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Production and Operations Management Systems

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Production and Operations Management Systems Chapter 4: Capacity Management and Aggregate Production Planning Sushil K. Gupta Martin K. Starr 2014 * – PowerPoint PPT presentation

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Title: Production and Operations Management Systems


1
Production and Operations Management Systems
  • Chapter 4 Capacity Management and Aggregate
    Production Planning
  • Sushil K. Gupta
  • Martin K. Starr
  • 2014

2
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.

3
After reading this chapter, you should be able to
(continued)
  • Compare constant (or level) production with a
    chasing policywhere 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.

4
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.

5
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

6
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 lt 1
  • Jobs, machines, materials, workers, and methods
    interact resulting in different E values.

7
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)

8
Theoretical vs. Actual capacity
  • Actual 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
  • The storm limits power that can be delivered.
  • Water main break decreases flow to the fire
    department.
  • Supplier of tubes for Toms of Maine has a
    strike, and it is now necessary to find a new
    source.

9
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.

10
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.

11
Example 1 Data
  • 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.

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
12
Example 1 Level Plan
Demand Data Demand Data Level Production Plan Level Production Plan Level Production Plan Level Production Plan
Month Expected 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 Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand 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.

13
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.

14
Example 1 Chase Plan
Demand Data Demand Data Demand Data Chase Production Plan Chase Production Plan Chase Production Plan
Month Expected Demand Cumulative Demand Production Plan Cumulative Production 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        
Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand
  • 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.

15
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.

16
Example 1 Hybrid (Mixed) Plan
  • 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.

Demand Data Demand Data Demand Data Mixed Production Plan Mixed Production Plan Mixed Production Plan
Month Expected Demand Cumulative Demand Production Plan Cumulative Production 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        
Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand Note Inventory Cumulative Production - Cumulative Demand
17
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.

18
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.

19
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.
  •  

20
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.

21
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?

Other factors may need to be considered such as
the effect on morale caused by workforce
disruption
22
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

23
Example 2 Aggregate Manufacturers Production
Planning
  • 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.  

Month 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  
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
Note This example employs fractional numbers
for production per day. Therefore, rounding
errors can be expected to occur
24
Example 2 Cost and Capacity Data
  • Capacity Data Assumptions
  • Cost Data Assumptions
  • Production time/unit is 4 hours.
  • 8 hours per day for each worker.
  • The number of workers remains constant for entire
    month.
  • The plant currently produces 21 units per day.
  • Beginning inventory 0.
  • No defective items are produced.

Increase and decrease in production levels are
normally achieved by hiring and firing workers
25
Calculating Production Levels
  • Production 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.

26
Calculating Number of Workers
  • Number 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.  
  •  

27
Example 2 Level Plan
Month 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.

28
Sample Calculations for Level Plan
  • Production/Day 23.33 units.
  • Production in any given month Number of days in
    that month x 23.33.
  • The production numbers are rounded to the nearest
    integer.
  • For example, in January 513 is the number of
    units produced where (23.33 x 22
    513.26),
  • However, the demand in January is only 400 units.
    Therefore, 113 (513 - 400) units go into
    inventory.
  • In February, 467 (23.33 x 20) units are produced
    whereas the expected demand is for 440 units.
  • Therefore, 27 units (467 440) are added to
    inventory and the inventory level at the end of
    February is 140.
  • In March, the production is 513 (23.33 x 22)
    which is 87 units less than the demand (600
    units).
  • Therefore 87 units are withdrawn from inventory
    to meet the demand for March.
  • The inventory level at the end of March becomes
    53.
  • In this way, the calculations continue.

29
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

 Category Level Plan
Regular time Labor Cost 468,480
Over Time Labor Cost  
Inventory carrying Cost 17,425
Shortage Cost 46,200
Increasing Production level 466
Decreasing Production level  
Material Cost 585,600
Total Cost 1,118,171
Note rounding errors can make small changes in
the various totals
30
Example 2 Chase 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 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. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. There are no inventories or shortages in this plan. 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  
Change in Production Level - Up (Units) 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
Change in Production Level - Down (Units) 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  
Sample calculations for this plan are shown in
the next slide.
31
Sample Calculations for Chase Plan
  • In 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.
  • The costs of this plan are
  • Note rounding errors can make small changes in
    the various totals

Category Chase Plan
Regular time Labor Cost 468,480
Over Time Labor Cost  
Inventory carrying Cost  
Shortage Cost  
Increasing Production level 6,023
Decreasing Production level 7,234
Material Cost 585,600
Total Cost 1,067,336
32
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 Day Average Demand per Day (Jan to Jun) Average Demand per Day (Jan to Jun) Average Demand per Day (Jan to Jun) Average Demand per Day (Jan to Jun) Average Demand per Day (Jan to Jun) Average Demand per Day (Jan to Jun) Average Demand per Day (Jul to Sep) Average Demand per Day (Jul to Sep) Average Demand per Day (Jul to Sep) Average Demand per Day (Oct to Dec) Average Demand per Day (Oct to Dec) Average Demand per Day (Oct to Dec)  
Production per Day 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
Change in Production Level (Units) 2.04 0 0 0 0 0 3 0 0 -6 0 0  
Change in Production Level - Up (Units) 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
Change in Production Level - Down (Units) 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
Cost of Changing Production Level Down () 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
Number of Workers 11.52 11.52 11.52 11.52 11.52 11.52 13.17 13.17 13.17 10.41 10.41 10.41  
Sample calculations for this plan are shown in
the next slide.
33
Sample Calculations for Mixed (Hybrid) Plan
  • The 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.

The costs of this plan are
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
Note rounding errors can make small changes in
the various totals
34
Example 2 Level Production with Overtime
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 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
Change in Production Level (Units) -4.33 0 0 0 0 0 0 0 0 0 0 0  
Change in Production Level - Up (Units) 0 0 0 0 0 0 0 0 0 0 0 0 0
Change in Production Level - Down (Units) 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
Cost of Changing Production Level Down () 1299 0 0 0 0 0 0 0 0 0 0 0 1299
Number of Workers 8.34 8.34 8.34 8.34 8.34 8.34 8.34 8.34 8.34 8.34 8.34 8.34  
Sample calculations for this plan are shown in
the next slide.
35
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.

The costs of this plan are
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
Material Cost 585,600
Total Cost 1,122,259
Note rounding errors can make small changes in
the various totals
36
Cost Comparison
Cost Comparison Cost Comparison Cost Comparison Cost Comparison Cost Comparison
  Level Plan Chase Plan Hybrid Plan Level 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
37
Selection of a Production Plan
  • Table 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 Plan Hybrid 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 585,600 585,600 585,600 585,600
Total Cost 1,118,171 1,067,336 1,093,359 1,122,259
38
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.

39
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.

40
Aggregate Production Planning in a Service
Industry
  • In 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 manufacturers
    example is the inability to create a useful
    inventory when capacity to test is greater than
    demand for testing.

41
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
    aggregatedsome 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.

42
Data for Blood Testing Lab
  • Table below provides the number of working days
    for each month over a 12-month planning horizon.
  • The total yearly demand is 5,856 blood tests with
    an average of 488 testing units per month.
  • The demand varies from a high of 650 test kit
    units in August to a low of 350 units in October.
  • The total number of working days in the year is
    251.
  • The demand per day for each month and the average
    demand for the 12-month planning period are also
    included in this table.

43
Costs for Blood Testing Lab
The 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
Increase and decrease in production levels are
normally achieved by hiring and dismissal.
Changes are costly because blood-testing involves
responsibility for proficiency.
44
Level Plan for Blood Testing Lab
Month 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
45
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.

Total Idle Time Cost 3675
Total Back Order Cost 148,400
Regular Time Labor Cost 468,480
Material Cost 585,600
Changing Production Level 466
Total Cost 1,206,621
46
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