d - BUSI 403 Problem Set D Fall 2008 Due Problem 1 The...

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Unformatted text preview: BUSI 403 Problem Set D Fall 2008 Due: 09/25/08 Problem 1 The following information is given in the problem: Holding cost/unit/month Backorder cost/ unit/ month Hiring cost/worker Lay off cost/worker Production rate/worker/month Initial # workers available Wage/worker/month 15 40 200 800 1200 70 3000 a. Prepare a chase aggregate plan which displays the workforce level on a monthly basis. Compute the total cost of the plan. Month Demand Number Workers (before rounding) 1 75,000 62.50 63 0 7 189,000 0 5,600 2 80,000 66.67 67 4 0 201,000 800 0 3 60,000 50.00 50 0 17 150,000 0 13,600 4 50,000 41.67 42 0 8 126,000 0 6,400 5 80,000 66.67 67 25 0 201,000 5,000 0 6 65,000 54.17 55 0 12 165,000 0 9,600 7 45,000 37.50 38 0 17 114,000 0 13,600 8 60,000 50.00 50 12 0 150,000 2,400 0 9 75,000 62.50 63 13 0 189,000 2,600 0 10 66,000 55.00 55 0 8 165,000 0 6,400 11 74,000 61.67 62 7 0 186,000 1,400 0 12 90,000 75.00 75 13 0 225,000 2,600 0 Horizon Costs = 2,061,000 14,800 55,200 Total Horizon Cost = 2,131,000 Number Workers (after rounding) Number Workers Hired Number Workers Laid off Labor Costs ($) Hiring Costs ($) Laying Off Costs ($) The first row of the chase aggregate plan is calculated as follows: Month 1 Demand 75,000 Number Workers (before rounding) Number Workers (after rounding) Number Workers Hired Number Workers Laid off Labor Costs ($) Hiring Costs ($) 75000/1200= 62.50 63 0 70-63= 7 63*3000= 189,000 0 1 Laying Off Costs ($) 800*7= 5,600 BUSI 403 Problem Set D Fall 2008 Due: 09/25/08 b. Prepare a level aggregate plan using both inventories and backorders. Compute the total cost of the plan. Average monthly demand = 820,000 / 12 =68333.33 The number of workers required is calculated by dividing average monthly demand by capacity per worker, i.e., 68333.33/1200 = 57 Cumulative Demand (CD) Cumulative Production (CP) Ending Inventory Ending Backorders Labor Cost ($) Inventory Holding Cost ($) Backorder Cost ($) Month Demand Production 1 75,000 68,400 75,000 68,400 0 6,600 171,000 0 264,000 2 80,000 68,400 155,000 136,800 0 18,200 171,000 0 728,000 3 60,000 68,400 215,000 205,200 0 9,800 171,000 0 392,000 4 50,000 68,400 265,000 273,600 8,600 0 171,000 129,000 0 5 80,000 68,400 345,000 342,000 0 3,000 171,000 0 120,000 6 65,000 68,400 410,000 410,400 400 0 171,000 6,000 0 7 45,000 68,400 455,000 478,800 23,800 0 171,000 357,000 0 8 60,000 68,400 515,000 547,200 32,200 0 171,000 483,000 0 9 75,000 68,400 590,000 615,600 25,600 0 171,000 384,000 0 10 66,000 68,400 656,000 684,000 28,000 0 171,000 420,000 0 11 74,000 68,400 730,000 752,400 22,400 0 171,000 336,000 0 12 90,000 68,400 820,000 820,800 800 0 171,000 12,000 0 2,052,000 2,127,000 1,504,000 Total L/I/B Costs = 5,683,000 Total cost = Total L/I/B Cost + Initial laying off cost = 5,683,000 + (70-57)*800 = 5,693,400 The first row of the level aggregate plan is calculated as follows: Month 1 Demand Production Cumulative Demand Cumulative Production Ending Inventory Ending Backorders Labor Costs ($) Inventory Costs ($) Backorder Costs ($) 75,000 57*1200= 68,400 75,000 68,400 0 7500068400= 6600 57*3000= 171,000 0 6600*40= 264,000 c. Based on the total cost in part a) and part b), which plan is better? Based on the total cost, the chase aggregate plan performs better. 2 BUSI 403 Problem Set D Fall 2008 Due: 09/25/08 Problem 2 a. Prepare a level aggregate plan using inventories but no back orders. Please display the amount of ending inventory each month. Compute the total cost of the plan. Production rate required to meet demand without backorders over 12 month period is at least 77,500 (max of cumulative demand/period) units per month. To produce 77,500 units per month, 77,500 / 1200 =64.58 ~ 65 workers are needed. The company has 70 workers on staff; hence, 5 workers should be laid off at the beginning of January 2009. This yields a production rate of 65*1200 = 78,000 units per month. Cumulative Cumulative Demand Demand(CD) (CD) / Period # Workers Cumulative Production (CP) Ending Inventory Ending Backorders Labor Costs ($) Inventory Holding Costs ($) Backorder Costs ($) Month Demand 1 75,000 75,000 75,000 65 78,000 3,000 0 195,000 45,000 0 2 80,000 155,000 77,500 65 156,000 1,000 0 195,000 15,000 0 3 60,000 215,000 71,667 65 234,000 19,000 0 195,000 285,000 0 4 50,000 265,000 66,250 65 312,000 47,000 0 195,000 705,000 0 5 80,000 345,000 69,000 65 390,000 45,000 0 195,000 675,000 0 6 65,000 410,000 68,333 65 468,000 58,000 0 195,000 870,000 0 7 45,000 455,000 65,000 65 546,000 91,000 0 195,000 1,365,000 0 8 60,000 515,000 64,375 65 624,000 109,000 0 195,000 1,635,000 0 9 75,000 590,000 65,556 65 702,000 112,000 0 195,000 1,680,000 0 10 66,000 656,000 65,600 65 780,000 124,000 0 195,000 1,860,000 0 11 74,000 730,000 66,364 65 858,000 128,000 0 195,000 1,920,000 0 12 90,000 820,000 68,333 65 936,000 116,000 0 195,000 1,740,000 0 2,340,000 12,795,000 Total L/I/B Costs = 0 15,135,000 Total Cost = 15,135,000 +5 * 800 = 15,139,000 b. Prepare a level aggregate plan with a starting inventory of 50000 motherboards. Inventories are allowed but no backorders. What is the total cost of this plan? With a starting inventory of 50000, the net demand in January is by 75,000-50,000=25,000. The production rate required to meet demand without backorders over 12 months is at least 64,166.67 (max of cumulative net demand/periods) units per month. To produce 64,166.67 units per month, 64,166.67 / 1200 =53.47 ~ 54 workers are needed. The company has 70 workers on staff; hence, 16 workers should be laid off at the beginning of January 2009. This yields a production rate of 54*1200 = 64,800 units per month 3 BUSI 403 Problem Set D Fall 2008 Due: 09/25/08 CND/ Cumulative No. of Periods Cumulative Actual Demand (CD) Cumulative Production+ Starting Inventory (CPI) Ending Inventory Ending Backorders Labor Costs ($) Inventory Costs ($) Backorder Costs ($) Month Demand Net Demand Cumulative Net Demand (CND) 1 75,000 25,000 25,000 25,000 75,000 114,800 39,800 0 162,000 597,000 0 2 80,000 80,000 105,000 52,500 155,000 179,600 24,600 0 162,000 369,000 0 3 60,000 60,000 165,000 55,000 215,000 244,400 29,400 0 162,000 441,000 0 4 50,000 50,000 215,000 53,750 265,000 309,200 44,200 0 162,000 663,000 0 5 80,000 80,000 295,000 59,000 345,000 374,000 29,000 0 162,000 435,000 0 6 65,000 65,000 360,000 60,000 410,000 438,800 28,800 0 162,000 432,000 0 7 45,000 45,000 405,000 57,857 455,000 503,600 48,600 0 162,000 729,000 0 8 60,000 60,000 465,000 58,125 515,000 568,400 53,400 0 162,000 801,000 0 9 75,000 75,000 540,000 60,000 590,000 633,200 43,200 0 162,000 648,000 0 10 66,000 66,000 606,000 60,600 656,000 698,000 42,000 0 162,000 630,000 0 11 74,000 74,000 680,000 61,818 730,000 762,800 32,800 0 162,000 492,000 0 12 90,000 90,000 770,000 64,167 820,000 827,600 7,600 0 162,000 114,000 0 1,944,000 6,351,000 0 Total L/I/B Costs = Total cost = Total L/I/B Cost + Initial laying off cost = 8,295,000 + (70-54)*800 = 8,307,800 4 8,295,000 BUSI 403 Problem Set D Fall 2008 Due: 09/25/08 Problem 3 The following information is given in the problem: Hiring cost/worker Laying off cost/worker Answer rate/worker/month/credit card Answer rate/worker/month/personal banking Initial # workers available Monthly working hours/ worker Wage/worker/month a. 400 200 20 30 50 160 2500 Please provide a monthly workforce requirement plan for year 2009 using chase plan. What is the total cost of this plan? Credit Card Personal Banking # Agents Needed # Agents Needed (after rounding) # Agents Hired # Agents Laid off Labor Costs ($) Hiring Costs ($) Laying Off Costs ($) 507k/(160 *60) = 52.81 35.42+52.81= 88.23 89 Max(0, 89-50)= 39 Max(0, 50-89)= 0 2500*89= 222,500 39*400= 15,600 0 471,000 49.06 76.15 77 0 12 192,500 0 2,400 41.25 360,000 37.50 78.75 79 2 0 197,500 800 0 24.38 390,000 40.63 65.00 65 0 14 162,500 0 2,800 268,000 27.92 429,000 44.69 72.60 73 8 0 182,500 3,200 0 294,000 30.63 570,000 59.38 90.00 90 17 0 225,000 6,800 0 7 206,000 21.46 531,000 55.31 76.77 77 0 13 192,500 0 2,600 8 290,000 30.21 312,000 32.50 62.71 63 0 14 157,500 0 2,800 9 290,000 30.21 402,000 41.88 72.08 73 10 0 182,500 4,000 0 10 222,000 23.13 480,000 50.00 73.13 74 1 0 185,000 400 0 11 306,000 31.88 402,000 41.88 73.75 74 0 0 185,000 0 0 12 394,000 41.04 489,000 50.94 91.98 92 18 0 230,000 7,200 0 2,315,000 38,000 Demand # Agents Needed (before rounding) Demand # Agents Needed (before rounding) 1 17k*20= 340,000 340k/(160 *60)= 35.42 16.9k*30= 507,000 2 260,000 27.08 3 396,000 4 234,000 5 6 Month Total Cost = 10,600 2,363,600 b. If the company decides to use a level plan, what is the monthly workforce level should be maintained in 2009? What is the total cost of this plan? From part (a) we know that 92 agents are required to meet the highest demand, meaning that additional 42 agents need to be hired. Therefore 92 agents should be maintained at all time in 2009. # Agent Needed # Agents Hired # Agents Laid off Labor Cost Hiring Cost Laying Off Cost Total Cost 92 42 0 2,760,000 16,800 0 2,776,800 5 ...
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