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MSCI 432 (2)
Chapter 4

Solutions for Chapter 4 The professor gave us these solutions , very helpful - Winter 2010

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Management Sciences
MSCI 432
Binyamin Mantin

Nahmias Chapter 4. 4.2. Discuss the cost penalties incurred by a firm that holds too much inventory and one that holds too little inventory. 4.2 Too much: a) Money that is tied up in inventories could be invested elsewhere. b) Costs of supporting inventory could be high, including cost of storage (such as refrigeration costs), taxes, insurance, etc. c) Production/distribution inefficiencies could arise. d) Stock can become obsolete. Too little: a) Insufficient stock to meet customer demand. b) Production inefficiencies could arise. For example, in a sequential production process, a lack of sufficient buffer inventory could cause production to come to a halt. 4.8 a) Month Ending Inventory Jan. 160 Feb. -1305 March -1225 April -700 May -480 June 1020 b) The total number of excess demands = 1305 incurred in February only. Hence the cost = (1305)(10) = $13,050. If backorders are filled on a LIFO basis then the cost is the same whether excess demands are lost or backordered. However, if backorders are filled on a FIFO basis the cost in the backorder case will be larger. c) From part (a): cumulative backorders = 3710 which gives the cost = (3710)(10) = $37,100. d) The criterion used in part (b) would be appropriate in a competitive retail environment where the customer would normally go elsewhere if demand cannot be filled immediately. The criterion used in part (c) would be appropriate if the customer must wait for the item, or if the demand is for a part that causes a production process to be delayed. 4.10. A speciality coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The coffeehouse estimates that it cots $45 in paperwork and labour to place an order for the coffee, and holding costs are based on a 20 percent annual interest rate. a. Determine the optimal order quantity for Colombian coffee. b. What is the time between placements of orders? c. What is the average annual cost of holding and setup due to this item? d. If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory. 4.10 λ = 280 c = 2.40 K = 45 I = .20 2Kλ (2)(45)(280) a) Q* = = = 229 h (.2)(2.40) b) T = Q*/λ = 229/280 = .8179 yrs. (= 9.81 months) c) G* = 2Kλh = (2)(45)(280)(.2)(2.40= $109.98 d) 229 3 wks R 9.82 mos. r = λγ = (280)(3/52) = 16.15 r = 16 units 4.11. For the question described in Problem 10, draw a graph of the amount of inventory on order. Using your graph, determine the average amount of inventory on order. Also compute the demand during the replenishment lead time. How to these quantities differ? 4.11 (not drawn to scale) 3 wks 3 wks 229 42.53 wks 42.53 wks Avg = (229 x 3)/42.53 = 16.1538 Demand during lead time = λγ = (280/52)(3) = 16.1538 (exactly the same). 4.13.Consider the coffeehouse discussed in Problem 10. Suppose that its setup cost for ordering was really $15. Determine the error made in calculating the annual cost of holding and setup incurred as a result of its using the wrong value of K. (Note that this implies that its current order policy is suboptimal.) 4.13 True optimal Q = (2)(15)(280= 132
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