Linear Programming and Resource Allocation Modeling

1Introduction

This book deals with the application of linear programming to firm decision making. In particular, an important resource allocation problem that often arises in actual practice is when a set of inputs, some of which are limited in supply over a particular production period, is to be utilized to produce, using a given technology, a mix of products that will maximize total profit. While a model such as this can be constructed in a variety of ways and under different sets of assumptions, the discussion that follows shall be limited to the linear case, i.e. we will consider the short‐run static profit‐maximizing behavior of the multiproduct, multifactor competitive firm that employs a fixed‐coefficients technology under certainty (Dorfman 1951, 1953; Naylor 1966).

How may we interpret the assumptions underlying this profit maximization model?

1. All‐around perfect competition – the prices of the firm’s product and variable inputs are given.
2. The firm employs a static model – all prices, the technology, and the supplies of the fixed factors remain constant over the production period.
3. The firm operates under conditions of certainty – the model is deterministic in that all prices and the technology behave in a completely systematic (nonrandom) fashion.
4. All factors and products are perfectly divisible – fractional (noninteger) quantities of factors and products are admissible at an optimal feasible solution.
5. The character of the firm’s production activities, which represent ...