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Unformatted text preview: Chapter 11 Inventory Models Learning Objectives 1. Learn where inventory costs occur and why it is important for managers to make good inventory policy decisions. 2. Learn the economic order quantity (EOQ) model. 3. Know how to develop total cost models for specific inventory systems. 4. Be able to use the total cost model to make howmuchtoorder and whentoorder decisions. 5. Extend the basic approach of the EOQ model to inventory systems involving production lot size, planned shortages, and quantity discounts. 6. Be able to make inventory decisions for singleperiod inventory models. 7. Know how to make order quantity and reorder point decisions when demand must be described by a probability distribution. 8. Learn about lead time demand distributions and how they can be used to meet acceptable service levels. 9. Be able to develop order quantity decisions for periodic review inventory systems. 10. Understand the following terms: inventory holding costs backorder cost of capital quantity discounts ordering costs goodwill costs economic order quantity (EOQ) probabilistic demand constant demand rate lead time demand distribution reorder point service level lead time singleperiod inventory model lead time demand periodic review cycle time safety stock 11  1 Chapter 11 Solutions: 1. a. * 2 2(3600)(20) 438.18 0.25(3) o h DC Q C = = = b. 3600 (5) 72 250 r dm = = = c. * 250 250(438.18) 30.43 days 3600 Q T D = = = d. 1 1 3600 (438.18)(0.25)(3) (20) $328.63 2 2 438.18 h o D TC QC C Q = + = + = 2. Annual Holding Cost 1 1 (438.18)(0.25)(3) $164.32 2 2 h QC = = Annual Ordering Cost 3600 (20) 164.32 438.18 o D C Q = = Total Cost = $328.64. 3. * 2 2(5000)(32) 400 2 O h DC Q C = = = 5000 20 units per day 250 250 D d = = = a. r = dm = 20(5) = 100 Since r ≤ Q * , both inventory position and inventory on hand equal 100. b. r = dm = 20(15) = 300 Since r ≤ Q * , both inventory position and inventory on hand equal 300. c. r = dm = 20(25) = 500 Inventory position reorder point = 500. One order of Q * = 400 is outstanding. The onhand inventory reorder point is 500  400 = 100. d. r = dm = 20(45) = 900 Inventory position reorder point = 900. Two orders of Q * = 400 are outstanding. The onhand inventory reorder point is 900  2(400) = 100. 11  2 Inventory Models 4. a. * 2 2(12,000)(25) 1095.45 (0.20)(2.50) o h DC Q C = = = b. 1200 (5) 240 250 r dm = = = c. * 250 250(1095.45) 22.82 12,000 Q T D = = = d. Holding 1 1 (1095.45)(0.20)(2.50) $278.86 2 2 h QC = = Ordering 12,000 (25) 273.86 1095.45 o D C Q = = Total Cost = $547.72 5. For Q = 1000 TC = 1/2(1000)(0.20)(2.50) + (12,000/1000)(25) = 250 + 300 = $550 The cost increase of using Q = 1000 is only $550  $547.72 = $2.28. Thus the order quantity of 1000 is acceptable....
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 Spring '09
 shakroh
 Math, Q*

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