A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs

Abstract

This paper studies a single-machine scheduling problem with the objective of minimizing the total tardiness for a set of independent jobs. The processing time of a job is modeled as a step function of its starting time and a specific deteriorating date. The total tardiness as one important objective in practice has not been concerned in the studies of single-machine scheduling problems with step-deteriorating jobs. To overcome the intractability of the problem, we propose a heuristic named simple weighted search procedure (SWSP) and a general variable neighborhood search algorithm (GVNS) to obtain near optimal solutions. Extensive numerical experiments are carried out on randomly generated test instances in order to evaluate the performance of the proposed algorithms. By comparing to the CPLEX optimization solver, the heuristic SWSP and the standard variable neighborhood search, it is shown that the proposed GVNS algorithm can provide better solutions within a reasonable running time.