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Aggregate-Planning

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					Aggregate Planning
     Dealing with the Problem Complexity
           through Decomposition
                                           Corporate Strategy

 Aggregate Unit            Aggregate Planning
 Demand              (Plan. Hor.: 1 year, Time Unit: 1 month)

                                           Capacity and Aggregate Production Plans

 End Item (SKU)       Master Production Scheduling
 Demand              (Plan. Hor.: a few months, Time Unit: 1 week)

                                           SKU-level Production Plans

Manufacturing       Materials Requirement Planning
and Procurement     (Plan. Hor.: a few months, Time Unit: 1 week)
lead times
                                            Component Production lots and due dates

Part process      Shop floor-level Production Control
plans             (Plan. Hor.: a day or a shift, Time Unit: real-time)
                     Aggregate Planning Problem
                      Aggr. Unit
                      Production Reqs     Corporate Strategy



Aggregate
Unit Demand                                                            Aggregate
                                                                       Production Plan


                          Aggregate Planning
Aggregate
Unit Availability                                                     Required
(Current Inventory                                                    Production Capacity
Position)



           Aggregate Production Plan:            Production Capacity Plan:
           •Aggregate Production levels          •Workforce level(s)
           •Aggregate Inventory levels           •Overtime level(s)
           •Aggregate Backorder levels           •Subcontracted Quantities
         Product Aggregation Schemes
•Items (or Stock Keeping Units - SKU’s): The final products delivered to the
(downstream) customers
•Families: Group of items that share a common manufacturing setup cost;
i.e., they have similar production requirements.

•Aggregate Unit: A fictitious item representing an entire product family.
•Aggregate Unit Production Requirements: The amount of (labor) time
required for the production of one aggregate unit. This is computed by
appropriately averaging the (labor) time requirements over the entire set of
items represented by the aggregate unit.
•Aggregate Unit Demand: The cumulative demand for the entire set of items
represented by the aggregate unit.

 Remark: Being the cumulate of a number of independent demand series, the
 demand for the aggregate unit is a more robust estimate than its constituent
 components.
         Computing the Aggregate Unit
           Production Requirements
  Washing machine         Required labor time    Item demand as % of
  Model Number            (hrs)                  aggregate demand
  A5532                   4.2                    32

  K4242                   4.9                    21

  L9898                   5.1                    17

  3800                    5.2                    14

  M2624                   5.4                    10

  M3880                   5.8                    06


Aggregate unit labor time = (.32)(4.2)+(.21)(4.9)+(.17)(5.1)+(.14)(5.2)+
                                    (.10)(5.4)+(.06)(5.8) = 4.856 hrs
      Pure Aggregate Planning Strategies
  1. Demand Chasing: Vary the Workforce Level
                  PC WC HC FC

          D(t)                                          P(t) = D(t)

                                                        W(t)

•D(t): Aggregate demand series
•P(t): Aggregate production levels
•W(t): Required Workforce levels
•Costs Involved:
     •PC: Production Costs
         •fixed (setup, overhead)
         •variable (materials, consumables, etc.)
     •WC: Regular labor costs
     •HC: Hiring costs: e.g., advertising, interviewing, training
     •FC: Firing costs: e.g., compensation, social cost
   Pure Aggregate Planning Strategies
2. Varying Production Capacity with Constant Workforce:
                  PC SC WC OC UC

      D(t)                                       P(t)
                                                 S(t)
                                                 O(t)
                                                 U(t)
                                W = constant
•S(t): Subcontracted quantities
•O(t): Overtime levels
•U(t): Undertime levels
•Costs involved:
     •PC, WC: as before
     •SC: subcontracting costs: e.g., purchasing, transport, quality, etc.
     •OC: overtime costs: incremental cost of producing one unit in overtime
     •(UC: undertime costs: this is hidden in WC)
    Pure Aggregate Planning Strategies
3. Accumulating (Seasonal) Inventories:
                 PC WC IC

     D(t)                                           P(t)

                                                    I(t)

                                  W(t), O(t), U(t), S(t) = constant
•I(t): Accumulated Inventory levels
•Costs involved:
      •PC, WC: as before
      •IC: inventory holding costs: e.g., interest lost, storage space, pilferage,
      obsolescence, etc.
        Pure Aggregate Planning Strategies
     4. Backlogging:
                          PC WC BC

          D(t)                                         P(t)

                                                       B(t)

                                     W(t), O(t), U(t), S(t) = constant

•B(t): Accumulated Backlog levels
•Costs involved:
     •PC, WC: as before
     •BC: backlog (handling) costs: e.g., expediting costs, penalties, lost sales
     (eventually), customer dissatisfaction
Typical Aggregate Planning Strategy
A “mixture” of the previously discussed pure options:

                PC WC HC FC OC UC SC IC BC

                                                            P
       D                                                    W
                                                            H
                                                            F
       Io                                                   O
                                                            U
                                                            S
      Wo                                                    I
                                                            B

                               +
Additional constraints arising from the company strategy; e.g.,
    •maximal allowed subcontracting
    •maximal allowed workforce variation in two consecutive periods
    •maximal allowed overtime
    •safety stocks
    •etc.
              Solution Approaches
• Graphical Approaches: Spreadsheet-based simulation
• Analytical Approaches: Mathematical (mainly linear
  programming) Programming formulations
               Analytical Approach:
         A Linear Programming Formulation
      min TC = St ( PCt*Pt+WCt*Wt+OCt*Ot+HCt*Ht+FCt*Ft+
                    SCt*St+ICt*It+BCt*Bt )
     s.t.
Prod. Capacity:      t, (u_l_r)*Pt  (s_d)*(w_d)t*Wt+Ot
Material Balance: t, Pt+It-1+St = (Dt-Bt)+Bt-1+It

Workforce Balance: t, Wt = Wt-1+Ht-Ft
                     ( Any additional policy constraints )
Var. sign restrictions: t, Pt, Wt, Ot, Ht, Ft, St, It, Bt  0

    Time unit: month / unit_labor_req. /shift_duration (in hours) /
    (working_days) for month t
     Demand (vs. Capacity) Options or
        Proactive Approaches to
          Aggregate Planning
• Influencing demand variation so that it aligns to available
  production capacity:
   – advertising
   – promotional plans
   – pricing
   (e.g., airline and hotel weekend discounts, telecommunication
      companies’ weekend rates)
• “Counter-seasonal” product (and service) mixing: Develop
  a product mix with antithetic (seasonal) trends that level
  the cumulative required production capacity.
   – (e.g., lawn mowers and snow blowers)
• => The outcome of this type of planning is communicated
  to the overall aggregate planning procedure as (expected)
  changes in the demand forecast.

				
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