Class Notes (807,938)
MSCI 432 (10)
Lecture

# Solutions for Chapter 3 The professor gave us these solutions , very helpful - Winter 2010

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School
University of Waterloo
Department
Management Sciences
Course
MSCI 432
Professor
Binyamin Mantin
Semester
Fall

Description
Nahmias Chapter#3 ANS. a) Smoothing costs are those that result from making changes from one planning period to the next. In aggregate planning, the most disruptive change usually is changing the work force level. Even with fixed work force sizes, however, changes in production levels can also be disruptive. b) A bottleneck occurs when the capacity of the productive system is insufficient to meet a sudden surge in the demand. Bottlenecks can also occur in a particular part of the productive system due to the breakdown of a key piece of equipment or the shortage of a critical resource. c) System capacity is relate d to the idea of bottlenecks. Capacity is exceeded when unanticipated surges in the demand occur, scarce resources are unavailable, or there is a drop in the labour pool due to strikes or a change in worker demographics. d) The planning horizon is the number of periods of demand forecas t used to generate the aggregate plan. If the horizon is too shor t, there may be insufficient time to build inventories to meet future demand surges and if it is too long the reliability of the demand forecasts is likely to be low. ANS The primary difficulty would be to properl y define an aggregate unit of production. Since the workers have a variety of different skills and the jobs accepted by the shop are very different, it is unlikely that aggregate planning would be very useful for this type of operation. ANS a) Cum Cum Net Net #Units/ #Units Demand Demand Worker /Worker Forecast Forecast Min # Year (in 1000) (in 1000) (in 1000) (in 1000) Workers 1 30 30 280 280 10 2 30 60 120 400 7 3 30 90 200 600 7 4 30 120 110 710 6 5 30 150 135 845 6 Minimum constant work force = 10 workers b) Cum Cum #Units/ Yearly Yearly Net Ending Year Worker Production Production Demand Inventory 1 30 300 300 280 20 2 30 300 600 400 200 3 30 300 900 600 300 4 30 300 1200 710 490 5 30 300 1500 845 655 1665 CH = 500, CF = 1,000, CI = .04 per package and payroll cost s are \$25,000 per year per worker. There are exactly 10 - 3 = 7 workershired in year 1. Hence the total cost of the constant work force plan i(500)(7) + (.04)(1665000) + (10)(25,000)(5) = \$1,320,100. ANS a) k = \$60,000/250 = \$240 per worker per day (A) (B) Cum Predict Cum [B/A] *Cum #Units #Units Net Net Min # *Monthly Monthly *End Working /Worker /Worker Demand Demand Workers Product Product Invent. Mo Days (\$000) (\$000) (\$000) (\$000) (\$000) (\$000) (\$000) (\$000) 1 22 5.28 5.28 3280 3280 622 4102.56 4102.56 822.56 2 16 3.84 9.12 3800 7080 777 2983.68 7086.24 6.24 3 21 5.04 14.16 2200 9280 656 3916.08 11002.32 1722.32 4 19 4.56 18.72 1000 10280 550 3543.12 14545.44 4265.44 5 23 5.52 24.24 4900 15180 627 4289.04 18834.48 3654.48 6 20 4.80 29.04 6250 21430 738 3729.60 22564.08 1134.08 7 24 5.76 34.80 3750 25180 724 4475.52 27039.60 1859.60 8 12 2.88 37.68 3100 28280 751 2237.76 29277.36 997.36 9 19 4.56 42.24 1750 30030 711 3543.12 32820.48 2790.48 10 22 5.28 47.52 1450 31480 663 4102.56 36923.04 5443.04 11 20 4.80 52.32 1200 32680 625 3729.60 40652.64 7972.64 12 16 3.84 56.16 1750 34430 614 2983.68 43636.32 9206.32 Total \$39,874.56 *Note: These figures assume the minimum constant workforce of 777 workers each month. Minimum constant work force = 777 workers b) CH = 200 CF = 400 Initial # workers = 675 Beg. inv = 120000 Workers added = 102 End inv = 100000 Total ending inventory= 39,874,560 + 100,000 = \$39,974,560 Inventory costs per month = .25/12 = . 020833/\$/month. Hence total hiring + inventory costs for the constant work force plan are (200)(102) + (.020833)(39,974,560) = \$853,190 ANS a) Att. Att. Total Month Belts(#) Belts(hrs) Hand(#) Hand(hrs) Case# Case(hrs) Hrs. 1 2500 5000 1250 3750 240 1440 10190 2 2800 5600 680 2040 380 2280 9920 3 2000 4000 1625 4875 110 660 9535 4 3400 6800 745 2235 75 450 9485 5 3000 6000 835 2505 126 756 9261 6 1600 3200 375 1125 45 270 4595 b)  Cum Cum Min.  Working Working Working Demand Workforce Month Days Hours Hours Hours (Ratio) 1 22 154 154 10190 67 2 20 140 294 20110 69 3 19 133 427 29645 70 4 24 168 595 39130 66 5 21 147 742 48391 66 6 17 119 861 52986 62 Hence the minimum constant work force size is 70. It is probably not advantageous to bring the work force level up to 70 workers. The cess demand can be absorbed by overtime or by employing part-time workers. The firm can be more flexible by keeping the number of full-time employees to a minimum. c) If a plan is to ut ilize only regular time employees, then excess demand must be absorbed by overtime. Since there are 46 employees with the firm, we obtain (A) Working (Regular Required Overtime Month Hours Hours Hours Hours 1 154 7084 10,190 3106 2 140 6440 9,920 3408 3 133 6118 9,535 3417 4 168 7728 9,485 1757 5 147 6762 9,261 2499 6 119 5474 4,595 Totals: 39,606 14,259 Cost of plan = (39,606)(8.50) + (14,259)(14.00) = 336,651 + 199,626 = \$536,277 d) Here we will determine the size of the work force necessary to meet monthly demands as closely as possible and add additional employees to meet the excess demand. (A) (B) (C) (D=[B/
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