Solution of Special Linear Programming Problems with Additional Constraints

Abstract

This paper gives a method of solution for linear programming problems whose constraints can be split into two sets, the first having a special structure, such as that of the transportation problem for example, while the second set is quite general. A problem with only the first set of constraints is referred to as a favoured problem, while a problem with both sets is called a complete problem.

The proposed method is basically the simplex procedure specialized for a problem with a particular structure, and the feasibility and optimality criteria and the rules for basis change are the same as those used in the simplex procedure. However, the method takes advantage of the simple algorithms developed for the favoured problem and uses them to solve the complete problem in an efficient manner.

Such problems could also be solved by the Decomposition Principle and, vice versa, Decomposition problems can be solved by the present method. The two methods are, however, essentially different in their approach to the problem.