A single-machine scheduling with a truncated linear deterioration and ready times

Abstract

Recently, machine scheduling problems with deteriorating jobs have received interestingly attention from the scheduling research community. Majority of the research assumed that the actual job processing time is an increasing function of its starting time. However, no job can remain undeteriorated indefinitely in real life situations. This paper considers a single-machine scheduling problem with a truncated linear deteriorating effect and ready times. By the truncated linear deteriorating effect, it means that the actual processing time of a job is a function of its starting time and a control parameter. The objective is to minimize the makespan. A mixed integer programming model and a branch-and-bound algorithm coupled with several dominance properties and two lower bounds are developed to search for the optimal solution. In addition, an ant colony and a Tabu search algorithm where each is refined by the three improvements are also proposed for a near-optimal solution, respectively. A computational experiment is then conducted to evaluate the impacts of the used parameters on the performances of the proposed algorithms.