Production and Operations Management Systems Chapter 4: Capacity Management and Aggregate Production...

Production and Operations Management Systems

Chapter 4: Capacity Management and Aggregate Production Planning

Sushil K. Gupta

Martin K. Starr

2014

1

After reading this chapter, you should be able to:

Define and measure capacity

Make clear what aggregation does and why that is important.

Explain the function of aggregate planning (AP).

Discuss the systems nature of AP in terms of classes of resources and product-mix families.

Explain standard units of work.

Relate the importance of forecasting to AP.

2

After reading this chapter, you should be able to (continued):

Compare constant (or level) production with a chasing policy—where supply chases demand.

Detail the cost structure for aggregate planning.

Develop aggregate plans using overtime and subcontracting.

Distinguish between planning for manufacturing and service industries.

3

Definitions of Capacity

Definition of Available Capacity: The amount of resource time that is available to deliver product. This translates into the maximum number of units of goods or services that can be delivered in a given period of time. These units can be used for inventory or for shipment to customers.

Example: There are 3 machines. These 3 provide 120 hours of available capacity per week. It takes 2 hours to make a unit. So available capacity translates into 60 units. Less efficient machines take longer, so fewer units can be made. In that case, actual capacity is less than available capacity.

4

Classic Formula for Capacity Utilized*

C = T x E x U

C = actual capacity used (std. hours*)

T = available capacity (max cap.)

E = efficiency (percent)

U = utilization (percent)

*all times are in standard hours

5

Capacity Stated in Standard Hours Time is measured in standard hours to provide a basis for

aggregating different jobs on different machines. Pick the fastest production systems (machines, people, etc.) as

the basis for the production time standard. E = 1 for best-in-class efficiency (best machine-best job) Less-than-best efficiency is < 1 Jobs, machines, materials, workers, and methods interact

resulting in different E values.

6

Example using the Equation for Capacity Utilized T = 120 standard hours - std. hrs. E = 90% of standard time (E = 0.9) U = 92.6% (machine breakdown, U = 0.9259) C = T x E x U = 100 std. hrs. R = 100/120 = 0.833 (ratio actual/available) D = demand = 120 std. hrs. (D - C) = 20 std. hrs.(unfilled orders to be carried over to next

week)

7

Theoretical vs. Actual capacityActual Capacity is the Greatest Output rate achievable with the Real process.

It is less than the theoretical capacity because of breakdowns, under-utilized facilities etc.

Some examples that reduce theoretical capacity include:oThe storm limits power that can be delivered.oWater main break decreases flow to the fire department.oSupplier of tubes for Tom’s of Maine has a strike, and it is now necessary to find a new source.

8

Aggregate Production Planning

An aggregate production plan provides the production rate and the number of workers required in each period (generally a month).

These are medium term plans that span over a period of 6 to 18 months.

The plans are made at the aggregate demand level which includes demand for all products.

The definition of aggregate is a collection, conglomeration, assemblage.

9

Types of Production Plans

The following three plans will be presented:

Level Plan: The number of units produced in each month is constant at a chosen level.

Chase Plan: The number of units produced in a given month is equal to the exact demand in that month.

Mixed or Hybrid Plan: The number of units produced is constant at a given level for a few months and then changes. The level may change several times.

10

Example 1: Data

Period 1 2 3 4 5 6 7 8 9 10 11 12 Total Average

Demand 210 440 600 300 480 610 560 800 200 400 380 540 5520 460

The fluctuating demand for 12 periods (months) is given in the second row in the table below.

The total demand is 5,520 units and the average demand is 460 units per month.

Problem: Develop a production plan.

A production plan gives the number of units to be produced in each month.

11

Example 1: Level Plan

Demand Data Level Production Plan

MonthExpected Demand

Production Plan

Cumulative Demand

Cumulative Production

Inventory

1 210 460 210 460 250

2 440 460 650 920 270

3 600 460 1250 1380 130

4 300 460 1550 1840 290

5 480 460 2030 2300 270

6 610 460 2640 2760 120

7 560 460 3200 3220 20

8 800 460 4000 3680 -320

9 200 460 4200 4140 -60

10 400 460 4600 4600 0

11 380 460 4980 5060 80

12 540 460 5520 5520 0

Total 5520 5520

Average 460

Note: Inventory = Cumulative Production - Cumulative Demand

In this plan the production quantity is constant at the average demand level, 460 (= 5,520/12) units per month.

The plan results in inventory in some months and shortages in other months. See table on right hand side (RHS).

The inventory level in any month is the difference between cumulative production and cumulative demand in that month.

12

Example 1: Graph for Level Plan

The solid line shows cumulative demand; cumulative production is depicted by the dotted line.

In some periods the dotted line is above the solid line (indicating inventory).

In other periods the dotted line is below the solid line (indicating shortages).

This plan is not suitable for service industries because services cannot be inventoried.

13

Example 1: Chase Plan

Demand Data Chase Production Plan


Cumulative Demand

Production Plan


Inventory

1 210 210 210 210 0

2 440 650 440 650 0

3 600 1250 600 1250 0

4 300 1550 300 1550 0

5 480 2030 480 2030 0

6 610 2640 610 2640 0

7 560 3200 560 3200 0

8 800 4000 800 4000 0

9 200 4200 200 4200 0

10 400 4600 400 4600 0

11 380 4980 380 4980 0

12 540 5520 540 5520 0

Total 5520


In the Chase plan, production is equal to the demand in every period.

There are no inventories and no shortages in this plan. See table on RHS.

14

Example 1: Graph for Chase Plan

The cumulative production and cumulative demand graphs overlap as shown in figure on RHS.

No inventories and no shortages occur.

15

Example 1: Hybrid (Mixed) PlanDemand Data Mixed Production Plan


Cumulative Demand

Production Plan


Inventory

1 210 210 440 440 230

2 440 650 440 880 230

3 600 1250 440 1320 70

4 300 1550 440 1760 210

5 480 2030 440 2200 170

6 610 2640 440 2640 0

7 560 3200 680 3320 120

8 800 4000 680 4000 0

9 200 4200 380 4380 180

10 400 4600 380 4760 160

11 380 4980 380 5140 160

12 540 5520 380 5520 0

Total 5520


Produce 440 units (average demand of the first six months) per month for months 1 thru 6.

Change the production level to 680 units per month for the next two months (average demand of months 7 and 8).

Produce 380 units (average demand of last four months) per month for the last four months.

16

Example 1: Graph for Hybrid Plan

The proposed plan is depicted graphically in figure on RHS.

There could be inventories and/or shortages in this plan.

Inventories occur but no shortages exist in this plan.

Hybrid plans are based on judgment; and different hybrid plans will give different inventory/shortage levels.

17

Regular Time Production Capacity, Overtime and Subcontracting

Feasibility of the three plans depends on the productive capacity of the plant.

Capacity constraints exist; these plans are developed within those constraints.

Assume: single shift regular time production capacity is 480 units per month.

This is sufficient for the level plan in which production is 460 units per month.

There will be idle capacity of 20 (480 – 460) units per month.

If planned production exceeds the regular time production capacity in any month then production using overtime and/or subcontracting may be needed. This is discussed in the next slide for the hybrid plan.

18

Regular Time Production Capacity, Overtime and Subcontracting (continued)

In the hybrid plan, 440 units are produced every month during regular time for the first six months. Therefore, there will be idle capacity of 40 (480-440) units in each of the first six month.

Similarly, during the last 4 months the idle capacity will be 100 (480-380) units per month since the production level is 380 units per month. In months 7 and 8, the production level is 680 units per month of which 480 units can be produced during regular time.

The additional 200 units have to be obtained by working overtime and/or through subcontracting.

19

Regular Time Production Capacity, Overtime and Subcontracting (continued)

There are always limits on overtime production and amount of subcontracting.

Suppose overtime is limited to 20% of regular time production meaning 96 (20% of 480) units can be produced using overtime per month.

Therefore, 480 units can be produced during regular time and 96 units can be produced using overtime in months 7 and 8.

The remaining 104 (680 – 480 – 96) units will be obtained through subcontracting.

The maximum number of units that can be subcontracted depends on the availability of appropriate suppliers.

20

Best Plan?

Which plan is the best? There are cost implications for each plan. The plan that minimizes the total cost is the best cost plan.* What are the costs?

21

*Other factors may need to be considered such as the effect on morale caused by workforce disruption

Costs in APP

Cost of carrying (holding) inventories. Cost of shortages or back orders. Regular time production cost. Overtime production cost. Cost of subcontracting or outsourcing. Cost of idle facilities and workers. Cost of changing production levels – up or down. This is

usually accomplished by hiring or firing workers. Material Cost

22

Example 2: Aggregate Manufacturer’s Production Planning

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TotalAverag

eExpected Demand (Units)

400 440 600 396 480 610 560 650 450 350 380 540 5856 488

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251 Demand per Day (Units)

18.18 22.00 27.27 18.86 24.00 27.73 29.47 29.55 20.45 16.67 19.00 27.00 23.33

The table below gives the expected demand (row 2) and number of working days per month (row 3) for a 12-month planning horizon. The total number of working days in the year is 251.

The total yearly demand is 5,856 product units (henceforth called units) with an average of 488 units per month.

The demand varies from a high of 650 units in August to a low of 350 units in October. The demand per day for each month and the average demand for the 12-month planning

period (23.33) are also included in the following table.

23

*Note: This example employs fractional numbers for production per day. Therefore, rounding errors can be expected to occur

Example 2: Cost and Capacity DataCapacity Data Assumptions

o Production time/unit is 4 hours.

o 8 hours per day for each worker. o The number of workers remains

constant for entire month.

o The plant currently produces 21 units per day.

o Beginning inventory = 0.o No defective items are produced.

Cost Data Assumptions

24

Shortage cost per unit per period $100

Inventory carrying (holding) costs per unit per period cost

$25

Cost of increasing production level per unit* $200

Cost of decreasing production level per unit* $300

Regular time labor cost per hour $20

Overtime labor cost per hour $30

Subcontracting (outsourcing) cost per unit $650

Material cost per unit $100

*Increase and decrease in production levels are normally achieved by hiring and firing workers

Calculating Production LevelsProduction level per day in any month = Production in that month/working days in that month

Suppose in a given month, say March, we expect to produce 600 units and the number of working days is 22. Then to produce 600 units in 22 days,

Production level per day = 600/22 = 27.27.

The fractional result can be interpreted in various ways. It can be rounded up with extra production being treated as inventory.

Alternatively, it can be rounded down and extra units are completed using overtime. We deal with a production level of 27.27 units as production of 27 units on that given day; then, production continues to work on the unfinished product on the next day.

25

Calculating Number of WorkersNumber of Workers = (Units x Production Time per Unit)/Hours Worked

Suppose each employee works for 8 hours per day and required production time is 4 hours per unit.

To achieve a production level of 27.27 in March, the required number of workers is: (27.27 x 4)/8 = 13.64.

A work force of 13.64 is considered as 13 full time workers and 0.64 part time workers.

26

Example 2: Level PlanMonth Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total Average

Expected Demand (Units) 400 440 600 396 480 610 560 650 450 350 380 540 5856 488

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251

Production per Day (Units) 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33

Total Production (Units) 513 467 513 490 467 513 443 513 513 490 467 467 5856

Inventory Addition/ Shortages (Units) 113 27 -87 94 -13 -97 -117 -137 63 140 87 -73

Ending Inventory/ Shortages (Units) 113 140 53 147 134 37 -80 -216 -153 -13 73 0

Ending Inventory (Units) 113 140 53 147 134 37 0 0 0 0 73 0 697

Ending Shortages (Units) 0 0 0 0 0 0 80 216 153 13 0 0 462

Inventory Cost ($) 2825 3500 1325 3675 3350 925 0 0 0 0 1825 0 17425

Shortage Cost ($) 0 0 0 0 0 0 8000 21600 15300 1300 0 0 46200

Change in Production Level (Units) 2.33 0 0 0 0 0 0 0 0 0 0 0

Change in Production Level - Up (Units)

2.33 0 0 0 0 0 0 0 0 0 0 0 2

Change in Production Level - Down (Units)

0.00 0 0 0 0 0 0 0 0 0 0 0 0

Cost of Changing Production Level Up ($)

466.14 0 0 0 0 0 0 0 0 0 0 0 466

Cost of Changing Production Level Down ($)

0.00 0 0 0 0 0 0 0 0 0 0 0 0

Sample calculations for this plan are shown in the next two slides.

27

Sample Calculations for Level Plano Production/Day = 23.33 units.o Production in any given month = Number of days in that month x 23.33.o The production numbers are rounded to the nearest integer. o For example, in January 513 is the number of units produced where

(23.33 x 22 = 513.26),o However, the demand in January is only 400 units. Therefore, 113 (513 - 400) units

go into inventory. o In February, 467 (23.33 x 20) units are produced whereas the expected demand is

for 440 units. o Therefore, 27 units (467 – 440) are added to inventory and the inventory level at

the end of February is 140. o In March, the production is 513 (23.33 x 22) which is 87 units less than the demand

(600 units). o Therefore 87 units are withdrawn from inventory to meet the demand for March. o The inventory level at the end of March becomes 53. o In this way, the calculations continue.

28

Sample Calculations for Level Plan (continued)

Shortages occur in any month if (production + inventory) is less than demand.

The inventory and shortage costs in each month are calculated by multiplying the end of month inventory or shortage by the respective costs.

The costs of this plan are:

29

Category Level Plan

Regular time Labor Cost $468,480Over Time Labor Cost Inventory carrying Cost $17,425Shortage Cost $46,200Increasing Production level $466Decreasing Production level Material Cost $585,600Total Cost $1,118,171

Note: rounding errors can make small changes in the various totals

Example 2: Chase PlanMonth Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total

Expected Demand (units)

400 440 600 396 480 610 560 650 450 350 380 540 5856

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251

Production per Day (units)

18.18 22.00 27.27 18.86 24.00 27.73 29.47 29.55 20.45 16.67 19.00 27.00

Total Production (units)

400 440 600 396 480 610 560 650 450 350 380 540 5856

Inventory Addition/ Shortages (units)

There are no inventories or shortages in this plan.

Change in Production Level (Units)

-2.82 3.82 5.27 -8.42 5.14 3.73 1.75 0.07 -9.09 -3.79 2.33 8.00


0.00 3.82 5.27 0.00 5.14 3.73 1.75 0.07 0.00 0.00 2.33 8.00 30.11


2.82 0.00 0.00 8.42 0.00 0.00 0.00 0.00 9.09 3.79 0.00 0.00 24.11

Number of Workers 9.09 11.00 13.64 9.43 12.00 13.86 14.74 14.77 10.23 8.33 9.50 13.50

30

Sample calculations for this plan are shown in the next slide.

Sample Calculations for Chase PlanIn this plan there are no inventories or shortages.

However, the production level has to be adjusted in each month. For example,

In January the production level is 18.18 units per day. Therefore, the production level is reduced by 2.82 (21-18.18) units.

In February the production level increases to 22 and the level has to be adjusted upward by 3.82 (level in February – level in January = 22-18.18) units.

Note: rounding errors can make small changes in the various totals.



31

Category Chase Plan

Regular time Labor Cost $468,480Over Time Labor Cost Inventory carrying Cost Shortage Cost Increasing Production level $6,023Decreasing Production level

$7,234

Material Cost $585,600Total Cost $1,067,336

Example 2: Hybrid (Mixed) Plan Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total

Expected Demand (Units)

400 440 600 396 480 610 560 650 450 350 380 540 5856

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251

Production per DayAverage Demand per Day (Jan to Jun)

Average Demand per Day (Jul to Sep)

Average Demand per Day (Oct to Dec)

23.04 23.04 23.04 23.04 23.04 23.04 26.35 26.35 26.35 20.82 20.82 20.82

Total Production (Units)

507 461 507 484 461 507 501 580 580 437 416 416 5856

Inventory Addition/ Shortages (Units)

107 21 -93 88 -19 -103 -59 -70 130 87 36 -124

Ending Inventory/ Shortages (Units)

107 128 35 122 103 0 -59 -130 0 87 124 0

Ending Inventory (Units)

107 128 35 122 103 0 0 0 0 87 124 0 706

Ending Shortages (Units)

0 0 0 0 0 0 59 130 0 0 0 0 189

Inventory Cost ($) 2675 3200 875 3050 2575 0 0 0 0 2175 3100 0 $17,650

Shortage Cost ($) 0 0 0 0 0 0 5900 13000 0 0 0 0 $18,900


2.04 0 0 0 0 0 3 0 0 -6 0 0


2.04 0.00 0.00 0.00 0.00 0.00 3.31 0.00 0.00 0.00 0.00 0.00 5.35


0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.53 0.00 0.00 5.53

Cost of Chaning Production Level Up ($)

407.87 0.00 0.00 0.00 0.00 0.00 661.97 0.00 0.00 0.00 0.00 0.00 $1,070


0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1658.86 0.00 0.00 $1,659


32


Sample Calculations for Mixed (Hybrid) PlanThe production level is constant at 23.04 units per day for the first six month which is the average demand for the first six months, January to June.

Then it changes to 26.35 which is the average demand for the next three months.

Finally the production level changes to 20.82 which is the average demand for the last three months.

This plan entails inventories, shortages, and changing production levels up and down.

The calculations are done in the same way as for the level and chase plans.

Category Hybrid Plan

Regular time Labor Cost $468,480

Over Time Labor Cost

Inventory carrying Cost $17,650

Shortage Cost $18,900

Increasing Production level $1,070

Decreasing Production level $1,659

Material Cost $585,600

Total Cost $1,093,359

33



Example 2: Level Production with OvertimeMonth Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total

Expected Demand (Units) 400 440 600 396 480 610 560 650 450 350 380 540 5856

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251

Production per Day (Units) 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67 16.67

Regular Time Production (Units)

367 333 367 350 333 367 317 367 367 350 333 333 4184

Overtime Production (Units)

33 107 233 46 147 243 243 283 83 0 47 207 1672

Total production (Units) 400 440 600 396 480 610 560 650 450 350 380 540 5856

Ending Inventory/ Shortages (Units)

0 0 0 0 0 0 0 0 0 0 0 0

Ending Inventory (units) 0 0 0 0 0 0 0 0 0 0 0 0 0

Ending Shortages (Units) 0 0 0 0 0 0 0 0 0 0 0 0 0

Inventory Cost ($) 0 0 0 0 0 0 0 0 0 0 0 0 0

Shortage Cost ($) 0 0 0 0 0 0 0 0 0 0 0 0 0


-4.33 0 0 0 0 0 0 0 0 0 0 0


0 0 0 0 0 0 0 0 0 0 0 0 0


4 0 0 0 0 0 0 0 0 0 0 0 4.33

Cost of Changing Production Level Up ($)

0 0 0 0 0 0 0 0 0 0 0 0 0


1299 0 0 0 0 0 0 0 0 0 0 0 1299


34


Sample calculations for Level Production with Overtime

Level production is set at 16.67 units per day which is equal to the minimum of the production per day in 12 months.

The minimum production per day (16.67) is for October.

The difference between the demand and production in any month is the number of units to be produced during over time.

For example, the production in January is 367 (16.67 x 22) units. Therefore, overtime production will be 33 (400-367).

In this plan 4,184 units are produced during regular time and 1,672 units are produced during overtime for a total of 5,856 units.

Category Level Plan with Over Time

Regular time Labor Cost $334,720

Overtime Labor Cost $200,640

Inventory carrying Cost

Shortage Cost

Increasing Production level

Decreasing Production level $1,299



35



Cost Comparison

36

Cost Comparison

Level Plan Chase Plan Hybrid PlanLevel Plan with

Overtime

Regular time Labor Cost $468,480 $468,480 $468,480 $334,734

Overtime Labor Cost $200,636

Inventory carrying Cost $17,425 $17,650

Shortage Cost $46,200 $18,900

Increasing Production level $466 $6,023 $1,070

Decreasing Production level $7,234 $1,659 $1,299

Material Cost $585,600 $585,600 $585,600 $585,600

Total Cost $1,118,171 $1,067,336 $1,093,359 $1,122,269

Selection of a Production PlanTable on RHS gives the cost comparison of the four production plans discussed above.

The Chase Plan is the least expensive plan and is a top candidate for being selected.

However, other non-financial considerations must also be taken into account when choosing the final plan.

Level Plan Chase PlanHybrid Plan

Level Plan with Overtime

Regular time Labor Cost

$468,480 $468,480 $468,480 $334,720

Overtime Labor Cost

$200,640

Inventory carrying Cost

$17,425 $17,650

Shortage Cost $46,200 $18,900 Increasing Production level

$466 $6,023 $1,070

Decreasing Production level

$7,234 $1,659 $1,299

Material Cost $585,600 $585,600 $585,600 $585,600Total Cost $1,118,171 $1,067,336 $1,093,359 $1,122,259

37

Beginning Conditions

Beginning conditions specify the existing inventory level and the existing production level per day when planning starts.

The same beginning conditions must be used in each plan for comparing the costs. The beginning inventory is used to reduce the production requirements of the first period while solving the problem.

For example, if the beginning inventory for Example 2 discussed earlier was 100 units, then the demand in the first month will be reduced to 300 (400-100) because the 100 units in stock can be used to meet the demand of the first month.

We assumed a beginning inventory of zero in Example 2.

38

Beginning Conditions (continued)

The existing production level affects the cost of changing the production level (up or down) in the first month.

In Example 2, we assumed the existing production level per day to be 21 units.

Therefore, the production level was: Increased by 2.33 (23.33 – 21) in the level plan. Decreased by 2.82 (21 – 18.18) in the chase plan, Increased by 2.04 (23.04 – 21) in the hybrid plan and Decreased by 4.33 (21 – 16.67) in the level plan with overtime.

39

Aggregate Production Planning in a Service IndustryIn a service industry the service or “product” cannot be stored.

A blood-testing laboratory provides a good illustration of a service system with testing capacity that cannot be fully used when there is not enough demand. Technicians’ time cannot be stored when technicians are idle.

On the other hand, when demand is greater than the technical capacity to supply tests, the tests must be postponed or subcontracted or done on overtime.

The big difference with the manufacturer’s example is the inability to create a useful inventory when capacity to test is greater than demand for testing.

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Aggregate Planning in a Blood Testing Lab Blood tests are the product of the blood testing lab.

Because all tests are individual and unique, they can only be made on demand.

Demand for tests of different kinds are aggregated—some take longer than others and use different kinds of materials and equipment.

The aggregation is based on averaging across the normal mix of blood test procedures. Demand, in this example, is stated in units (occasionally as test kit units).

For sake of comparison, this service case and the prior manufacturing case use the same set of numbers for demand levels, production capacity, and applicable costs applied to different strategies for matching supply and demand. The difference to note is that the manufacturer can store units in inventory to meet later demand but the blood-testing laboratory cannot.

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Data for Blood Testing Lab

o Table below provides the number of working days for each month over a 12-month planning horizon.

o The total yearly demand is 5,856 blood tests with an average of 488 testing units per month.

o The demand varies from a high of 650 test kit units in August to a low of 350 units in October.

o The total number of working days in the year is 251. o The demand per day for each month and the average demand for the 12-month

planning period are also included in this table.

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Costs for Blood Testing LabThe back order cost (arises because the lab is not able to provide the blood test on time in the given month).

$100

Idle time costs (occurs when there is too much capacity for testing. This is higher than regular time labor cost due to idle apparatus).

$25

Cost of increasing production level per unit* $200

Cost of decreasing production level per unit* $300

Regular time labor cost per hour $20

Overtime labor cost per hour--not used $30

Subcontracting (outsourcing) cost per unit--not used $650

Material cost per unit $100

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*Increase and decrease in production levels are normally achieved by hiring and dismissal. Changes are costly because blood-testing involves responsibility for proficiency.

Level Plan for Blood Testing LabMonth Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total

Expected Demand 400 440 600 396 480 610 560 650 450 350 380 540 5856

Working Days 22 20 22 21 20 22 19 22 22 21 20 20 251

Production per Day 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33 23.33

Total Production 513 467 513 490 467 513 443 513 513 490 467 467 5,856

Idle Time (+) or Back Orders (-) *

113 27 -87 94 -13 -97 -117 -137 63 140 87 -73

Idle Time (+) or Net Back Orders **

113 27 -87 7 -13 -110 -227 -364 -301 -161 -74 -147

Idle Time 113 27 0 7 0 0 0 0 0 0 0 0 147

Back Orders 0 0 87 0 13 110 227 364 301 161 74 147 1484

Idle Time Cost 2,825 675 0 175 0 0 0 0 0 0 0 0 3,675

Back Order Cost 0 0 8700 0 1300 11,000 22,700 36,400 30,100 16,100 7,400 14,700 148,400

Change in Production Level

2 0 0 0 0 0 0 0 0 0 0 0

Change in Production Level – UP

2 0 0 0 0 0 0 0 0 0 0 0 2

Change in Production Level – Down

0 0 0 0 0 0 0 0 0 0 0 0 0

Cost of Changing Production Level UP

466 0 0 0 0 0 0 0 0 0 0 0 466

Cost of Changing Production Level Down

0 0 0 0 0 0 0 0 0 0 0 0 0

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Level Plan: Total Costs

The total cost of this plan is $1,206,621.

Various cost components are given in the table on RHS. This plan is 7.5% worse than the worst of all of the prior plans. The total backorder costs are too large.

That suggests two things.

First, increase the number of technicians and let the idle cost go up; second, opt for a chasing strategy. It might do better.

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Total Idle Time Cost $3675

Total Back Order Cost $148,400

Regular Time Labor Cost

$468,480


Changing Production Level

$466


Thank you

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