Goal Programming For Strategic Planning ? Introduction

Many systems which are modelled mathematically result in a model where the relationships between some or all of the parameters are found to be non-linear. These systems are usually complicated further by a desire to make the system achieve multiple and often conflicting objectives or goals simultaneously. Rozwadowski (1970) developed a model to describe the total discounted net profit of a mine as a function of the amount of ore developed and of the grade of the amount of ore mined. Dynamic programming was used to determine the policy which gave the maximum net present value. In this paper it is shown that the relationships between the variables can be approximated by piecewise linear functions. This is amenable to solution by an algorithm based on the simplex algorithm of linear programming. The goals of maximizing the net present value, the total net profit and the total gold output are incorporated simultaneously into a goal programming formulation of the system. The resulting model is characterized by a large number of disconnected constraints. These are decomposed into several smaller problems and the problem solved. The solution is examined to discover the sensitivity of the system to changes in certain parameters. In particular the interaction between the three goals is analysed to determine whether there is conflict between any of the goals and, if so, what the trade-offs between the conflicting goals are.