New Approach to Solve Assignment Problems with Branch and Bound Algorithm

Abstract

This paper presents a new branch and bound algorithm for solving the assignment problems that uses a lower bound based with branching procedure. This is special type of linear programming problem dealing with the allocation of various resources to the various activities on one to one basis. Most of the business organization operates in traditional and old fashioned manner. Decision making is based on judgment and is quite subjective. Consequently, the entire process of decision making may lead to uncertain and unwanted results. Industries need more scientific and data driven strategies to achieve higher goals and to avoid risks of failure. The assignment problem deals with the maximum profit assigning of jobs or objects to agents such that each job is assigned to precisely one person subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column and row generation and also branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem. First, a generalized assignment issue that is solved by an existing Hungarian approach that only employs column generation is solved in this study by employing both row and column generation, and the optimal solution is obtained, which is similarly similar. The study is classified according to the objective, solution methodologies and related considerations. This paper hopes to give the reader an idea about the best job assigning that is modeled in this paper, discuss the formulation of assignment problem, its efficacy, enumerate the benefits gained and identify areas for further improvement.