Linear Programming and Resource Allocation Modeling

Preface

Economists, engineers, and management scientists have long known and employed the power and versatility of linear programming as a tool for solving resource allocation problems. Such problems have ranged from formulating a simple model geared to determining an optimal product mix (e.g. a producing unit seeks to allocate its limited inputs to a set of production activities under a given linear technology in order to determine the quantities of the various products that will maximize profit) to the application of an input analytical technique called data envelopment analysis (DEA) – a procedure used to estimate multiple‐input, multiple‐output production correspondences so that the productive efficiency of decision making units (DMUs) can be compared. Indeed, DEA has now become the subject of virtually innumerable articles in professional journals, textbooks, and research monographs.

One of the drawbacks of many of the books pertaining to linear programming applications, and especially those addressing DEA modeling, is that their coverage of linear programming fundamentals is woefully deficient – especially in the treatment of duality. In fact, this latter area is of paramount importance and represents the “bulk of the action,” so to speak, when resource allocation decisions are to be made.

That said, this book addresses the aforementioned shortcomings involving the inadequate offering of linear programming theory and provides the foundation for the development of DEA. ...