Linear Programming with Costs and Incomes in Two or More Separated Currencies

Abstract

If the balance of payments of any country is to be kept favourable, it is essential that decision makers at all levels in that country be aware of the influences alternative policies have on this balance. The normal formulation of a linear program matrix does not reveal this information, neither does it separate costs from incomes in working out the objective function and opportunity costs.

The modification to matrix layout suggested enables costs and incomes to be shown separately, and further enables each to be detailed in any number of currencies. In U.K. problems one would deal normally in pounds and use dollars to denote all foreign currencies. By examination of vectors in the solution matrix it is possible to see the total effect of each variable on costs and incomes, each split into the correct currencies, so that net pound or net dollar effects can be found.

To obtain full benefit from this exercise the decision-maker has to be prepared to take note of balance of payments influences, as well as direct influences on his own profits. A major side-benefit is that the act of separating monies into local and foreign categories brings an added awareness, at many levels of an organization, of the possible effects different policies may have on the balance of payments. This system is currently being used in the Chilean steel industry in order to rationalize their import and export policies.