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CHAPTER 13:AGGREGATE PLANNING

Teaching Notes

In the earlier chapters, we have looked at certain problems that involve long range planning such asfacility location, layout and major equipment purchase decisions. Aggregate planning involves mediumrange planning. The planning horizon for medium range plans varies from a couple of months to 18months. A major component of aggregate planning is to plan aggregate production and inventory levels toachieve a desired level of customer service. In preparing the aggregate plan, a major consideration is tocheck the desired production plan against the estimated capacity. On the other hand, in determining theestimated capacity, we must take into account the expected demand and the resulting medium rangeproduction plan.

We use the term aggregate plan in lieu of medium range production plan for two reasons:

1. It generally involves the production plan for a group or a family of products (aggregation of

products).

2. It aggregates daily or weekly (short-range) demand and the resulting production plan(aggregation of time periods).

Even though the aggregate plan is a function of many different factors, the key factor is the forecasteddemand over the length of the medium-range planning horizon. After developing an aggregate planconsistent with the forecasted demand and capacity, it is disaggregated into shorter time periods. Theprocess of disaggregation is the beginning of short range planning using master scheduling and operationsscheduling. Both master scheduling and operations scheduling are designed to implement the mediumrange plan on the shop floor.

In determining the aggregate plan, integration and communication between various functions of the firmare vital. Expected changes in the work force levels need to be communicated to the human resourcesdepartment, while any major equipment purchases, layout changes and capacity additions must involvethe approval of the finance department. On the other hand, changes in anticipated inventory levels andespecially, expected stockouts must be discussed with the marketing department.

Answers to Discussion and Review Questions

1. Three levels of planning that involve operations managers are:

a. Business plan: It establishes production and capacity strategies.

b. Production plan: It establishes production capacity and intermediate term aggregateproduction schedule.

c. Master schedule: It establishes schedules for specific products (disaggregation of productionplan).

2. The three phases are forecasting demand, aggregate planning, and disaggregatingthe overall plan.

3. Aggregate planning involves developing a general plan for employment, output,and inventory levels. The goal is to develop a plan which makes efficient use of theresources of an organization. Planners attempt to determine the best way to meetforecasting demand requirements within the constraints imposed by long-term decisions.

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4. The need for aggregate planning is to begin to translate long-term decisions intoshort-term operating plans. Aggregate planning constitutes the intermediate step in thisprocess.

5. In both manufacturing and service, managers can vary the size of the workforceand subcontract work. Manufacturers have the additional option of varying the size of

inventories.6. The difficulty relates to finding a common unit on which to base aggregate planswhen there is a variety of products or services to contend with.

7. a. Maintaining a constant workforce has the advantage of makingestimation of labor costs relatively easy, is good for morale, and minimizes hiring andlayoff costs. However, inventory carrying costs tend to be high.

b. Since labor force has to be continually adjusted, hiring and layoff costs tend to behigh. Due to the instability of the labor force, employee morale is low. However, theinventory carrying costs are very low because production is matched with demand, resultingin little or no inventory.

c. Varying the workforce can cause morale problems. Moreover, working overtimegenerally is less productive, increases quality problems, and increases the risk ofaccidents.

8. Informal techniques are visual, easy to comprehend, and enable planners tocompare alternatives. Their chief limitation is that they do not necessarily produceoptimum solutions.

9. a. Spreadsheets are intuitively appealing and easy to understand, but solutions are notnecessarily optimal.

b. Linear Programming (LP): LP approach is a method of obtaining optimalsolutions to problems involving allocation of limited resources. The objective of linearprogramming is either maximization of profit or minimization of cost. In AggregatePlanning, the objective is usually the minimization of costs related to labor time (regular

and overtime), inventory carrying, hiring and layoffs. LP is a valid approach if the costand variable relationships and assumptions are linear and demand can be treated asdeterministic. Even for fairly small problems, LP approach requires computerization dueto massive data manipulation and calculations.

c. Simulation: It is a highly flexible computerized trial-and-error approach thatprovides testing of the model under different conditions, assumptions or scenarios. Itprovides a what-if capability to identify possible options to a given aggregate planningproblem based on trial-and-error. Simulation requires the use of the computer. Therefore,computer programming and customization of different conditions and scenarios may betime consuming.

10. The master schedule has three inputs: the beginning inventory, forecasts for each

period of the schedule, and customer outputs. Its outputs are projected inventory,production requirements, and uncommitted (available-to-promise) inventory.

Taking Stock

1. When we freeze a portion of the master schedule, we make the schedule more stable and reduce thenervousness of the schedule. However, freezing the schedule also leads to inflexibility andreduced customer service because we will not be able to respond to the demands of the customersin a timely fashion.

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2. Purchasing agents, production planning and control manager, planners, schedulers, and marketingpersonnel need to interface with the master schedule. Purchasing agents, planners and schedulersneed direct information from the MPS to order the parts, manage the inventories of the parts andschedule the machines in producing the parts going into the end items master scheduled. Theproduction planning and control manager needs the MPS information to determine capacity needs ofthe labor, machinery and equipment. Marketing personnel need this information so that they could let

their customers know if there is a delay in the completion of an order. In the case of capacityconstrained manufacturing, marketing personnel also need to provide the master scheduler with keyinformation as to which orders to delay and which orders are crucial to try to complete on time.

3. The new communication tools made it easier to communicate changes in the master schedule.Therefore, when a change is necessary in the master schedule (addition or a deletion of an order,change in the due date or the quantity of an order), it can be communicated to the masterscheduler faster through new communication tools (e-mail, fax, etc.). The master scheduler cantake this information, and through the utilization of a computerized production planning andcontrol system, incorporate the changes to the schedule (assuming the changes are feasible). Afterincorporating the changes and making sure that the MPS is feasible he/she can disseminate theinformation to the appropriate parties and to the shop floor very quickly so that the manufacturingsystem can respond to the changes in a timely fashion.

Critical Thinking Exercise

Compared to manufacturing environments, service environments often experience more pronouncedvariations in demand over shorter time intervals. Moreover, employing inventory as a cushion is not alwaysan option for a service organization. However, services often have a higher degree of flexibility thanmanufacturing operations, which allows more ability to respond to demand fluctuations with relativelyquick changes in capacity. Services are able to make quick adjustments to capacity relatively easily, whilechanging capacity for a manufacturing firm can be a difficult and more time consuming proposition.

Memo Writing Exercise(included on the DVD)1. Aggregate Planning is the planning of the overall, general use of resources basedon expected demand. It involves determining the levels of production or service for onequarter to 1.5 years into the future. Based on the forecasted demand, capacity levels, currentinventory level, size of the workforce, production and service requirements are aggregatedinto one product or service.

Aggregate Planning determines the level of output for a given service or product bymanaging the capacity using different production strategies. After it is developed,Aggregate Planning is disaggregated into separate products and shorter time periods. Animportant feature of Aggregate Planning is that the Master Schedule is formed bydisaggregating it. In other words, it serves as the basis of the Master Schedule (MRP) andthe resulting detailed shop floor schedule. The absence of a clear aggregate plan can cause

serious problems in capacity planning, workforce scheduling, customer service andproduction efficiency.

2. Chase strategy matches production with varying demand rates. This strategyinvolves either varying the workforce levels or varying the capacity by using eitherovertime or subcontracting. The primary advantage of using Chase strategy is thatinventory carrying cost is minimized. The main disadvantage is the additional cost ofchanging the workforce level (hiring, layoffs and employee morale) or the cost ofovertime/subcontracting.


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Level strategy maintains a constant workforce and constant production. It has theadvantage of minimizing hiring and layoff costs and keeping employee morale high.However, inventory carrying costs tend to be high.


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Solutions

1.From example 1.Period 1 2 3 4 5 6 TotalForecast 200 200 300 400 500 200 1,800

OutputRegular 300 300 300 0 450 450 1,800OvertimeSubcontract

Output-Forecast 100 100 0 (400) (50) 250

InventoryBeginning 0 100 200 200 0 0

Ending 100 200 200 0 0 0

Average 50 150 200 100 0 0 500Backlog 0 0 0 200 250 0 450

Costs:Output

Regular $600 600 600 0 900 900 3,600OvertimeSubcontract

Inventory 50 150 200 100 0 0 500Backorder @ 5 0 0 0 1,000 1,250 0 2,250

Total $650 750 800 1,100 2,150 900 6,350

2. a. (Other plans are possible)

Period 1 2 3 4 5 6 TotalForecast 200 200 300 400 500 200 1,800Output

Regular 290 290 290 290 290 290 1,740Overtime 20 20 20 60

Output-Forecast 90 90 10 (90) (190) 90

InventoryBeginning 0 90 180 190 100 0Ending 90 180 190 100 0 0Average 45 135 185 145 50 0 560

Backlog 0 0 0 0 90 0 90

Costs:Regular 2 $580 580 580 580 580 580 $3,480Overtime @ 3 0 0 60 60 60 0 180

Inventory @ 1 45 135 185 145 50 0 560Backorder 5 0 0 0 0 450 0 450

Total $625 715 825 785 1,140 580 4,670


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Solutions (continued)

2. b. (Other plans are possible)Period 1 2 3 4 5 6 Total

Forecast 200 200 300 400 500 200 1,800Output

Regular 290 290 290 290 290 290 1,740Subcontract 10 50 60

Output-Forecast 90 90 (10) (100) (160) 90

InventoryBeginning 0 90 180 170 70 0Ending 90 180 170 70 0 0Average 45 135 175 120 35 0 510

Backlog 0 0 0 0 90 0 90

Costs:

Regular @ 2 $580 580 580 580 580 580 $3,480

Subcontract @ 6 0 0 0 60 300 0 360Inventory @ 1 45 135 175 120 35 0 510Backorder @ 5 0 0 0 0 450 0 450

Total $625 715 755 760 1,365 580 $4,800


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3.Period 1 2 3 4 5 6 Total

Forecast 200 200 300 400 500 200 1,800Output

Regular 280 280 280 280 280 280 1,680Overtime 0 0 40 40 40 0 120

Subcontract 0 0 0 0 0 0 0Output-

Forecast 80 80 20 (80) (180) 80Inventory

Beginning 0 80 160 180 100 0Ending 80 160 180 100 0 0

Average 40 120 170 140 50 0 520Backlog 0 0 0 0 80 0 80

Costs:

OutputRegular 2 $560 560 560 560 560 560 $3,360Overtime @ 3 0 0 120 120 120 0 360Subcontract @ 6 0 0 0 0 0 0 0

Inventory 1 40 120 170 140 50 0 520Backorder @ 5 0 0 0 0 400 0 400

Total $600 680 850 820 1,120 560 $4,640

4.Period 1 2 3 4 5 6 Total

Forecast 200 200 300 400 500 200 1,800Output

Regular 280 280 280 280 280 280 1,680Subcontract 0 0 20 50 50 0 120Output-

Forecast 80 80 0 (70) (170) 80Inventory

Beginning 0 80 160 160 90 0Ending 80 160 160 90 0 0Average 40 120 160 125 45 0 490

Backlog 0 0 0 0 80 0 80

Costs:Regular @ 2 $560 560 560 560 560 560 $3,360

Subcontract 6 0 0 120 300 300 0 720Inventory @ 1 40 120 160 125 45 0 490Backorder @ 5 0 0 0 0 400 0 400

Total $600 680 840 985 1,305 560 $4,970

No. The above plan costs: ($4,970 4,640) = $330 more than the plan in example 2.


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5. a.

Period 1 2 3 4 5 6 7 8 Total

Forecast 120 135 140 120 125 125 140 135 1,040Output

Regular 120 130 130 120 125 125 130 130 1,010Overtime 5 10 10 5 30Subcontract

Output - Forecast 0 (5) (10) 0 0 0 (10) (5)Inventory

BeginningEndingAverage

Backlog

Costs:Output

Regular @ 60 $7,200 7,800 7,800 7,200 7,500 7,500 7,800 7,800 $60,600Overtime @ 90 450 900 900 450 2,700Subcontract

Inventory @ 5Backorder

Total 7,200 8,250 8,700 7,200 7,500 7,500 8,700 8,250 $63,300

b.Period 1 2 3 4 5 6 7 8 Total

Forecast 120 135 140 120 125 125 140 135 1,040Output

Regular 130 130 130 130 130 130 130 130 1,040OvertimeSubcontract

Output - Forecast 10 (5) (10) 10 5 5 (10) (5)Inventory

Beginning 0 10 5 0 5 10 15 5Ending 10 5 0 5 10 15 5 0Average 5 7.5 2.5 2.5 7.5 12.5 10 2.5

Backlog 5

Costs:Output

Regular @ 60 $7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 $62,400OvertimeSubcontract @ 50

Inventory @ $2 10 15 5 5 15 25 20 5 100

Backorder @ $90 450 450Total $7,810 7,815 8,255 7,805 7,815 7,825 7,820 7,805 $62,950


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6. a.

Period 1 2 3 4 5 6 7 Total

Forecast 250 300 250 300 280 275 270Output

Regular 250 275 250 275 275 275 250 1,850Overtime 25 25 5 20 75Subcontract

Output - ForecastInventory

BeginningEndingAverage

Backlog

Costs:Output

Regular @ 40 $10,000 11,000 10,000 11,000 11,000 11,000 10,000 $74,000Overtime @ 60 1,500 1,500 300 1,200 4,500Subcontract

InventoryBackorder

Total $10,000 12,500 10,000 12,500 11,300 11,000 11,200 $78,500

b.

Period 1 2 3 4 5 6 7 Total

Forecast 250 300 250 300 280 275 270 1,925Output

Regular 275 275 275 275 275 275 250 1,900OvertimeSubcontract 5 20 25

Output - Forecast 25 25 25 25 0 0 0Inventory

Beginning 0 25 0 25 0 0 0Ending 25 0 25 0 0 0 0Average 12.5 12.5 12.5 12.5 0 0 0 50

Backlog 0 0 0 0 0 0 0 0

Costs:Regular 11,000 11,000 11,000 11,000 11,000 11,000 10,000 76,000Overtime 0Subcontract 250 1,000 1,250

Inventory 25 25 25 25 100Backorder 0

Total 11,025 11,025 11,025 11,025 11,250 11,000 11,000 77,350


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7. a. No backlogs are allowed

Period Mar. Apr. May Jun. July Aug. Sep. Total

Forecast 50 44 55 60 50 40 51 350Output

Regular 40 40 40 40 40 40 40 280Overtime 8 8 8 8 8 3 8 51Subcontract 2 0 3 12 2 0 0 19


Beginning 0 0 4 0 0 0 3Ending 0 4 0 0 0 3 0Average 0 2 2 0 0 1.5 1.5 7

Backlog 0 0 0 0 0 0 0 0

Costs:Regular 3,200 3,200 3,200 3,200 3,200 3,200 3,200 22,400Overtime 960 960 960 960 960 360 960 6,120Subcontract 280 0 420 1,680 280 0 0 2,660

Inventory 0 20 20 0 0 15 15 70

Total 4,440 4,180 4,600 5,840 4,440 3,575 4,175 31,250

b. Level strategy

Period Mar. Apr. May Jun. July Aug. Sep. Total

Forecast 50 44 55 60 50 40 51 350Output

Regular 40 40 40 40 40 40 40 280Overtime 8 8 8 8 8 8 8 56Subcontract 2 2 2 2 2 2 2 14


Beginning 0 0 6 1 0 0 1Ending 0 6 1 0 0 1 0Average 0 3 3.5 .5 0 .5 .5 8

Backlog 0 0 0 9 9 0 0 18

Costs:Regular 3,200 3,200 3,200 3,200 3,200 3,200 3,200 22,400Overtime 960 960 960 960 960 960 960 6,720Subcontract 280 280 280 280 280 280 280 1,960

Inventory 30 35 5 0 5 5 80Backlog 180 180 360

Total 4,440 4,470 4,475 4,625 4,620 4,445 4,445 31,520


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8. a. Level production supplemented with overtime as needed.

Period 1 2 3 4 5 6 Total

Forecast 4,000 4,800 5,600 7,200 6,400 5,000 33,000Output

Regular 5,000 5,000 5,000 5,000 5,000 5,000 30,000Overtime 1,600 1,400 3,000

Output - Forecast 1,000 200 600 600 0 0 0Inventory

Beginning 1,000 1,200 600 0 0Ending 1,000 1,200 600 0 0 0Average 500.0 1,100.0 900.0 300.0 0.0 0.0 2,800

Backlog 0 0 0 0 0 0 0

Costs:Regular @ 10 50,000 50,000 50,000 50,000 50,000 50,000 300,000Overtime @ 16 0 0 0 25,600 22,400 0 48,000

Inventory @ 1 500 1,100 900 300 0 0 2,800Back orders @ 10 0 0 0 0 0 0 0

Total 50,500 51,100 50,900 75,900 72,400 50,000 350,800

b. Combination of overtime, inventory and subcontracting to handle variations indemand. Max. overtime = 500, max. subcontracting = 500 units.


Forecast 4,000 4,800 5,600 7,200 6,400 5,000 33,000Output

Regular 5,000 5,000 5,000 5,000 5,000 5,000 30,000Overtime 500 500 500 500 500 2,500Subcontract 500 500

Output - Forecast 1,500 700 100 1,700 400 0 0Inventory

Beginning 1,500 2,200 2,100 400 0Ending 1,500 2,200 2,100 400 0 0Average 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 50,000 300,000Overtime @ 16 8,000 8,000 8,000 8,000 8,000 0 40,000Subcontract @ 20 0 0 0 0 10,000 0 10,000

Inventory @ 1 750 1,850 2,150 1,250 200 0 6,200Back orders @ 10 0 0 0 0 0 0 0

Total 58,750 59,850 60,150 59,250 68,200 50,000 356,200


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c. Overtime up to 750 units per period maximum to handle variations in demand.


Forecast 4,000 4,800 5,600 7,200 6,400 5,000 33,000Output

Regular 5,000 5,000 5,000 5,000 5,000 5,000 30,000Overtime 750 750 750 750 3,000

Output - Forecast 1,000 950 150 1,450 650 0 0Inventory

Beginning 1,000 1,950 2,100 650 0Ending 1,000 1,950 2,100 650 0 0Average 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 50,000 300,000Overtime @ 16 0 12,000 12,000 12,000 12,000 0 48,000

Hire/Lay off 0Inventory @ 1 500 1,475 2,025 1,375 325 0 5,700Back 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 a because $350,800 < 353,700 < 356,200.

9.


Forecast 160 150 160 180 170 140 960Output

Regular 150 150 150 150 160 160 920Overtime 10 10 0 10 10 10 50

Subcontract 0 0 10 10 0 0 20Output- Forecast 0 10 0 10 0 0Inventory

Beginning 0 0 10 10 0 0Ending 0 10 10 0 0 0Average 0 5 10 5 0 0 20

Backlog 0 0 0 0 0 0 0

Costs:Regular 7,500 7,500 7,500 7,500 8,000 8,000 46,000Overtime 750 750 0 750 750 750 3,750Subcontract 0 0 800 800 0 0 1,600

Inventory 20 40 20 80Backlog 0 0 0 0 0 0

Total 8,250 8,270 8,340 9,070 9,050 8,750 51,430


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10. Plan B: Hire one worker and subcontract. Workforce = 20 + 1 = 21 workers.

Period 1 2 3 4 5 6 7 8 9 TotalForecast 190 230 260 280 210 170 160 260 180 1,940

Output

Regular 210 210 210 210 210 210 210 210 210 1,890Overtime Subcontract 10 20 20 50

Out ut-Forecast 30 0 30 70 0 40 50 50 30

InventorBe innin 0 30 30 0 0 0 0 20 0Endin 30 30 0 0 0 0 20 0 0Avera e 15 30 15 0 0 0 10 10 0 80

Backlo 0 0 0 70 70 30 0 30 0 200

Costs:Out ut

Regular @ 6 $1,260 1,260 1,260 1,260 1,260 1,260 1,260 1,260 1,260 $11,340

OvertimeSubcontract 8 80 160 160 0 0 0 0 0 0 $400Inventor 5 75 150 75 0 0 0 50 50 0 $400Backorder 10 0 0 0 700 700 300 0 300 0 $2,000Total $1,415 1,570 1,495 1,960 1,960 1,560 1,310 1,610 1,260 $14,140

The total cost for Plan B is $14,140 plus $200 to hire one additional worker. Total = $14,340.

Plan C: No additional workers are to be hired. It is assumed that the present workforce is retained. Onlysubcontracting is to be used with a maximum of 20 per period.

Period 1 2 3 4 5 6 7 8 9 TotalForecast 190 230 260 280 210 170 160 260 180 1,940

Output

Regular 200 200 200 200 200 200 200 200 200 1,800

Overtime Subcontract 20 20 20 20 20 20 0 20 0 140

Out ut-Forecast 30 10 40 60 10 50 40 40 20

InventorBe innin 0 30 20 0 0 0 0 20 0Endin 30 20 0 0 0 0 20 0 0Avera e 15 25 10 0 0 0 10 10 0 70

Backlo 0 0 20 80 70 20 0 20 0 210

Costs:Output

Regular @ 6 $1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 $10,800Overtime

Subcontract 8 160 160 160 160 160 160 0 160 0 $1,120Inventor 5 75 125 50 0 0 0 50 50 0 $350Backorder 10 0 0 200 800 700 200 0 200 0 $2,100Total $1,435 1,485 1,610 2,160 2,060 1,560 1,250 1,610 1,200 $14,370

Plan Total Cost Rank

A $14,290 3B 14,370 2C 14,370 1

The lowest cost is for Plan A = $14,290.


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11. Assume that the $5 cost per unit for the temporary workers is in addition to $6 per unit for regulartime cost. Part-time workers are to be hired to produce at least 170 units.

Period 1 2 3 4 5 6 7 8 9 TotalForecast 190 230 260 280 210 170 160 260 180 1 940Out ut

Re ular 200 200 200 200 200 200 200 200 200 1,800Part-Time 50 50 50 150Subcontract

Output-Forecast 10 20 10 30 10 30 40 60 20

InventorBe innin 0 10 30 20 0 0 10 50 0Ending 10 30 20 0 0 10 50 0 10Average 5 20 25 10 0 5 30 25 5 125

Backlog 0 0 0 10 20 0 0 10 0 40

Costs:Out ut

Regular 6 $1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 1,200 $10,800

Part-Time 11 550 550 550 $1,650SubcontractInventory 5 25 100 125 50 0 25 150 125 25 $625Backorder 10 0 0 0 100 200 0 0 100 0 $400Total $1 225 1 850 1 875 1 900 1 400 1 225 1 350 1 425 1 225 $13 475

20 x 9 = 180 The same number of part-time workers must be used in any period where they are used.It is assumed that a worker (part-time) will work for the entire period producing 10 units.With these constraints it is necessary to produce more than 170 units by using part-timeworkers. Employ 5 temporary workers during periods 2, 3, and 4 with a total cost of$13,475.

30 x 6 = 18040 x 5 = 20050 x 4 = 20060 x 3 = 18070 x 3 = 210


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12. Objective here is to minimize backlogs.

Period 1 2 3 4 5 6 7 8 9 TotalForecast 190 230 260 280 210 170 160 260 180 2 570

Out utRe ular 200 200 200 200 200 200 200 200 200 2,400

Overtime 25 25 25 25 25 15 170Subcontract 0 0 0 0 0 0 0 0 0Out ut-

Forecast 35 5 35 55 15 45 40 60 20Inventor

Be innin 0 35 30 0 0 0 0 40 0Endin 35 30 0 0 0 0 40 0 0Avera e 17.5 32.5 15 0 0 0 20 20 0 252

Backlo 0 0 5 60 45 0 0 20 0 130

Costs:Out ut

Re ular 6 $1 200 1 200 1 200 1 200 1 200 1 200 1 200 1 200 1 200 $10 800Overtime 9 225 225 225 225 225 135 0 0 $1,260Subcontract 0 0 0 0 0 0 0 0 0

Inventor 5 87.5 162.5 75 0 0 0 100 100 0 $525Backorder 10 0 0 50 600 450 0 0 200 0 $1,300Total $1,512.5 1,587.5 1,550 2,025 1,875 1,335 1,300 1,500 1,200 $13,885

If minimization of cost is the primary objective (instead of Min. backlogs), overtime units in period 6could be reduced to 0. The cost for this plan is $13,885.


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13. Several solutions are possible. Here is one.

Period 1 2 3 4 5 6 7 8 9 Total

Forecast 190 230 260 280 210 170 160 260 180 1,940Output

Regular 210 210 210 210 210 180 180 180 180 1,770Overtime 10 25 25 10 70

Subcontract 20 20 20 20 20 100

Output-

Forecast 20 10 (5) (25) 0 10 40 (50) 0

Inventory

Beginning 0 20 30 25 0 0 10 50 0

Ending 20 30 25 0 0 10 50 0 0

Average 10 25 27.5 12.5 0 5 30 25 0 135

Backlog 0 0 0 0 0 0 0 0 0

Costs:Output

Regular @ 6 $1,260 1,260 1,260 1,260 1,260 1,080 1,080 1,080 1080 $10,620

Overtime @ 9 0 90 225 225 0 0 0 90 0 $630

Subcontract @ 8 0 160 160 160 0 0 160 160 0 $800

Hiring @ 200 200 0 0 0 0 0 0 0 0 $200

Layoff-firing @100 0 0 0 0 0 300 0 0 0 $300

Inventory @ 5 50 125 137.5 62.5 0 25 150 125 0 $675

Backorder @ 10 0 0 0 0 0 0 0 0 0 $0

Total 1,510 1,635 1,782.5 1,707.5 1,260 1,405 1,390 1,455 1,080 $13,225


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14.

1 0 1 91Period 1 2 3 Unused Cap Total+1 Be . Inv. 0 1 2 0

100 0 0 90 10061 Re . 60 61 62 0

1450 50 0 30 500

81 Over. 80 81 82 00 50 0 10 50

91 Sub. 90 91 92 00 30 0 90 120

60 Re . 63 60 61 0

24 500 0 31 500

80 Over. 83 80 81 04 50 0 11 50

90 Sub. 93 90 91 04 20 100 1 120

59 Re . 66 63 60 0

38 4 500 32 500

79 Over. 86 83 80 08 4 50 12 50

89 Sub. 96 93 90 08 4 100 2 100

Demand 550 700 750 90 2,090

15.

2 0 2 92 TotalPeriod 1 2 3 4 Ca .21 Be . Inv. 0 2 4 0

100 0 0 +90 10062 Re . 60 62 64 0

1450 50 0 +30 50082 Over. 80 82 84 0

0 50 0 +10 5092 Sub. 90 92 94 0

0 0 30 90 12060 Re . 63 60 62 0

2

5 500 0 +32 50080 Over. 83 80 82 0

5 50 0 +12 5090 Sub. 93 90 92 0

5 50 70 +2 12058 Re . 66 63 60 0

3

10 5 500 +34 50078 Over. 86 83 80 0

10 5 50 +14 5088 Sub. 96 93 90 010 5 100 +4 100

Demand 550 700 750 90 2,090

The solution is optimal with a total cost of $124.960.


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16.Number of sources: 10 Number of destinations: 4

Destinations

1 2 3 4 Su l1 0 1 2 0 1002 60 61 62 0 5003 80 81 82 0 504 90 91 92 0 1205 63 60 61 0 500

Sources 6 83 80 81 0 507 93 90 91 0 1208 66 63 60 0 4409 86 83 80 0 50

10 96 93 90 0 100

Demand 550 700 750 30

Iteration: 3 Total cost: $126,650

Destinations1 2 3 4 Su l

1 100 0 0 90 1002 450 50 0 30 5003 0 50 0 10 504 0 90 0 30 1205 4 500 0 31 500

Sources 6 4 ( 10 ) ( 40 ) 11 507 4 0 120 1 1208 8 4 440 32 4409 8 4 50 12 50

10 8 4 100 2 100

Demand 550 700 750 30( ) = number of units to ship, other entries are reduced costs.

Optimal solution:Iteration: 3Total shipping cost : $126,650Shi 100 units from source 1 to dest. 1Shi 450 units from source 2 to dest. 1Shi 50 units from source 2 to dest. 2Shi 50 units from source 3 to dest. 2Shi 90 units from source 4 to dest. 2Shi 500 units from source 5 to dest. 2Shi 30 units from source 4 to dest. 4Shi 40 units from source 6 to dest. 3Shi 120 units from source 7 to dest. 3Shi 440 units from source 8 to dest. 3Shi 50 units from source 9 to dest. 3Shi 100 units from source 10 to dest. 3Shi 10 units from source 6 to dest. 2

Additional cost = $126,650 $124,730 = $1,920


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17.Problem title: 914 AP

Number of sources: 10Number of destinations: 4

Destinations1 2 3 4 Supply

1 0 2 4 0 100

2 60 62 64 0 5003 80 82 84 0 504 90 92 94 0 1205 63 60 62 0 500

Sources 6 83 80 82 0 507 93 90 92 0 1208 66 63 60 0 4409 86 83 80 0 50

10 96 93 90 0 100

Demand 550 700 750 30Iteration: 3Total Cost: $127,000

Destinations

1 2 3 4 Su l1 100 0 0 90 1002 450 50 0 30 5003 0 ( 50 ) 0 10 504 0 90 0 30 1205 5 ( 500 ) 0 32 500

Sources 6 5 10 40 12 507 5 0 ( 120 ) 2 1208 10 5 440 34 4409 10 5 ( 50 ) 14 50

10 10 5 100 4 100

Demand 550 700 750 30( ) = number of units to ship, other entries are reduced costs.

Optimal solution:Iteration: 3Total shipping cost: $127,00Shi 100 units from source 1 to dest. 1Shi 450 units from source 2 to dest. 1Ship 50 units from source 2 to dest. 2Shi 50 units from source 3 to dest. 2Ship 90 units from source 4 to dest. 2Shi 500 units from source 5 to dest. 2Ship 30 units from source 4 to dest. 4Shi 40 units from source 6 to dest. 3Shi 120 units from source 7 to dest. 3Shi 440 units from source 8 to dest. 3

Shi 50 units from source 9 to dest. 3Shi 100 units from source 10 to dest. 3Shi 10 units from source 6 to dest. 2

Additional cost = $127,000 $126,650 = $350


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18. a. Initially, David should develop one aggregate plan for the next sixmonths in order to determine his output rate, employment levels and changes, inventorylevels and changes, back orders, and subcontracting. This will help him to achieve a planthat will more effectively and efficiently utilize the organizations resources to satisfy

expected demand. For the first two months though, David will need to disaggregate hisplan into a short-run master schedule for each size wheel. Adjustments will be made in theplanning process as needs arise over time and the planning horizon gets shorter.

b. and c.

Nov. Dec. Jan. Feb. Mar. April Total

Forecast 1,500 1,400 900 1,200 1,500 1,700 8,200

Output Reg. 1,400 1,400 1,400 1,400 1,400 1,400 8,400

OutputOvertime

17 17 17 17 17 15 100

OutputMinus

Forecast

(83) 17 517 217 (83) (285) 300

InventoryBegin

0 0 0 451 668 585 300

Ending 0 0 451 668 585 300

Average 0 0 225.5 559.5 626.5 442.5 1,854

Backlog 83 66 0 0 0 0 149.0

Cost Reg. 7,000 7,000 7,000 7,000 7,000 7,000 42,000

Overtime 127.50 127.50 127.50 127.50 127.50 112.50 750

Inventory 0 0 225.50 559.5 626.5 442.5 1,854

Backorders $498 396 0 0 0 0 894

PersonnelLayoffs

800.00 800

Totals $8,425.50 $7,523.50 $7,353.00 $7,687 $7,754 $7,555 $46,298


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19. June July

64 1 2 3 4 5 6 7 8

Forecast 30 30 30 30 40 40 40 40

Customer

Orders33 20 10 4 2

Projectedon-handinventory

31 71 41 11 41 71 31 61

MPS 70 70 70 70

ATP 31 36 68 70 70

Week

InventoryFrom Pre-vious Wk. Requirements

NetInventoriesBefore MPS (70) MPS

ProjectedOn-HandInventory

1 64 33 31 31

2 31 30 1 70 71

3 71 30 41 414 41 30 11 11

5 11 40 29 70 41

6 41 40 1 70 71

7 71 40 31 31

8 31 40 9 70 61

20. June July

64 1 2 3 4 5 6 7 8

Forecast 30 30 30 30 40 40 40 40

Customer

Orders 33 25 16 11 8 3Projectedon-handinventory

31 1 41 11 41 1 31 61

MPS 70 70 70 70

ATP 6 43 59 70 70

Week

InventoryFrom Pre-vious Wk. Requirements

NetInventoriesBefore MPS (70) MPS

ProjectedOn-HandInventory

1 64 33 31 31

2 31 30 1 1

3 1 30 29 70 414 41 30 11 11

5 11 40 29 70 41

6 41 40 1 1

7 1 40 39 70 31

8 31 40 9 70 61


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Case: Eight Glasses a Day

Strategy 1: Level production supplemented by up to 10 tank loads a month from overtime.

Period May Jun. Jul. Aug. Sep. Oct. TotalForecast 50 60 70 90 80 70 420

Out utRe ular 60 60 60 60 60 60 360Overtime 10 10 10 10 10 10 60Subcontract

Out ut - Forecast 20 10 0 20 10 0Inventor

Be innin 0 20 30 30 10 0Endin 20 30 30 10 0 0Avera e 10 25 30 20 5 0 90

Backlo 0 0 0 0 0 0Costs:

Re ular $10 600 600 600 600 600 600 3,600Overtime $16 160 160 160 160 160 160 960

Inventory 20 50 60 40 10 0 180Backlo 0 0 0 0 0 0 0Total 780 810 820 800 770 760 4,740

Strategy 2: A combination of overtime, inventory and subcontracting.

Period May Jun. Jul. Aug. Sep. Oct. TotalForecast 50 60 70 90 80 70 420Out ut

Re ular 60 60 60 60 60 60 360Overtime 10 10 10 10 10 50Subcontract 10 10

Out ut - Forecast 10 10 0 20 0 0Inventor

Be innin 0 10 20 20 0 0Endin 10 20 20 0 0 0

Avera e 5 15 20 10 0 0 50Backlo 0 0 0 0 0 0 0Costs:

Re ular $10 600 600 600 600 600 600 3,600Overtime $16 0 160 160 160 160 160 800Subcontract $18 180 180

Inventor 10 30 40 20 0 0 100Backlog 0 0 0 0 0 0 0Total 610 790 800 780 940 760 4,680


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Strategy 3: Using inventory up to 15 tank loads a month from overtime.

Period Ma Jun. Jul. Au . Se . Oct. TotalForecast 50 60 70 90 80 70 420Out ut

Regular 60 60 60 60 60 60 360Overtime 5 15 15 15 10 60

SubcontractOut ut - Forecast 10 5 5 15 5 0Inventor

Be innin 0 10 15 20 5 0Endin 10 15 20 5 0 0Avera e 5 12.5 17.5 12.5 2.5 0 50

Backlo 0 0 0 0 0 0 0Costs:

Re ular $10 600 600 600 600 600 600 3,600Overtime $16 0 80 240 240 240 160 960Subcontract $18

Inventor 10 25 35 25 5 0 100Backlo 0 0 0 0 0 0 0Total 610 705 875 865 845 760 4,660

Since $4,660 < $4,680 < $4,740, the company should choose the third strategy.

chap013 rev

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