Aggregate Production Planning

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Aggregate Production Planning

• (APP)

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Aggregate Production Planning (APP)

• Matches market demand to company resources
• Plans production 6 months to 12 months in advance
• Expresses demand, resources, and capacity in
  general terms
• Develops a strategy for economically meeting
  demand
• Establishes a companywide game plan for
  allocating resources

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Inputs and Outputs to Aggregate Production
Planning
Company Policies
Strategic Objectives
Capacity Constraints
Demand Forecasts
Financial Constraints
Aggregate Production Planning
Size of Workforce
Units or dollars subcontracted, backordered,
or lost
Production per month (in units or )
Inventory Levels

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Strategies for Meeting Demand

• 1. Use inventory to absorb fluctuations in
  demand
• (level production)
• 2. Hire and fire workers to match demand (chase
  demand)
• 3. Maintain resources for high demand levels
• 4. Increase or decrease working hours (over
  undertime)
• 5. Subcontract work to other firms
• 6. Use part-time workers
• 7. Provide the service or product at a later
  time period (backordering)

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Strategy Details

• Level production - produce at constant rate use
  inventory as needed to meet demand
• Chase demand - change workforce levels so that
  production matches demand
• Maintaining resources for high demand levels -
  ensures high levels of customer service
• Overtime undertime - common when demand
  fluctuations are not extreme

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Strategy Details

• Subcontracting - useful if supplier meets quality
  time requirements
• Part-time workers - feasible for unskilled jobs
  or if labor pool exists
• Backordering - only works if customer is willing
  to wait for product/services

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Level Production
Demand
Production
Units
Time

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Chase Demand
Demand
Units
Production
Time

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APP Example

• The Bavarian Candy Company (BCC) makes a variety
  of candies in three factories worldwide. Its line
  of chocolate candies exhibits a highly seasonal
  pattern with peaks in winter months and valleys
  during the summer months. Given the costs and
  quarterly sales forecasts, determine whether a
  level production or chase demand production
  strategy would be more economically meet the
  demand for chocolate candies.

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APP Using Pure Strategies
Quarter Sales Forecast (kg) Spring 80,000 Summer
50,000 Fall 120,000 Winter 150,000

• Hiring cost 100 per worker
• Firing cost 500 per worker
• Inventory carrying cost 0.50 per kilogram per
  quarter
• Production per employee 1,000 kilograms per
  quarter
• Beginning work force 100 workers

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Level Production Strategy

• Sales Production
• Quarter Forecast Plan Inventory
• Spring 80,000 100,000 20,000
• Summer 50,000 100,000 70,000
• Fall 120,000 100,000 50,000
• Winter 150,000 100,000 0
• 400,000 140,000
• Cost 140,000 kilograms x 0.50 per kilogram
  70,000

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Chase Demand Strategy

• Sales Production Workers Workers Workers
• Quarter Forecast Plan Needed Hired Fired
• Spring 80,000 80,000 80 - 20
• Summer 50,000 50,000 50 - 30
• Fall 120,000 120,000 120 70 -
• Winter 150,000 150,000 150 30 -
• 100 50
• Cost (100 workers hired x 100) (50 workers
  fired x 500)
• 10,000 25,000 35,000

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LP FormulationDefineHt hired for period
tFt fired for period tIt inventory at end
of period tPt Production in period tWt
Workforce in period t

• Min Z 100 (H1 H2 H3 H4) 500 (F1 F2
  F3 F4) 0.50 (I1 I2 I3 I4)

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Min Z 100 (H1 H2 H3 H4) 500 (F1 F2
F3 F4) 0.50 (I1 I2 I3 I4)

• Subject to
• P1 - I1 80,000 (1) Demand
• I1 P2 - I2 50,000 (2) constraints
• I2 P3 - I3 120,000 (3)
• I3 P4 - I4 150,000 (4)

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Min Z 100 (H1 H2 H3 H4) 500 (F1 F2
F3 F4) 0.50 (I1 I2 I3 I4)Subject
to P1 - I1 80,000 (1) Demand I1
P2 - I2 50,000 (2) constraints I2 P3 - I3
120,000 (3) I3 P4 - I4 150,000 (4)

• P1 - 1,000 W1 0 (5) Production
• P2 - 1,000 W2 0 (6) constraints
• P3 - 1,000 W3 0 (7)
• P4 - 1,000 W4 0 (8)

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Min Z 100 (H1 H2 H3 H4) 500 (F1
F2 F3 F4) 0.50 (I1 I2 I3 I4)Subject
to P1 - I1 80,000 (1) Demand I1
P2 - I2 50,000 (2) constraints I2 P3 - I3
120,000 (3) I3 P4 - I4 150,000 (4)
P1 - 1,000 W1 0 (5) Production P2 - 1,000
W2 0 (6) constraints P3 - 1,000 W3
0 (7) P4 - 1,000 W4 0 (8)

• W1 - H1 F1 100 (9) Work force
• W2 - W1 - H2 F2 0 (10) constraints
• W3 - W2 - H3 F3 0 (11)
• W4 - W3 - H4 F4 0 (12)

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Min Z 100 (H1 H2 H3 H4) 500 (F1
F2 F3 F4) 0.50 (I1 I2 I3 I4)

• Subject to
• P1 - I1 80,000 (1) Demand
• I1 P2 - I2 50,000 (2) constraints
• I2 P3 - I3 120,000 (3)
• I3 P4 - I4 150,000 (4)
• P1 - 1,000 W1 0 (5) Production
• P2 - 1,000 W2 0 (6) constraints
• P3 - 1,000 W3 0 (7)
• P4 - 1,000 W4 0 (8)
• W1 - H1 F1 100 (9) Work force
• W2 - W1 - H2 F2 0 (10) constraints
• W3 - W2 - H3 F3 0 (11)
• W4 - W3 - H4 F4 0 (12)

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• LP Solution
• Z 32,000
• H1 0, F1 20, I1 0, P180000
• H2 0, F2 0, I2 30000, P280000
• H3 10, F3 0, I3 0, P390000
• H4 60, F4 0, I4 0, P4150000

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Summary APP By Linear Programming

• Min Z 100 (H1 H2 H3 H4) 500 (F1 F2
  F3 F4) 0.50 (I1 I2 I3 I4)
• Subject to
• P1 - I1 80,000 (1) Demand
• I1 P2 - I2 50,000 (2) constraints
• I2 P3 - I3 120,000 (3)
• I3 P4 - I4 150,000 (4)
• P1 - 1,000 W1 0 (5) Production
• P2 - 1,000 W2 0 (6) constraints
• P3 - 1,000 W3 0 (7)
• P4 - 1,000 W4 0 (8)
• W1 - H1 F1 100 (9) Work force
• W2 - W1 - H2 F2 0 (10) constraints
• W3 - W2 - H3 F3 0 (11)
• W4 - W3 - H4 F4 0 (12)

where Ht hired for period t Ft fired
for period t It inventory at end of period
t LP Solution Z 32,000 H1 0, F1 20, I1
0, P180000 H2 0, F2 0, I2 30000,
P280000 H3 10, F3 0, I3 0, P390000 H4 60,
F4 0, I4 0, P4150000

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APP By The Transportation Method

• Expected Regular Overtime Subcontract
• Quarter Demand Capacity Capacity Capacity
• 1 900 1000 100 500
• 2 1500 1200 150 500
• 3 1600 1300 200 500
• 4 3000 1300 200 500
• Regular production cost per unit 20
• Overtime production cost per unit 25
• Subcontracting cost per unit 28
• Inventory carrying cost per unit per period 3
• Beginning inventory 300 units

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Production Plan

• Strategy Variable
• Period Demand Reg Prodn Overtime Sub End Inv
• 1 900 1000 100 0 500
• 2 1500 1200 150 250 600 3 1600 1300 200 500 1
  000 4 3000 1300 200 500 0 Total 7000 4800 650
  1250 2100

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• Regular Production Cost (4,800 20)96,000
• Overtime Production Cost (650 25) 16,250
• Subcontracting Cost (1,250 28)
  35,000
• Inventory Cost (2,100 3)
  6,300
• The Total Cost of the Plan
  153,550

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Linear Programming Formulation

• Let
• Dt units required in period t, (t 1,,T)
• m number of sources of product in any period
• Pit capacity, in units of product, of source i
  in period t, (i 1,,m)
• Xit planned quantity to be obtained from source
  i in period t
• cit variable cost per unit from source i in
  period t
• ht cost to store a unit from period t to period
  t1
• It inventory level at the end of period t,
  after satisfying the requirement in period t

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Optimal Value (Z) 153,550

• XR1
• XR2
• XR3
• XR4
• XO1
• XO2
• XO3
• XO4
• XS1
• XS2
• XS3
• XS4

• 1000
• 1200
• 1300
• 1300
• 0
• 150
• 200
• 200
• 0
• 350
• 500
• 500

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Strategies for Managing Demand

• Shift demand into other periods
• incentives, sales promotions, advertising
  campaigns
• Offer product or services with counter-cyclical
  demand patterns
• create demand for idle resources

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Aggregate Planning for Services

• 1. Most services cant be inventoried
• 2. Demand for services is difficult to predict
• 3. Capacity is also difficult to predict
• 4. Service capacity must be provided at the
  appropriate place and time
• 5. Labor is usually the most constraining
  resource for services

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Services Example

• The central terminal at the Deutsche Cargo
  receives airfreight from aircraft arriving from
  all over Europe and redistributes it to aircraft
  for shipment to all European destinations. The
  company guarantees overnight shipment of all
  parcels, so enough personnel must be available to
  process all cargo as it arrives. The company now
  has 24 employees working in the terminal. The
  forecasted demand for warehouse workers for the
  next 7 months is 24, 26, 30, 28, 28, 24, and 24.
  It costs 2,000 to hire and 3,500 to lay off
  each worker. If overtime is used to supply labor
  beyond the present work force, it will cost the
  equivalent of 2,600 more for each additional
  worker. Should the company use a level capacity
  with overtime or a matching demand plan for the
  next six month?

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The Level Capacity with Overtime Plan
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The Matching Demand Plan
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• The cost of the Level Capacity with Overtime
  41,600
• The total cost of the Matching Demand plan
  12,000 21,000 33,000
• Hence, since the cost of matching demand plan is
  less than the level capacity plan with overtime
  and would be the preferred plan

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• Aggregate Planning Example 1
• A manufacturer produces a line of household
  products fabricated from sheet metal. To
  illustrate his production planning problem,
  suppose that he makes only four products and that
  his production system consists of five production
  centers stamping, drilling, assembly, finishing
  (painting and printing), and packaging. For a
  given month, he must decide how much of each
  product to manufacture, and to aid in this
  decision, he has assembled the data shown in
  Tables 1 and 2. Furthermore, he knows that only
  2000 square feet of the type of sheet metal used
  for products 2 and 4 will be available during the
  month. Product 2 requires 2.0 square feet per
  unit and product 4 uses 1.2 square feet per unit.

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• TABLE 1 Production Data for Example 1
• PRODUCTION
  RATES IN HOURS PER UNIT
• 
  
  Production
• DEPARTMENT PRODUCT 1 PRODUCT 2 PRODUCT
  3 PRODUCT 4 Hours
• 
  
  Available
• Stamping 0.03
  0.15 0.05 0.10
  400
• Drilling 0.06
  0.12 ----- 0.10
  400
• Assembly 0.05
  0.10 0.05 0.12
  500
• Finishing 0.04
  0.20 0.03 0.12
  450
• Packaging 0.02
  0.06 0.02 0.05
  400

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• TABLE 2 Product Data for Example 1
• 
  
• NET SELLING
  VARIABLE SALES POTENTIAL
• PRODUCT PRICE/UNIT COST/UNIT
  MINIMUM MAXIMUM
• 1 10
  6 1000 6000
• 2 25
  15 ----- 500
• 3 16
  11 500 3000
• 4 20
  14 100 1000

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• A Linear Program of Example 1
• Define xi be the number of units of Product i to
  be produced per month, i 1, 2, 3, and 4.

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• Solution of Example 1 using LINGO Software
  Package (get a free copy of this package from the
  web site at www.lindo.com)
• Objective value 42600.00
• Variable Value Reduced Cost
• X1 5500.000 0.0000000
• X2 500.0000 0.0000000
• X3 3000.000 0.0000000
• X4 100.0000 0.0000000

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• Row Slack or Surplus Dual
  Price
• PROFIT 42600.00 1.0000000
• STAMPING 0.0000000 0.0000000
• DRILLING 0.0000000 66.66666
• ASSEMBLY 13.00000 0.0000000
• FINISHING 28.00000 0.0000000
• PACKAGING 195.0000 0.0000000
• SHEETMETAL 880.0000 0.0000000
• MINPROD1 4500.000 0.0000000
• MAXPROD1 500.0000 0.0000000
• MAXPROD2 0.0000000 2.0000000
• MINPROD3 2500.000 0.0000000
• MAXPROD3 0.0000000 5.000000
• MINPROD4 0.0000000 -0.6666667
• MAXPROD4 900.0000 0.0000000

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• Ranges in which the basis is unchanged
• Objective Coefficient Ranges
• Current Allowable Allowable
• Variable Coefficient Increase Decrease
• X1 4.000000 INFINITY INFINITY
• X2 10.00000 INFINITY INFINITY
• X3 5.000000 INFINITY INFINITY
• X4 6.000000 INFINITY INFINITY

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• Righthand Side Ranges
• Row Current Allowable Allowable
• RHS Increase Decrease
• STAMPING 400.0000 INFINITY 100.0000
• DRILLING 400.0000 INFINITY 3000.000
• ASSEMBLY 500.0000 INFINITY 500.0000
• FINISHING 450.0000 INFINITY 5500.000
• PACKAGING 400.0000 INFINITY 0.0
• SHEETMETAL 2000.000 INFINITY 13.00000
• MINPROD1 1000.000 INFINITY 28.00000
• MAXPROD1 6000.000 INFINITY 195.0000
• MAXPROD2 500.0000 INFINITY 880.0000
• MINPROD3 500.0000 INFINITY 4500.000
• MAXPROD3 3000.000 INFINITY 500.0000
• MINPROD4 100.0000 INFINITY 2500.000
• MAXPROD4 1000.000 INFINITY 900.0000