Review Problems for Chapter 13 EXAMPLE 1 Planners for a company that makes several models of skateboards are about to prepare the aggregate plan that will cover six periods. They have assembled the following information: They now want to evaluate a plan that calls for a steady rate of regular-time output, mainly using inventory to absorb the uneven demand but allowing some backlog. Overtime and subcontracting are not used because they want steady output. They intend to start with zero inventory on hand in the first period. Prepare an aggregate plan and determine its cost using the preceding information. Assume a level output rate of 300 units (skateboards) per period with regular time (i.e., 1,800Г·6 = 300). Note that the planned ending inventory is zero. There are 15 workers, and each can produce 20 skateboards per period. 1. Refer to Example 1. The president of the firm has decided to shut down the plant for vacation and installation of new equipment in period 4. After installation, the cost per unit will remain the same, but the output rate for regular time will be 450. Regular output is the same as in Example 1 for periods 1, 2, and 3; 0 for period 4; and 450 for each of the remaining periods. Note, though, that the forecast of 400 units in period 4 must be dealt with. Prepare the aggregate plan, and compute its total cost. Solution: From example 1. Period 1 Forecast 200 Output Regular 300 Overtime Subcontract OutputForecast 100 Inventory Beginning 0 3 300 4 400 5 500 6 200 Total 1,800 300 300 0 450 450 1,800 100 0 (400) (50) 250 100 200 200 0 0 Ending 100 200 200 0 0 0 Average Backlog 50 0 150 0 200 0 100 200 0 250 0 0 500 450 $600 600 600 0 900 900 3,600 50 0 150 0 200 0 100 1,000 0 1,250 0 0 500 2,250 $650 750 800 1,100 2,150 900 6,350 Costs: Output Regular Overtime Subcontract Inventory Backorder @ 5 Total 2. 2 200 Manager T. C. Downs of Plum Engines, a producer of lawn mowers and leaf blowers, must develop an aggregate plan given the forecast for engine demand shown in the table. The department has a normal capacity of 130 engines per month. Normal output has a cost of $60 per engine. The beginning inventory is zero engines. Overtime has a cost of $90 per engine. a. b. Solution: a. Develop a chase plan that matches the forecast and compute the total cost of your plan. Compare the costs to a level plan that uses inventory to absorb fluctuations. Inventory carrying cost is $2 per engine per month. Backlog cost is $90 per engine per month. Period Forecast Output Regular Overtime Subcontract Output - Forecast Inventory Beginning Ending Average Backlog Costs: Output Regular @ 60 Overtime @ 90 Subcontract Inventory @ 5 Backorder Total 1 120 2 135 120 130 5 4 120 5 125 6 125 7 140 8 135 Total 1,040 130 10 120 125 125 130 10 130 5 1,010 30 (10) 0 0 0 (10) $7,200 7,800 450 7,800 900 7,200 7,500 7,500 7,800 900 7,800 $60,600 450 2,700 7,200 8,700 7,200 7,500 7,500 8,700 8,250 $63,300 5 125 6 125 7 140 8 135 Total 1,040 130 130 130 130 1,040 5 5 (10) 5 10 7.5 10 15 12.5 15 5 10 0 (5) 8,250 3 140 (5) b. Period 1 2 3 4 Forecast 120 135 140 120 Output Regular 130 130 130 130 Overtime Subcontract Output - Forecast 10 (5) (10) 10 Inventory Beginning 0 10 5 0 Ending 10 5 0 5 Average 5 7.5 2.5 2.5 Backlog 5 Costs: Output Regular @ 60 $7,800 7,800 7,800 7,800 Overtime Subcontract @ 50 Inventory @ $2 10 15 5 5 Backorder @ $90 450 Total $7,810 7,815 8,255 7,805 3. (5) 5 0 2.5 7,800 7,800 7,800 7,800 $62,400 15 25 20 5 7,815 7,825 7,820 7,805 100 450 $62,950 Nowjuice, Inc., produces bottled pickle juice. A planner has developed an aggregate forecast for demand (in cases) for the next six months. Use the following information to develop aggregate plans. Develop an aggregate plan using each of the following guidelines and compute the total cost for each plan. Which plan has the lowest total cost? 1. 2. 3. Use level production. Supplement using overtime as needed. Use a combination of overtime (500 cases per period maximum), inventory, and subcontracting (500 cases per period maximum) to handle variations in demand. Use overtime up to 750 cases per period and inventory to handle variations in demand. Solution: Period Forecast Output Regular Overtime Output - Forecast Inventory Beginning Ending Average Backlog Costs: Regular @ 10 Overtime @ 16 Inventory @ 1 Back orders @ 10 Total 1. Level production supplemented with overtime as needed. 1 2 3 4 5 6 Total 4,000 4,800 5,600 7,200 6,400 5,000 33,000 5,000 5,000 5,000 1,000 200 вЂ“600 1,000 500.0 0 50,000 0 500 0 50,500 1,000 1,200 1,200 600 1,100.0 900.0 0 0 50,000 0 1,100 0 51,100 50,000 0 900 0 50,900 5,000 1,600 вЂ“600 600 0 300.0 0 50,000 25,600 300 0 75,900 5,000 1,400 0 0 0 0.0 0 50,000 22,400 0 0 72,400 5,000 0 0 0 0.0 0 50,000 0 0 0 50,000 30,000 3,000 0 2,800 0 300,000 48,000 2,800 0 350,800 2. Combination of overtime, inventory and subcontracting to handle variations in demand. Max. overtime = 500, max. subcontracting = 500 units. Period 1 2 3 4 5 6 Total Forecast 4,000 4,800 5,600 7,200 6,400 5,000 33,000 Output Regular 5,000 5,000 5,000 5,000 5,000 5,000 30,000 Overtime 500 500 500 500 500 2,500 Subcontract 500 500 Output - Forecast 1,500 700 вЂ“100 вЂ“1,700 вЂ“400 0 0 Inventory Beginning 1,500 2,200 2,100 400 0 Ending 1,500 2,200 2,100 400 0 0 Average 750.0 1,850.0 2,150.0 1,250.0 200.0 0.0 6,200 Backlog 0 0 0 0 0 0 0 Costs: Regular @ 10 50,000 50,000 50,000 50,000 50,000 50,000 300,000 Overtime @ 16 8,000 8,000 8,000 8,000 8,000 0 40,000 Subcontract @ 20 0 0 0 0 10,000 0 10,000 Inventory @ 1 750 1,850 2,150 1,250 200 0 6,200 Back orders @ 10 0 0 0 0 0 0 0 Total 58,750 59,850 60,150 59,250 68,200 50,000 356,200 3. Overtime up to 750 units per period maximum to handle variations in demand. Period 1 2 3 4 5 6 Total Forecast 4,000 4,800 5,600 7,200 6,400 5,000 33,000 Output Regular 5,000 5,000 5,000 5,000 5,000 5,000 30,000 Overtime 750 750 750 750 3,000 Output - Forecast 1,000 950 150 вЂ“1,450 вЂ“650 0 0 Inventory Beginning 1,000 1,950 2,100 650 0 Ending 1,000 1,950 2,100 650 0 0 Average 500 1,475 2,025 1,375 325 0.0 5,700 Backlog 0 0 0 0 0 0 0 Costs: Regular @ 10 50,000 50,000 50,000 50,000 50,000 50,000 300,000 Overtime @ 16 0 12,000 12,000 12,000 12,000 0 48,000 Hire/Lay off 0 Inventory @ 1 500 1,475 2,025 1,375 325 0 5,700 Back orders @ 10 0 0 0 0 0 0 0 Total 50,500 63,475 64,025 63,375 62,325 50,000 353,700 We should choose the plan generated in part 1, because $350,800 < 353,700 < 356,200. 4. Refer to Solved Problem 1 (Refer to textbook, 9th edition, page 626). Prepare an aggregate plan that uses some combination of laying off ($100 per worker), subcontracting ($8 per unit, maximum of 20 units per period, must use for three consecutive periods), and overtime ($9 per unit, maximum of 25 per period, maximum of 60 for the planning horizon). Compute the total cost, and compare it with any of the other plans you have developed. Which plan has the lowest total cost? Assume you start with 21 workers. Solution: Several solutions are possible. Here is one. Period Forecast Output Regular Overtime Subcontract OutputForecast Inventory Beginning Ending Average Backlog 1 190 2 230 3 260 4 280 5 210 6 170 7 160 8 260 9 180 Total 1,940 210 210 10 20 210 25 20 210 25 20 210 180 180 180 20 180 10 20 1,770 70 100 0 10 40 (50) 0 25 0 12.5 0 0 0 0 0 0 10 5 0 10 50 30 0 50 0 25 0 0 0 0 0 1,260 1,260 225 225 160 160 0 0 0 0 137.5 62.5 0 0 1,782.5 1,707.5 1,260 0 0 0 0 0 0 1,260 1,080 0 0 0 300 25 0 1,405 1,080 0 160 0 0 150 0 1,390 1,080 90 160 0 0 125 0 1,455 1080 0 0 0 0 0 0 1,080 20 10 (5) 0 20 10 0 20 30 25 0 30 25 27.5 0 Costs: Output Regular @ 6 $1,260 Overtime @ 9 0 Subcontract @ 8 0 Hiring @ 200 200 Layoff-firing @100 0 Inventory @ 5 50 Backorder @ 10 0 Total 1,510 1,260 90 160 0 0 125 0 1,635 (25) EXAMPLE 3 Given the following information set up the problem in a transportation table and solve for the minimum-cost plan: 135 $10,620 $630 $800 $200 $300 $675 $0 $13,225 5. Refer to Example 3. Suppose that an increase in warehousing costs and other costs brings inventory carrying costs to $2 per unit per month. All other costs and quantities remain the same. Determine a revised solution to this transportation problem. Solution: вЂ“2 1 Period 21 Beg. Inv. 0 2 0 2 100 62 Reg. 82 Over. 0 60 50 80 Sub. 60 Reg. 80 Over. 0 2 5 90 Sub. 58 Reg. 78 Over. 88 3 Demand 10 550 The solution is optimal with a total cost of $124.960. +34 50 500 0 +14 90 100 750 120 0 80 93 5 700 +2 500 5 96 50 0 60 83 10 Sub. +12 70 5 86 500 0 92 63 10 +32 0 50 66 120 0 82 90 5 90 0 50 93 50 0 62 80 500 0 +10 30 500 83 +30 94 60 100 0 84 0 0 63 0 64 92 Total Cap. +90 0 50 90 5 4 82 0 92 вЂ“92 4 0 62 450 1 2 3 50 0 +4 90 100 2,090 6. Prepare a master schedule like that shown in the above Figure given this information: The forecast for each week of an eight-week schedule is 50 units. The MPS rule is to schedule production if the projected on-hand inventory would be negative without it. Customer orders (committed) are as follows: Use a production lot size of 75 units and no beginning inventory. Solution: Forecast Customer Orders Projected on-hand inventory MPS ATP 1 50 June 2 3 50 50 4 50 52 35 20 12 23 48 73 23 75 23 75 40 75 43 Week 1 2 3 4 5 6 7 8 7. 5 50 July 6 7 50 50 8 50 48 73 48 75 75 75 75 23 75 75 Net Projected Inventory Inventories On-Hand From Previous Wk. Requirements Before MPS (70) MPS Inventory 0 23 48 73 23 48 73 23 52 50 50 50 50 50 50 50 вЂ“52 вЂ“27 вЂ“2 23 вЂ“27 вЂ“2 23 вЂ“27 75 75 75 вЂ“ 75 75 вЂ“ 75 23 48 73 23 48 73 23 48 Determine the available-to-promise (ATP) quantities for each period for Problem 6. Solution: Given above.