The focus area of this paper is on the assignment problem with budget constraints which is one of the application area of combinatorial optimization that operates on the domain of those optimization problems,in which the set of feasible solutions is discrete or can be reduced to discrete,and in which the goal is to find the best solution. It is particularly concerned with solving the unconstrained assignment problems with Hungarian algorithm and the constrained assignment problem by cutting plane or outer linearization algorithm for solving the Lagrangian dual problem in which, at each iteration,the function that approximates the dual function is optimized. The paper is divided in to two chapters. In the first chapter,the classical assignment problem,the problem of finding optimum (minimum or maximum) cost or profit assignment a set of workers or resources to jobs or activities to gather with its mathematical formulation,solution methods and special cases in assignment problems were considered. Under the second chapter, we have considered generalization of the classical assignment problem concerning resource(or budget) constraints, due to the variety of real life problems.
Assignment Problem is one of the first fundamental problems in the area of combinatorial optimization. Despite its historical roots, the problem has tremendous importance to date, due to its numerous real life applications in like facility location, personnel scheduling, job scheduling, production planning, project assignment, task assignment, time-tabling, vehicle routing, storage space allocation, etc. This book comprises some real life assignment and related problems involving imprecise cost/time parameters. In order to represent those imprecise parameters, interval numbers have been used here as this representation is the best among others. The associated problems have been solved using Genetic Algorithm efficiently. A salient feature of this book is that most of the algorithms have been written in a lucid manner with suitable examples using figures. This book should interest academicians, OR/GA practitioners and executives of different industries and business organizations.