Foundation of Linear Programming

Abstract

The aim and scope of this paper are the infusion of purposeful action by decision makers with an explicit understanding of analytical linear programming (LP) tools in order that the managers will implement strategic results correctly. The advances in computing software have brought LP tools to the desktop for a variety of applications to support managerial decision-making. However, it is already recognized that current LP tools do not answer the managerial questions satisfactorily. For instance, there is a costly difference between the mathematical and managerial interpretations of sensitivity analysis. The LP software packages provide sensitivity results about the optimality of a basis and not about the optimality of the values of the decision variables, and the shadow prices that are of interest to the manager. Society has developed the largest sensitivity region based on “optimal solution,” not that which “preserves the basis” that allows for simultaneous dependent/independent changes. The aim and results of this article are found further in the work.

Solving Solid Transportation Problem with Multi-Choice Cost and Stochastic Supply and Demand

“…Rao (1984) described the chance constrained and two stage programming methods for solving a stochastic linear programming problem. Arsham (2012) presented the foundation of linear programming with a managerial perspective from solving system of inequalities to software implementation. Mahapatra et al (2010) have presented the fuzzy programming technique to obtain the compromise solution of multi-objective stochastic transportation problem.…”