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Aggregate Production Planning

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Title: Aggregate Production Planning


1
Aggregate Production Planning
  • (APP)


2
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


3
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

4
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)


5
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


6
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


7
Level Production
Demand
Production
Units
Time

8
Chase Demand
Demand
Units
Production
Time

9
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.

10
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


11
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


12
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


13
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)

14
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)

15
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)

16
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)

17
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)

18
  • 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

19
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

20
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


26
  • 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

27
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

28
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29
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

30
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


31
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


32
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?


33
The Level Capacity with Overtime Plan
34
The Matching Demand Plan
35
  • 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

36
  • 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.

37
  • 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

38
  • 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

39
  • 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.

40
  • 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

41
  • 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

42
  • 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

43
  • 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
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