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Chapter 12

# Chapter 12 - Chapter 12 Determining Optimal Level of...

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Chapter 12: Determining Optimal Level of Product Availability Exercise Solutions 1. = + = + = 120 50 50 * C C C CSL o u u 0.2941 Optimal lot-size = ) , , ( * * 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 12-1 illustrates these computations 2. With revised forecasting: = + = + = 120 50 50 * C C C CSL o u u 0.2941 Optimal lot-size = ) , , ( * * 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

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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 12-2 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 . 0 1 ( 10000 10 ) 1 ( = × × - × = - D year CSL HQ Optimal CSL = 8889 . 0 10 80 80 = + = + C C C o u u Optimal safety stock = (NORMSINV (0.8889)) (707) = 863 units EXCEL worksheet 12-3 illustrates these computations 4. Using the current policy: = + = + = 10 30 30 * C C C CSL o u u 0.75 Optimal lot-size = ) , , ( * * 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 lot-size = ) , , ( * * 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, μ , σ , 1)] = \$521,024 Expected overstock = ( O μ ) NORMDIST ( (O – μ )/ σ , 0, 1, 1) + σ NORMDIST ( (O – μ )/ σ , 0, 1, 0) = 11,407 So, it is evident that using South America option results in increased expected profits, but also increases the production capacity requirements needed at Champion. EXCEL worksheet 12-4 illustrates these computations 5. Current sourcing (one line): Reguplo: = + = + = 20 100 100 * C C C CSL o u u 0.8333 Optimal lot-size = ) , , ( * * σ μ CSL O NORMINV = = NORMINV(0.8333,10000,1000) = = 10,967 Given that p = \$200, s = \$80, c = \$100: 3

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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)] = \$970,018
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Chapter 12 - Chapter 12 Determining Optimal Level of...

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