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.

Scheduling flexible maintenance activities subject to job-dependent machine deterioration

Abstract: This paper considers single machine scheduling that integrates machine deterioration. The current maintenance state of the machine is determined by a maintenance level which drops by a certain, possibly job-dependent, amount while jobs are processed. A maintenance level of less than zero is associated with the machine's breakdown and is therefore forbidden. Consequently, maintenance activities that raise the maintenance level again may become necessary and have to be scheduled additionally. In what follows, two general types of maintenance activities are distinguished. In the full maintenance case, maintenance activities are always executed until the machine has reached the maximum maintenance level. In contrast to this, the schedule in the partial maintenance case has to additionally determine the duration of maintenance activities. By combining both cases with regular objective functions such as minimization of maximum tardiness, minimization of the sum of completion times, or minimization of the number of tardy jobs, we obtain a new set of specific single-stage scheduling problems. Besides motivating and introducing these problems, we shall also analyze the computational complexity of general and specific cases.

Single-machine scheduling with dynamic arrivals : Decomposition results and an improved algorithm

Abstract: This article considers the single-machine dynamic scheduling problem where the jobs have different arrival times and the objective is to minimize the sum of completion times. This problem is known to be strongly NP-hard. We develop decomposition results for this problem such that a large problem can be solved by combining optimal solutions for several smaller problems. The decomposition results can be used with any implicit enumeration method to develop an optimal algorithm. Our computational experiment indicates that the computational efficiency of the currently best available branch-and-bound algorithm can be improved with the use of our decomposition results. © 1996 John Wiley & Sons, Inc.

Lot Sizing with Non-Zero Setup Times for Rework

Abstract: In this paper we consider a single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. In each cycle after the normal production of each product the machine is setup for the rework of the defectives of the same product and then the rework process starts. We assume that the setup time for the normal production process as well as the rework process is non-zero. This paper has two objectives. The first objective is to obtain the economic batch quantity (EBQ) for a single product. The second objective is to extend the result of the first objective to the multi-product case. Adopting the common cycle scheduling policy we obtain optimal batch sizes for each product such that the total cost of the system per unit time is minimized.

A new model for single machine scheduling with uncertain processing time

Abstract: Uncertain single machine scheduling problem for batches of jobs is an important issue for manufacturing systems. In this paper, we use uncertainty theory to study the single machine scheduling problem with deadlines where the processing times are described by uncertain variables with known uncertainty distributions. A new model for this problem is built to maximize expected total weight of batches of jobs. Then the model is transformed into a deterministic integer programming model by using the operational law for inverse uncertainty distributions. In addition, a property of the transformed model is provided and an algorithm is designed to solve this problem. Finally, a numerical example is given to illustrate the effectiveness of the model and the proposed algorithm.