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.

Single machine scheduling with deadlines to minimize the weighted number of tardy jobs

Abstract: This paper considers as single machine scheduling problem in which jobs have due dates and deadlines. A job may be completed after its due date, but not after its deadline, in which case it is tardy. A branch and bound algorithm is proposed to find a schedule which minimizes the weighted number of tardy jobs. It uses lower bounds which are derived using the dynamic programming state-space relaxation method. Computational experience with test problems having up to 300 jobs indicates that the lower bounds are extremely effective in restricting the size of the branch and bound search tree.

Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect

Abstract: Recently, scheduling with learning effects has received growing attention. A well-known learning model is called ‘sum-of processing-times-based learning’ where the actual processing time of a job is a non-increasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Motivated by this observation, this paper develops a truncated learning model in which the actual job processing time not only depends on the processing times of the jobs already processed but also depends on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. In this paper, some single-machine scheduling problems can be solved in polynomial time. Besides, the error bounds are also provided for the problems to minimise the maximum lateness and the total weighted completion time.

Scheduling tool changes and special jobs on a single machine to minimize makespan

Abstract: This paper considers a variation of the classical single machine scheduling problem with tool changes. In the variation, two sets of jobs, namely special jobs and normal jobs, are considered. By special jobs, we mean that each special job must be processed within the first prefixed time units of a tool life. To solve the scheduling problem with small size and moderate size, we propose two mathematical programming models. To solve the scheduling problem with large size, we propose three sets of algorithms and focus on the performance of six algorithms based on the studies of a new bin packing problem. Worst-case analysis is conducted. Numerical experiment shows that each of the six algorithms can solve instances with up to 5000 jobs in about 0.5 s with an average relative error less than 4%.

Novel Genetic Bees Algorithm applied to single machine scheduling problem

Abstract: The proposed novel Genetic Bees Algorithm (GBA) is an enhancement to the swarm-based Bees Algorithm (BA). It is called the Genetic Bees Algorithm because it has genetic operators. The structure of the GBA compared to the basic BA has two extra components namely, a Reinforced Global Search and a Jumping Function. The main advantage of adding the genetic operators to BA is that it will help the algorithm to avoid getting stuck in local optima. In this study the scheduling problem of a single machine was considered. When the basic BA was applied to solve this problem its performance was affected by its weakness in conducting global search to explore the search space. However, in most cases the proposed GBA overcame this issue due to the two new components which have been introduced.