L18_QuickResponse_r - Lecture 18 Quick Response with...

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Slide 1 Lecture 18 Quick Response with Reactive Capacity
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Slide 2 Le a rning  O b je c tive s Understand how mismatch cost is related to demand distribution Understand how reactive capacity helps in reducing the mismatch cost Evaluate a quick response system Unlimited expensive reactive capacity Limited inexpensive reactive capacity
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Slide 3 When is Mismatch Cost High?
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Slide 4 Recall: Newsvendor Model Mismatch cost reduces the profit Expected profit   = maximum profit   mismatch cost  Maximum profit =  Cu  X   μ   Measures Absolute measure = mismatch cost  Relative measure = mismatch cost / maximum profit Mismatch cost must be related with demand uncertainty  (when demand is  certain, mismatch cost = 0, e.g., EOQ – next class).
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Slide 5 Newsboy Revisited A newsboy orders newspapers for 25 cents each early in the morning and sells them at  a unit price of 85 cents during the day. He is paid 5 cents for each unsold copy in the  evening. Cu= $0.85   $0.25 = $0.60 per copy Co= $0.25   $0.05 = $0.20 per copy % 75 20 . 0 60 . 0 60 . 0 ) ( = + = Q F Possible demand D Probability Pr(D) Cumulative probability F(D) 100 25% 25% 200 25% 50% 300 25% 75% 400 25% 100% Q = 300 Sales S(D) =Min(D,Q) S(D) X Pr(D) 100 25 200 50 300 75 300 75 μ = Exp demand = 250   = Std of demand =111.8 σ Mismatch cost  = Co  X  Exp leftover inv +Cu  X  Exp lost sales    = 0.20  X  75 + 0.60  X  25 = $30 Maximum profit =  Cu  X   μ   = 0.6   X  250 = $150 Expected profit = $150 - $30 = $120 Exp sales = 225 Exp lost sales = 25 Exp leftover inv = 75
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Slide 6 Different Demand Patterns   Shifts up Possible demand D Probability Pr(D) Cumulative probability F(D) 200 25% 25% 300 25% 50% 400 25% 75% 500 25% 100% Q = 400 Sales S(D) =Min(D,Q) S(D) X Pr(D) 200 50 300 75 400 100 400 100 Exp sales = 325 Exp lost sales = 25 Exp leftover inv = 75 Mismatch cost  = Co  X  Exp leftover inv +Cu  X  Exp lost sales = $30 Maximum profit =  Cu  X   μ   = 0.6   X  350 = $210 Expected profit = $210 - $30 = $180 When expected demand  increases  Expected sales increases with the same amount. Mismatch cost does NOT change because expected lost sales and expected leftover  inventory do not change. Maximum profit increases and hence the expected profit increases. μ = Exp demand = 350   = Std of demand =111.8 σ
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Slide 7 Different Demand Patterns   Increased Variability Possible demand D Probability Pr(D) Cumulative probability F(D) 0 25% 25% 200 25% 50% 300 25% 75% 500 25% 100% Q = 300 Sales S(D) =Min(D,Q) S(D) X Pr(D) 0 0 200 50 300 75 300 75 Exp sales = 200 Exp lost sales = 50 Exp leftover inv =100 Mismatch cost  = Co  X  Exp leftover inv +Cu  X  Exp lost sales   
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This note was uploaded on 10/16/2011 for the course OM 335 taught by Professor Jonnalagedda during the Fall '08 term at University of Texas at Austin.

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L18_QuickResponse_r - Lecture 18 Quick Response with...

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