QM 670: Operations Management and Optimization: Case Studies and Linear Programming Applications Exam II
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QM 670 Exam II 1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable: Order Quantity Price/pair 0 - 99 $36 100 - 199 32 200 - 299 30 300+ 28 For a price of $36, the optimal order quantity is ___________. (4) Solution EOQ = sqrt (2*(500*4)*30/(0.2*36)) = 129.09 = 130 units As, for $36, only 0 - 99 can be ordered. So, EOQ is infeasible at this cost structure 2. Redo #1 if they allow backordered items with a shortage cost of $4/quarter. Optimal order quantity = ___________. (4) Solution If backordered items with shortage cost of $4/quarter was there, the decision will not change regarding optimal quantity.Page 2
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3. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable: Order Quantity Price/pair 0 - 99 $36 100 - 199 32 200 - 299 30 300+ 28 The optimal order quantity is ______________. (5) Solution For $36 EOQ = sqrt (2*(500*4)*30/(0.2*36)) = 129.09 = 130 units As, for $36, only 0 - 99 can be ordered, so this is not optimal For $32 EOQ = sqrt (2*(500*4)*30/(0.2*32 )) = 136.93 = 13 7 units For $30 EOQ = sqrt (2*(500*4)*30/(0.2*3 0 )) = 141.42 = 1 42 units As, for $3 0 , only 20 0 - 2 99 can be ordered, so this is not optimal For $28 EOQ = sqrt (2*(500*4)*30/(0.2*28 )) = 146.38 = 1 47 units As, for $30, only >300 can be ordered, so this is not optimalQM 670 Exam II 1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable: Order Quantity Price/pair 0 - 99 $36 100 - 199 32 200 - 299 30 300+ 28 For a price of $36, the optimal order quantity is ___________. (4) Solution EOQ = sqrt (2*(500*4)*30/(0.2*36)) = 129.09 = 130 units As, for $36, only 0 - 99 can be ordered. So, EOQ is infeasible at this cost structure 2. Redo #1 if they allow backordered items with a shortage cost of $4/quarter. Optimal order quantity = ___________. (4) Solution If backordered items with shortage cost of $4/quarter was there, the decision will not change regarding optimal quantity. 3. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of $30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable: Order Quantity Price/pair 0 - 99 $36 100 - 199 32 200 - 299 30 300+ 28 The optimal order quantity is ______________. (5) Solution For $36 EOQ = sqrt (2*(500*4)*30/(0.2*36)) = 129.09 = 130 units As, for $36, only 0 - 99 can be ordered, so this is not optimal For $32 EOQ = sqrt (2*(500*4)*30/(0.2*32 )) = 136.93 = 13 7 units For $30 EOQ = sqrt (2*(500*4)*30/(0.2*3 0 )) = 141.42 = 1 42 units As, for $3 0 , only 20 0 - 2 99 can be ordered, so this is not optimal For $28 EOQ = sqrt (2*(500*4)*30/(0.2*28 )) = 146.38 = 1 47 units As, for $30, only >300 can be ordered, so this is not optimal