Aggregate Planning

Dealing with the Problem Complexity through Decomposition

Aggregate Planning

Master Production Scheduling

Materials Requirement Planning

Aggregate UnitDemand

End Item (SKU)Demand

Corporate Strategy

Capacity and Aggregate Production Plans

SKU-level Production Plans

Manufacturingand Procurementlead times

Component Production lots and due dates

Part processplans

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

(Plan. Hor.: a few months, Time Unit: 1 week)

(Plan. Hor.: a few months, Time Unit: 1 week)

Shop floor-level Production Control(Plan. Hor.: a day or a shift, Time Unit: real-time)

Aggregate Planning Problem

Aggregate Planning

AggregateUnit Demand

AggregateUnit Availability(Current InventoryPosition)

Aggregate Production Plan

Required Production Capacity

Aggr. UnitProduction Reqs Corporate Strategy

Aggregate Production Plan:•Aggregate Production levels•Aggregate Inventory levels•Aggregate Backorder levels

Production Capacity Plan:•Workforce level(s)•Overtime level(s)•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 machineModel Number

Required labor time(hrs)

Item demand as % ofaggregate 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 Strategies1. Demand Chasing: Vary the Workforce Level

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

W(t)

PC WC HC FC

•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 Strategies2. Varying Production Capacity with Constant Workforce:

D(t) P(t)

O(t)

PC WC OC UC

U(t)

S(t)

SC

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:

D(t) P(t)

I(t)

PC WC IC

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 Strategies4. Backlogging:

D(t) P(t)

B(t)

PC WC BC

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 StrategyA “mixture” of the previously discussed pure options:

D

PC WC HC FC OC UC SC IC BC

PWHFOUSIB

+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.

Io

Wo

Solution Approaches

• Graphical Approaches: Spreadsheet-based simulation

• Analytical Approaches: Mathematical (mainly linear programming) Programming formulations

Analytical Approach:A Linear Programming Formulation

min TC = t ( PCt*Pt+WCt*Wt+OCt*Ot+HCt*Ht+FCt*Ft+

SCt*St+ICt*It+BCt*Bt )s.t.

t, Pt+It-1+St = (Dt-Bt)+Bt-1+It

t, Wt = Wt-1+Ht-Ft

t,(u_l_r)*Pt s_d)w_d)t*Wt+Ot

t, Pt, Wt, Ot, Ht, Ft, St, It, Bt 0

( )Any additional policy constraints

Prod. Capacity:

Material Balance:

Workforce Balance:

Var. sign restrictions:

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.