Module 3: Introduction to Aggregate Planning and Linear Programming

Forecasting can be defined as the estimate of future demand.

Aggregate planning is carried out once information about future demand is obtained from forecasting.

A poor Aggregate Plan can result in the following:
- Lost sales and profits if unable to meet demand
- A large amount of excess inventory and capacity which increases costs

The question 'What should the production capacity be such that the total production cost is minimized?' is known as the aggregate planning problem.

The following costs are used to calculate the minimum production capacity production cost:
- Regular Time cost
- Overtime cost
- Inventory cost
- Shortage cost

The formula for Total Capacity is:
Total Capacity = Regular Time Capacity + Overtime Capacity

Regular time production is assumed to be less costlier than overtime production.

Back order cost can be defined as the cost of back ordering per unit per month.

Increasing or decreasing the number of production employees does not affect the regular time production capacity.

Linear Programming

R(t) - Regular Time production used in time t
O(t) - Overtime production used in time t
D(t) - Demand during time t
S(t) - Shortage at the end of period t
U(t) - Under utilization in period t
H(t) - Number of people hired in period t
W(t) - Number of people working in period t
L(t) - Number of people laid off in period t

In the linear programming formulation 'I(t)' (the inventory at the end of the previous period) has to be defined as a unrestricted variable which can take positive value or a negative value.

Linear programming is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

In aggregate planning the planning horizon is often divided into Periods.

The physical resources of the company are assumed to be fixed during the planning horizon of interest.


The following help a company cope with demand fluctuations:

- Changing the size of the work force by hiring and firing.
- Varying the production rate by introducing overtime.
- Accumulating seasonal inventories.
- Planning backorders.

The following costs are relevant to aggregate production planning:
- Basic production costs
- Costs associated with changes in the production rate
- Inventory related costs

In aggregate production planning the following are examples of basic production costs
- Material costs
- Direct labor costs
- Overhead costs

In aggregate production planning the following are costs associated with changes in the production rate:
- Hiring costs
- Training costs
- Laying off personnel costs


In the Aggregate Planning Problem the following are examples of constraints:
- Limits on overtime
- Limits on layoffs
- Limits on capital available
- Limits on stockouts and backlogs