Chapter 11

# Chapter 11 - Chapter 11 Managing Economies of Scale in the...

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Unformatted text preview: Chapter 11: Managing Economies of Scale in the Supply Chain: Safety Inventory Exercise Solutions 1. D L = LD = (2)(300) = 600 σ L = σ D L = ) 200 ( 2 = 283 ss = F S-1 ( CSL ) × σ L = F S-1 (0.95) × 283 = 465 (where, F S-1 (0.95) = NORMSINV (0.95)) ROP = DL + ss = 600 + 465 = 1065 Excel Worksheet 11-1 illustrates these computations 2. D L = (T+L) D = (2+3)(300) = 1500 σ L = σ D L T + = ) 200 ( 3 2 + = 447 ss = F S-1 ( CSL ) × σ L = F S-1 (0.95) × 447 = 736 (where, F S-1 (0.95) = NORMSINV (0.95)) OUL = D(T+L) + ss = 1500 + 736 = 2236 Excel Worksheet 11-2 illustrates these computations 3. D L = LD = (2)(300) = 600 σ L = σ D L = ) 200 ( 2 = 283 ESC = (1 – fr ) Q = (1 – 0.99)500 = 5 We use the following expression to determine the safety stock (ss): ) ( )] ( 1 [ σ σ σ L S L L S ss f ss F ss ESC +-- = ESC = – ss [1 – NORMDIST ( ss / σ L , 0, 1, 1)] + σ L NORMDIST ( ss / σ L , 0, 1, 0). We utilize the GOALSEEK function in EXCEL in determining safety stock (ss) by using ss as the changing value that results in an ESC value of 5. 1 Excel Worksheet 11-3 illustrates these computations. Goal Seek set-up: SET CELL: C29 TO VALUE: 5 BY CHANGING CELL: C27 This results in an ss value of 477 and the reorder point of: ROP = DL + ss = 600 + 477 = 1,077 4. D L = LD = (2)(250) = 500 σ L = σ D L = ) 150 ( 2 = 212 ss = ROP – ss = 600 – 500 = 100 CSL = F(D L + ss, D L , σ L ) = F (600, 500, 212) = NORMDIST (600, 500, 212, 1) = 0.68 ) ( )] ( 1 [ σ σ σ L S L L S ss f ss F ss ESC +-- = ESC = – ss [1 – NORMDIST ( ss / σ L , 0, 1, 1)] + σ L NORMDIST ( ss / σ L , 0, 1, 0) = 43.86 Fill rate (fr) = 1- (ESC/Q) = 1- (43.86/1000) = 0.96 Excel Worksheet 11-4 illustrates these computations 5. D L = LD = (2)(250) = 500 σ L = s D L L D 2 2 2 + σ = 5 . 1 250 150 2 2 2 2 × + × = 431 ss = F S-1 ( CSL ) × σ L = F S-1 (0.95) × 431 = 709 (where, F S-1 (0.95) = NORMSINV (0.95)) ) ( )] ( 1 [ σ σ σ L S L L S ss f ss F ss ESC +-- = ESC = – ss [1 – NORMDIST ( ss / σ L , 0, 1, 1)] + σ L NORMDIST ( ss / σ L , 0, 1, 0) = 9 Fill rate (fr) = 1- (ESC/Q) = 1- (9/1000) = 0.991 2 Standard deviation of lead time Required safety inventory 1.50 709 1.00 539 0.50 405 0.00 349 Excel Worksheet 11-5 illustrates these computations 6. Following are the evaluations for the Khaki pants: Disaggregated Option : D L = LD = (4)(800) = 3200 σ L = σ D L = ) 100 ( 4 = 200 Coefficient of variation = μ σ / = 100/800 = 0.13 ss per store = F S-1 ( CSL ) × σ L = F S-1 (0.95) × 200 = 329 (where, F S-1 (0.95) = NORMSINV (0.95)) Total safety inventory = (329)(900) = 296,074 Total value of safety inventory = (296,074)(30) = \$8,882,210 Total annual safety inventory holding cost = (8,882,210)(0.25) = \$2,220,552 Holding cost per unit sold = 2220552/(800)(900) = \$3.08 Aggregated Option : kD D C = = (900)(800) = 720000 σ σ k C D = = ) 100 ( 900 = 3000 D L = LD C = (4)(800)(900) = 2,880,000 σ L = C D L σ = ) 3000 ( 4 = 6000 ss = F S-1 ( CSL ) × σ L = F S-1 (0.95) ×...
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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.

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Chapter 11 - Chapter 11 Managing Economies of Scale in the...

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