A branching algorithm to solve binary problem in uncertain environment: an application in machine allocation problem

Abstract

This paper studies a new algorithm to solve the uncertain generalized assignment problem. The presented technique is based on the concept of branch and bound rather than the usual simplex based techniques. At first, the problem is relaxed to the transportation model which is easy to handle and work with. The model, so obtained is solved by the conventional transportation technique. The obtained solution serves as starting solution for further sub problems. The ambiguity in parameters is represented by triangular fuzzy numbers. We propose a linear ranking function, called the grade function which is based on the centroid method. The grade function is used to rank the triangular fuzzy numbers. The proposed approach is justified numerically by showing its application in generalized machine allocation problem.