Single machine scheduling with two-agent for total weighted completion time objectives

This paper considers two-agent scheduling problem with a single machine which is responsible for processing jobs from two agents. The objective is to minimize the objective function of one agent, subject to an upper bound on the objective function of the other agent. The objectives considered in this paper are, (1) the minimization of total completion time and (2) the minimization of total weighted completion time. To solve these problems, one heuristic and an Ant Colony Optimization algorithm are proposed. The heuristic suggested in the paper are motivated by the Weighted Shortest Processing Time first (WSPT) rule. A numerical experiment is performed on randomly generated problem instances. The performance of the algorithm is evaluated by comparing it with the lower bound value of all three problems considered in the present paper.