The inventory manager of an Arelik store on Badat Caddesi wants to determine an optimal policy...
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The inventory manager of an Arçelik store on Bağdat Caddesi wants to determine an optimal policy that minimizes the average cost per week for refrigrators sold in the store. He observes the number of refrigrators available in the store at the end of each week and decides on the number of new refrigrators to order. Each order is received immediately so that it is available on the first day of the next week. The total demand D for the refrigrators during a week is a random variable with distribution P{D = 0} = 0.40, P{D = 1} = 0.50, and P{D = 2} = 0.10. Since the store can take at most 2 refrigrators, the manager can not order a quantity that will exceed the store capacity. There is a holding cost of 20 TL for each refrigrator that is observed to be in the store at the beginning of each week before an order is placed. Moreover, backordering is not allowed and 50 TL lost sale cost applies for each demand that can not be satisfied during the week. For example, if there is no refrigrator in the store and no order is placed, then lost sale is 100 TL with probability 0.1 (if demand equals 2) or 50 TL with probability 0.5 (if demand equals 1). In addition, there is a fixed ordering cost of 10 TL that is incurred whenever any order is placed. Analyze this inventory management problem using a Markov decision model by answering the following questions: a) Determine Pi(k) and Cik, b) Make a linear programming formulation to find the optimal policy (do not Perform only 1 iteration of the policy improvement algorithm assuming that the initial policy is not to order at all in any state. The inventory manager of an Arçelik store on Bağdat Caddesi wants to determine an optimal policy that minimizes the average cost per week for refrigrators sold in the store. He observes the number of refrigrators available in the store at the end of each week and decides on the number of new refrigrators to order. Each order is received immediately so that it is available on the first day of the next week. The total demand D for the refrigrators during a week is a random variable with distribution P{D = 0} = 0.40, P{D = 1} = 0.50, and P{D = 2} = 0.10. Since the store can take at most 2 refrigrators, the manager can not order a quantity that will exceed the store capacity. There is a holding cost of 20 TL for each refrigrator that is observed to be in the store at the beginning of each week before an order is placed. Moreover, backordering is not allowed and 50 TL lost sale cost applies for each demand that can not be satisfied during the week. For example, if there is no refrigrator in the store and no order is placed, then lost sale is 100 TL with probability 0.1 (if demand equals 2) or 50 TL with probability 0.5 (if demand equals 1). In addition, there is a fixed ordering cost of 10 TL that is incurred whenever any order is placed. Analyze this inventory management problem using a Markov decision model by answering the following questions: a) Determine Pi(k) and Cik, b) Make a linear programming formulation to find the optimal policy (do not Perform only 1 iteration of the policy improvement algorithm assuming that the initial policy is not to order at all in any state.
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ANSWER If the firm wants to establish optimal inventory policy it must adopt EOQ model of Inventory ... View the full answer
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
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