Branch and Bound Method to Solve Multiple Objective Function

Abstract

This paper presents a branch and bound algorithm for sequencing a set of n jobs on a single machine to minimize multiobjective: total cost of flow time, maximum earliness and sum of tardy jobs, when the jobs may have unequal ready time. Two lower bounds were proposed and  heuristic method to get an upper bound. Some special cases were proved and some dominance  rules were proposed and proved, the problem solved up to 35 jobs.