A Variable Neighborhood Search for the Single Machine Total Stepwise Tardiness Problem

Abstract

A new type of tardy cost, called stepwise tardiness, is considered in a single machine problem. The stepwise tardiness scheduling has been found in many practical situations. To the best of our knowledge, there exist few studies directly addressing the problem. In this paper, we develop a heuristic for the single machine total stepwise tardiness (SMTST) problem. In addition, a variable neighborhood search (VNS), which is a novel metaheuristic, is proposed to improve the quality of solution. The proposed VNS algorithm includes a new encoding scheme and three new neighborhood structures. The experimental results show that the proposed VNS algorithm can obtain a good performance for the considered problem.