Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives

We consider a single-machine scheduling problem with two-agents, each with a set of non-pre-emptive jobs, where two agents compete for the use of a single processing resource. A switchover time arises whenever a job of one agent is processed after a job of another agent. Each agent wants to minimize a certain objective function, which depends upon the completion time and switchover time of their own jobs only. This paper considers the minimization of total weighted completion time of the first agent subject to an upper bound on the makespan of the second agent. We introduce some properties to the problem. The properties describe the structure of an optimal solution which is being used for developing an optimal algorithm. We propose an optimal algorithm, a simple heuristic algorithm, and a particle-swarm-based meta heuristic algorithm to solve the problem. The heuristic algorithm is based on the weighted shortest process time-first rule. The performances of the heuristic and particle swarm algorithms are evaluated on randomly generated problem instances. We perform the numerical analysis to reveal the properties of the proposed problem.