment. Everyone had to do questions 1-3. The fourth question is a bonus (!) question. The last two questions are required by MSCI432.001/633 students only (MSCI432.002 can work on them as practice questions, but they won’t be graded). That is, MSCI432.001/633 students have to solve 5+1 questions, while MSCI432.002 students have to solve 3+1 questions. Q1. Discounting schemes. Olympix assembles and sells 104 units of its Vancouvex product every year. Each unit of Vancouvex requires 4 units of item A, 1 unit of item B, and 40 units of item C. These three components are purchased from three different suppliers. Each of the suppliers offer a 2% all unit discount on any replenishment of 100 units or higher of a single item. Ordering cost is $1.50 and % carrying cost is 0.24. Item Supplier Unit cost A A 14.20 B B 3.10 C C 2.40 a. Find the optimal ordering quantities for each of the items and the corresponding annual total cost. [3 marks X3] b. What is the primary difference between the ordering decisions made in a? Illustrate your answer graphically. [2 marks] Q2. Limit on shelf life. Some products have a limited shelf life. Assume a product, once delivered, has a shelf life of SL time units. Modify the EOQ decision to account for SL. [1 mark] Q3. Uncertain demand. A mail-order firm has four regional warehouses. Demand at each warehouse is normally distributed with a mean of 10,000 per week and a standard deviation of 2,000. Holding cost is 25%, and each unit of product costs the company $10. Each order incurs an ordering cost of $1,000 (primarily from fixed transportation costs), and lead time is 1 week. The company wants the probability of stocking out in a flow to be no more than 5 %. Assume 50 working weeks in a year. (note, the stockout definition we are using corresponds to the Type 1 service mentioned in Nahmias) a. Assuming that each warehouse operates independently, what should be the ordering policy at each warehouse? How much safety stock does each warehouse hold? How much average inventory is held (at all four warehouses combined), and at what annual cost? On average, how long does a unit of product spend in the warehouse before being sold? [5 marks] b. Assume that the firm has centralized all inventories in a single warehouse and that the probability of stocking out in a cycle can still be no more than 5%. Ideally, how much average inventory can the company now expect to hold, and at what cost? In this case, how long will a unit spend in the warehouse before being sold? [5 marks] Q4 is a bonus question! Q4. Order quantity under inflation. Suppose that the continuous discount rate is denoted by r; that is, a -it cost of c at time t has a present value of ce . Note that e is the constant 2.71829… We denote the continuous inflation rate by f. Thus, if K and c are the
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