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Unformatted text preview: Chapter 12: Determining Optimal Level of Product Availability Exercise Solutions 1. = + = + = 120 50 50 * C C C CSL o u u 0.2941 Optimal lotsize = ) , , ( * * σ μ CSL O NORMINV = = NORMINV(0.2941,100,40) = 78.34 Given that p = $200, s = $30, c = $150: Expected profits = ( p – s ) μ NORMDIST(( O – μ )/ σ , 0, 1, 1) – ( p – s ) σ NORMDIST((O – μ )/ σ , 0, 1, 0) – O (c – s) NORMDIST(O, μ , σ , 1) + O (p – c) [1 – NORMDIST(O, μ , σ , 1)] = $2,657 Expected overstock = ( O – μ ) NORMDIST ( (O – μ )/ σ , 0, 1, 1) + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 7.41 Expected understock = ( μ – O )[1 – NORMDIST ( (O – μ )/ σ , 0, 1, 1)] + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 29.07 EXCEL worksheet 121 illustrates these computations 2. With revised forecasting: = + = + = 120 50 50 * C C C CSL o u u 0.2941 Optimal lotsize = ) , , ( * * σ μ CSL O NORMINV = = NORMINV(0.2941,100,15) = 91.88 Given that p = $200, s = $30, c = $150: Expected profits = ( p – s ) μ NORMDIST(( O – μ )/ σ , 0, 1, 1) – ( p – s ) σ NORMDIST((O – μ )/ σ , 0, 1, 0) – O (c – s) NORMDIST(O, μ , σ , 1) + O (p – c) [1 – NORMDIST(O, μ , σ , 1)] = $4,121 1 Expected overstock = ( O – μ ) NORMDIST ( (O – μ )/ σ , 0, 1, 1) + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 2.78 Expected understock = ( μ – O )[1 – NORMDIST ( (O – μ )/ σ , 0, 1, 1)] + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 10.9 EXCEL worksheet 122 illustrates these computations 3. Mean demand during lead time =DL= (2000)(2) = 4000 Standard deviation of demand during lead time = σ L = L D σ = 500 2 = 707 Safety inventory = ROP – DL = 6000 – 4000 = 2000 CSL = NORMDIST (6000, 4000, 707, 1) = 0.9977 Cost of overstocking = (0.25)(40) = $10 Justifying cost of understocking: u C = 411 $ 52 2000 ) 9977 . 1 ( 10000 10 ) 1 ( = × × × = D year CSL HQ Optimal CSL = 8889 . 10 80 80 = + = + C C C o u u Optimal safety stock = (NORMSINV (0.8889)) (707) = 863 units EXCEL worksheet 123 illustrates these computations 4. Using the current policy: = + = + = 10 30 30 * C C C CSL o u u 0.75 Optimal lotsize = ) , , ( * * σ μ CSL O NORMINV = = NORMINV(0.75,20000,10000) = 26,745 Given that p = $60, s = $20, c = $30: Expected profits = ( p – s ) μ NORMDIST(( O – μ )/ σ , 0, 1, 1) 2 – ( p – s ) σ NORMDIST((O – μ )/ σ , 0, 1, 0) – O (c – s) NORMDIST(O, μ , σ , 1) + O (p – c) [1 – NORMDIST(O, μ , σ , 1)] = $472,889 Expected overstock = ( O – μ ) NORMDIST ( (O – μ )/ σ , 0, 1, 1) + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 8,236 Using South America option: = + = + = 5 30 30 * C C C CSL o u u 0.857 Optimal lotsize = ) , , ( * * σ μ CSL O NORMINV = = NORMINV(0.857,20000,10000) = 30,676 Given that p = $60, s = $25, c = $30: Expected profits = ( p – s ) μ NORMDIST(( O – μ )/ σ , 0, 1, 1) – ( p – s ) σ NORMDIST((O – μ )/ σ , 0, 1, 0) – O (c – s) NORMDIST(O, μ , σ , 1) + O (p – c) [1 – NORMDIST(O,...
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This note was uploaded on 09/17/2009 for the course INDUSTRIAL 0906547 taught by Professor Khaldontahboub during the Three '09 term at ADFA.
 Three '09
 khaldontahboub
 Supply Chain Management, Logistics

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