Linear Programming Approach to Aggregate Planning
Introduction
In the class we have dealt with meeting the demand by managing the inventory (by ordering from outside or producing our own items) for a single period of time. In this case study, you are going to use linear programming as a tool to extend what you have learnt about inventory models and to plan a factory schedule for an extended period of time (3 months).
Aggregate planning is an approach that is used to provide a plan for the production process, in advance of 2 to 18 months, so that the management has an idea about the required resources (raw materials, man power, inventory space, etc.) that are needed to produce their products at minimum operational costs.
The quantities of produced (regular and overtime), outsourced, backlogged and held in inventory items, and the number of hired and fired workers in each periods, for each period, are need to be decided in advance.
In order to apply aggregate planning approach, the followings are needed:
- Information about the available resources and their capacities.
- Demand forecast for the planning period.
- Different costs involved, such as unit regular time cost, unit over time cost, shortage cost, inventory cost, etc.
- And other organizational policies that affect the planning.
Case Study Description -
A steel company operates a foundry. The foundry casts three types of steel rolls that are machined in its machine shop. Machined rolls are used by other companies in their mills to manufacture various products. At the beginning of each quarter, the companies prepare their monthly needs of steel rolls and submit them to the foundry. The foundry manager then draws a production plan that is essentially constrained by the machining capacity of the shop. The foundry can directly purchase the rolls at a premium price from outside sources. A comparison between the cost per roll when acquired from the foundry and its outside purchase price is given in Table 1. Unit shortage cost is shown in Table 1 as well.
The processing time for each roll type is shown in Table 2. The estimated demand for the rolls is shown in Table 3.
Table 1.
|
Steel Roll
Type
|
Regular Time
Cost ($ per roll)
|
Over Time Cost
($ per roll)
|
Outsourcing Cost
($ per roll)
|
Shortage Cost
($ per roll)
|
Holding Cost
($ per roll per
month)
|
|
1
|
90
|
100
|
108
|
90
|
4
|
|
2
|
130
|
135
|
145
|
130
|
5
|
|
3
|
180
|
188
|
194
|
180
|
6
|