1. Aggregate Planning

2. 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)

3. Aggregate Planning Problem
Aggr. Unit
Production Reqs Corporate Strategy
Aggregate
Unit Demand Aggregate
Production Plan
Aggregate
Aggregate Planning
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

4. 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.

5. 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

6. 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

7. 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)

8. 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.

9. 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

10. 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.

11. Solution Approaches
• Graphical Approaches: Spreadsheet-based simulation
• Analytical Approaches: Mathematical (mainly linear
programming) Programming formulations

12. Analytical Approach:
A Linear Programming Formulation
min TC = Σt ( 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

13. 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.