Exam II - key

Demand per week n500 50 sl 94 lt 2 weeks oi 3 weeks

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Demand per week: N[500, 50]. SL% = 94%. LT = 2 weeks, OI = 3 weeks. 20) ROP = = 2 x 500 + 1.56 * x 50 = 1110.3 ≈ 1115 21) Safety stock under P-system = = = 100 Based on the z-table, = 0.89 and thus the service level with the safety stock is 81.33%. 22) h = \$2/unit, 50 weeks/yr, Annual demand D = 500 units/week x 50 weeks/yr = 25000 units/yr OI = = 0.6 yr = EOQ = 25000*0.6 = 15000 = = Therefore the setup (ordering) cost is \$9000 per order . Demand: U~[500, 1000]. C = \$75 / unit. C S = R-C = \$50 / unit. V = \$10 / Unit. 23) SL = (R-C) / (R-V) = 50 / (125-10) = 0.435 24) Q 0 = 500 + 0.435 x 500 = 717.39 718 25) If you stock optimal units, E[Leftover] = = 47.524; E[Sales] = Q – E[Leftover] = 718-47.524 = 670.476 Expected profit (718) = (R-C)E[Sales] – (C-V)E[Leftover] = 50x670.476 – 65x47.524 = 30434.74 If you stock average demand, E[Demand] = 750; E[Leftover] = = 62.5 E[Sales] = Q – E[Leftover] = 750-62.5 = 687.5 Expected profit (750) = (R-C)E[Sales] – (C-V)E[Leftover] = 50x687.5 – 65x62.5 = 30312.5 The extra profit is 30434.74 - 30312.5 = 122.24 26) C = \$75 / unit. C S = R-C = \$50 / unit. R = \$125 / unit. SL = (R-C) / (R-V) = 50 / (125-V) = 0.3333 V = -25 Here, the salvage value takes a negative value. This means that each unit of leftover will cost \$25 to the newsvendor. For example, if the leftover inventory should be scrapped at the end of selling period and the cost for scrap is \$25 per unit, then the salvage value will be -\$25. FOQ 50 policy: SS = 25 Period 0 1 2 3 4 5 6 7 8 9 10 11 1 2

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Demand 80 50 100 0 40 60 75 65 20 70 60 1 0 Q 50 50 100 0 50 50 50 100 0 100 50 0 Inventory 80 50 50 50 50 60 50 25 60 40 70 60 5 0 27) If a L4L lot sizing strategy was being used, the inventory at the end of period 12 would be 25 , which is the safety stock level. 28) If a POQ 3 strategy was being used, the Q at Period 1is 175 = (80+50+100)-80+25 Sample# \ Observation# X 1 X 2 X 3 X 4 X 5 Sum R 1 0.1 0.2 0.3 0.4 0.1 1.1 0.22 0.3 2 0.3 0.2 0.3 0.1 0.1 1 0.2 0.2 3 0.1 0.2 0.1 0.2 0.3 0.9 0.18 0.2 4 0.1 0.2 0.3 0.2 0.1 0.9 0.18 0.2 5 0.1 0.5 0.6 0.9 0.2 2.3 0.46 0.8 6 0.3 0.1 0.7 0.5 0.2 1.8 0.36 0.6 29) Control limits for the chart : 30) Control limits for the R-chart: UCL = 0.267 + 0.577x0.383 = 0.488 CL = 0.267 LCL = = 0.267 - 0.577x0.383 = 0.045 UCL = 2.115x0.383 = 0.811 CL = 0.383 LCL = 0x0.383 = 0 31) Out of control point(s) on either chart is none .
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• Spring '10
• panwalker
• 5th millennium, Centuries in the future, G-Unit

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