Assignment #5

• Problem 698/1
• Problem 698/2
• Problem 698/4
• Problem 698/10
• Problem 698/11
• Problem 698/16

698/1
D=3800/year or 76/week
value=$110/unit
L= 6 weeks
• a) Q/2 = 1000/2 = 500 units
• b) Pipeline inventory = D_W * L * average cost= 76 * 6 * 80 = $36,480


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• 698/2

D = 75/week
Q = 400
L = 2 weeks
Safety Stock = 150
value = $350/unit
• a) Pipeline ($) = 75 units * 2 weeks * $350 = $52,500
• b) Total = Pipeline + Cycle + Safety = 150 + 400/2 + 150 = 500 units/DC

Total system Inventory  = 5 DCs * 500 units= 2,500 units or  2,500* $350 = $875,000


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• 698/4

D = 4,000/year or D_W = 80/week
Q = 250
L = 3 weeks
Value = $450/unit
• a) Cycle = Q/2 = 250/2 = 125 units
• b) Pipeline = D_W * L = 80 * 3 = 240 units
Assuming half of the value added in manufacturing applies to pipeline inventory, each unit is worth $150 + $300/2 = $300
Thus the value of the pipeline inventory = 240 * $300 = $72,000

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• 698/10

D_W = 90/week; sigma = 15 pairs/week
S = $54/order
H = 27% * value = .27 * $11.70 = $3.159/year
Desired Service level = 80 % (z = .845)
L = 3 weeks
• a)Q^* = (2*D*S/H)^1/2 = (2*90*52*54/3.159)^1/2 = 400; TBO = Q/D = 400/90 = 4.444 weeks
• b) R = D*L + z * sigma * L^1/2 = 90 * 3 + .845 * 15 * 3^1/2 = 292
• c) On hand after withdrawal = 320 - 10 = 310.. Not yet.
• d) Q = 500

Holding = Q/2 (H) = 500/2 * 3.159 = $789.75/year.
Ordering = Number of orders/year * S = (90*52/500) * 54 = $505.44/year
Total = 789.75 + 505.44 = $1295.19/year.. Since Holding cost > ordering cost Q is too large
 
• e) C = 400/2 * 3.159 + (90*52/400)* 54 = $1263.60/year.. a savings of $31.59/year


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• 698/11
• a) correct Q^* = [2 * (52*60) * 54/ 3.159]^1/2= 327 units.

would have cost = (327/2) * 3.159 + [(52*60)/327] * 54 = $1031.73/year
but costs = 400/2 * 3.159 + (52 * 60/400) * 54 = $1053/year..
a difference of $21.27/year
 
• b) correct Q = [2 * (52*60) * 6/ 3.159]^1/2= 109 units

would have cost = (109/2) * 3.159 + [(52*60)/109] * 6 = $343.91/year
but costs = 327/2 * 3.159 + (52 * 60/327) * 6 = $573.75/year..
a difference of $229.83/year
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• 698/16

TBO = 6 weeks
L = 3 weeks
D_W = 100/week; sigma_W = 20/week
• a) average deamnd D_W * (L + TBO)= 100 * 9 = 900 units.

sigma = sigma_W(TBO + L)^1/2 = 20 * 9^1/2 = 60 units.
 
• z for 97.5% = 1.96

T = D_W *(TBO + L) + z * sigma = 900 + 1.96 * 60 = 1018
 
• c) Order size = 1018 - 350 = 668 units. To Top 

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