Global optima for linearly constrained business decision models

It is well-known that many business administration decision problems can be formulated as optimization problems. There are well over four hundred algorithms to solve such problems. However, these algorithms are custom-made for each specific type of problem. This has led to classification of problems, such as linear, fractional, quadratic, convex and non-convex programs. This paper presents a simple alternative approach to obtain global solutions to bounded linearly constrained optimization problems with differentiable objective functions. We propose an effective explicit enumeration scheme for solving a large class of problems with linear constraints and a differentiable objective function. The primary intention of this paper is to provide an optimization tool that can be understood easily and applied to a wide range of problems. The unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region. The proposed algorithm has the following useful features. It is a general-purpose algorithm; i.e., it employs one common treatment for all cases; it guarantees global optimization in each case unlike other general-purpose local optimization algorithms; it has simplicity because it is intuitive and requires only first order derivatives (gradient); and it provides useful information for sensitivity analysis. The solution algorithm and its applications to finance, economics, marketing, and production and operations management are presented in the context of numerical problems already solved by other methods.