A hybrid metaheuristic for the prize-collecting single machine scheduling problem with sequence-dependent setup times

This paper investigates a single machine scheduling problem with strong industrial background, named the prize-collecting single machine scheduling problem with sequence-dependent setup times. In this problem, there are n candidate jobs for processing in a single machine, each job has a weight (or profit) and a processing time, and during processing a symmetric sequence-dependent setup time exists between two consecutive jobs. Since there is a maximum available time limitation of the machine, it is generally impossible to complete the processing of all the candidate jobs within this time limitation. The objective is to find a job processing sequence of maximal job weights (or profits) over a subset of all candidate jobs whose makespan does not exceed the given time limitation. This problem can be considered as an application of the orienteering problem (OP) in the field of discrete manufacturing. We formulate this problem as a mixed integer linear programming (MILP) model and propose a hybrid metaheuristic combining the structures of scatter search and variable neighborhood search. Computational results on a large number of randomly generated instances with different structures show that the proposed hybrid metaheuristic outperforms CPLEX and two metaheuristics proposed for the OP.