A mathematical model and heuristic algorithms for an unrelated parallel machine scheduling problem with sequence-dependent setup times, machine eligibility restrictions and a common server

Abstract

Parallel machine scheduling problems with common servers have many industrial applications. In this paper, we study a generalized problem of scheduling with a common server, which is the unrelated parallel machine scheduling problem with sequence-dependent setup times and machine eligibility restrictions. The objective function involves the minimization of the total weighted tardiness. A mixed integer linear programming (MILP) model is proposed to solve this complex problem. Due to the NP hardness of the problem, tabu search (TS) and simulated annealing (SA) algorithms are proposed. The initial solutions of the algorithms are obtained by a modified apparent tardiness cost with setups (ATCS) dispatching rule. The proposed algorithms are compared using a randomly generated data set.