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# lec4 - 25 The holding cost for each seatbelt is \$2.50 per...

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1 Thu, 6 Sep 2000 IE221: Lecture 4 1 IE221: Operations Research – Probabilistic Methods Module I: Inventory Models Lecture 4, Fall 2001 Lehigh University IMSE Department Thu, 6 Sep 2000 IE221: Lecture 4 2 Lecture 4 Outline EOQ with Uncertain Demand n Definitions (nomenclature) n Case 1: Back-Order n Example n Case 2: Lost Sales n (r,q) and (s,S) Policies

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2 Thu, 6 Sep 2000 IE221: Lecture 4 3 Nomenclature q r L 1 L 2 t I(t) B 2 Muggle Airlines cycle 1 cycle 2 X 2 X 1 Thu, 6 Sep 2000 IE221: Lecture 4 4 The Lead Demand, X n X = D1 + D2 + … + D L n E[X] = E[L].E[D] n Var[X] = E[L].Var[D] + E[D] 2 .Var[L]
3 Thu, 6 Sep 2000 IE221: Lecture 4 5 Recall: Marginal Analysis At the optimum, TC (r*+ ) – TC (r*) 0 r* r*+ r TC (q,r) Thu, 6 Sep 2000 IE221: Lecture 4 6 Case 1: Back-Order Summary of results: D c hq r X P h D K q B * *) ( 2 * =

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4 Thu, 6 Sep 2000 IE221: Lecture 4 7 Example Each year, Muggle Airlines needs to replace numerous seatbelts. The airline estimates that this number is normally distributed with mean 750 and standard deviation
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Unformatted text preview: 25. The holding cost for each seatbelt is \$2.50 per month. The cost of placing each order is \$50 and the lead time is 1 month. Backlogging is allowed and the stockout cost (loss of goodwill etc) is assumed to be \$75. What would you recommend as the reorder point? Thu, 6 Sep 2000 IE221: Lecture 4 8 Case 2: Lost Sales n Summary of results D c hq hq r X P h D K q LS + = ≥ ≈ * * *) ( 2 * 5 Thu, 6 Sep 2000 IE221: Lecture 4 9 Example continued … Suppose no passenger is willing to fly without a seatbelt, and that each stockout would result in a lost profit of \$150 in addition to goodwill. How would you revise the reorder point, r*? Thu, 6 Sep 2000 IE221: Lecture 4 10 (r,q) and (s,S) policies n (r,q) also known as 2-bin policy n (s,S) policy (each demand can be for more than 1 unit) r t I(t) q “undershoots”...
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lec4 - 25 The holding cost for each seatbelt is \$2.50 per...

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