16 - Linear programming

Summary

The assumptions

Linear programming (LP) is a systematic, mathematical procedure for finding the optimal plan, or programme, for a given set of conditions. To use this method the conditions must be presented in the following form:

1. (1) a limited choice of several activities;

2. (2) certain fixed constraints affecting the choice;

3. (3) straight-line (linear) relationships.

These basic assumptions made in linear programming need further explanation.

The alternative activities may correspond with the crops and animals which could be produced on the farm being planned, but the word ‘activity’ as used in linear programming does not necessarily mean the same as (he word ‘enterprise’. Thus buying activities may be considered in drawing up the plan. Furthermore, several different activities might be associated with the same enterprise, where several alternative methods of production are possible. Yams grown in a mixture represent a different activity from yams grown alone; irrigated cotton represents a different activity from rainfed cotton. In some cases it may be appropriate to treat a particular crop mixture as a single activity. The choice must be limited to a suitable number of activities for calculation. For the simple examples to be worked out in this chapter, the number of activities is limited to two or three. However, larger problems only differ in the amount of arithmetic involved; the nature of the arithmetic is the same. For this reason most real linear programming problems are solved on computers which can deal with hundreds of alternative activities.