Linear Programming Vasek Chvatal

Build Strong Foundation of Optimization Techniques to Apply in Business

A. Planning Company Operations: The General Problem At more or less regular intervals, the management of an industrial enter­ prise is confronted with the problem of planning operations for a coming period. Within this category of management problems falls not only the overall planning of the company's aggregate production but problems of a more limited nature such as, for example, figuring the least-cost combina­ tion of raw materials for given output or the optimal transportation schedule. Any such problem of production planning is most rationally solved in two stages: (i) The first stage is to determine the feasible alternatives. For example, what alternative production schedules are at all compatible with the given capacity limitations? What combinations of raw materials satisfy the given quality specifications for the products? etc.

In Linear Programming: A Modern Integrated Analysis, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem and, unlike most books, the duality theorem is derived from Farkas's Lemma, which is proved as a convex separation theorem. The tedium of the simplex method is thus avoided.

Mechanism of Solving Linear Programming Problem using Simplex Method