Single-machine scheduling

About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.

Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs

Abstract: In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, to analyze the effect of different rules on the effectiveness of the beam search algorithms. The computational results show that using better rules improves the performance of the beam search heuristics. The detailed, filtered beam search (FBS) and recovering beam search (RBS) procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, the detailed beam search (DBS) algorithm requires excessive computation times, and the RBS procedure then becomes the heuristic of choice.

Single-Machine Scheduling with Release Times and Tails

Abstract: We study the problem of scheduling jobs with release times and tails on a single machine with the objective to minimize the makespan. This problem is strongly NP-hard, however it is known to be polynomially solvable if all jobs have equal processing time P. We generalize this result and suggest an O(n2 log nlog P) algorithm for the case when the processing times of some jobs are restricted to either P or 2P.

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

Abstract: This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.

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.

Beam search heuristics for quadratic earliness and tardiness scheduling

Abstract: In this paper, we present beam search heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. These heuristics include classic beam search procedures, as well as filtered and recovering algorithms. We consider three dispatching heuristics as evaluation functions, in order to analyse the effect of different rules on the performance of the beam search procedures. The computational results show that using better dispatching heuristics improves the effectiveness of the beam search algorithms. The performance of the several heuristics is similar for instances with low variability. For high variability instances, however, the detailed, filtered and recovering beam search (RBS) procedures clearly outperform the best existing heuristic. The detailed beam search algorithm performs quite well, and is recommended for small- to medium-sized instances. For larger instances, however, this procedure requires excessive computation times, and the RBS algorithm then becomes the heuristic of choice.