Linear Programming and Resource Allocation Modeling

This book provides the foundation for the development of data envelopment analysis. It is useful as a main resource or as a supplement in an economics or management science course. This book contains 14 chapters. Chapter 1 introduces the primal and dual problems via an optimum product mix problem, while Chapter 2 reviews the rudiments of vector and matrix operations. Chapter 3 covers the canonical and standard forms of a linear programming problem. The material in Chapter 4 addresses the computational aspects of linear programming. Next, Chapter 5 considers variations of the standard simplex theme. Duality theory is presented in Chapter 6, while Chapter 7 discusses single- and multiple- process production functions. Chapter 8 covers sensitivity analysis of the optimal solution, while Chapter 9 analyzes structural changes. Chapter 10 focuses on parametric programming and consequently sets the stage for the material presented in the next chapter. To this end, Chapter 11 employs parametric programming to develop concepts such as the demand function for a variable input and the supply function for the output of an activity. In Chapter 12, the concept of duality is revisited; the primal and dual problems are reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. Next, Chapter 13 covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming. Finally, data envelopment analysis (DEA) is covered in Chapter 14.