In classical deterministic scheduling problems, it is assumed that all jobs have to be processed. However, in many practical cases, mostly in highly loaded make-to-order production systems, accepting all jobs may cause a delay in the completion of orders which in turn may lead to high inventory and tardiness costs. Thus, in such systems, the firm may wish to reject the processing of some jobs by either outsourcing them or rejecting them altogether. The field of scheduling with rejection provides schemes for coordinated sales and production decisions by grouping them into a single model. Since scheduling problems with rejection are very interesting both from a practical and a theoretical point of view, they have received a great deal of attention from researchers over the last decade. The purpose of this survey is to offer a unified framework for offline scheduling with rejection by presenting an up-to-date survey of the results in this field. Moreover, we highlight the close connection between scheduling with rejection and other fields of research such as scheduling with controllable processing times and scheduling with due date assignment, and include some new results which we obtained for open problems.

A survey on offline scheduling with rejection

The existence of the learning effect in many manufacturing systems is undoubted; thus, it is worthwhile that it be taken into consideration during production planning to increase production efficiency. Generally, it can be done by formulating the specified problem in the scheduling context and optimizing an order of jobs to minimize the given time criteria. To carry out a reliable study of the learning effect in scheduling fields, a comprehensive survey of the related results is presented first. It reveals that most of the learning models in scheduling are based on the learning curve introduced by Wright. However, further study about learning itself pointed out that the curve may be an ldquoSrdquo-shaped function, which has not been considered in the scheduling domain. To fill this gap, we analyze a scheduling problem with a new experience-based learning model, where job processing times are described by ldquoSrdquo-shaped functions that are dependent on the experience of the processor. Moreover, problems with other experience-based learning models are also taken into consideration. We prove that the makespan minimization problem on a single processor is NP-hard or strongly NP-hard with the most of the considered learning models. A number of polynomially solvable cases are also provided.

Experience-Based Approach to Scheduling Problems With the Learning Effect

The integration in production planning, scheduling, maintenance and quality has gained much attention from researchers in recent years. These areas are usually treated independently, which yielded independent models for each function. It is widely believed that these separate models will provide suboptimal solutions, due to the fact that they are interrelated. Proper understanding of this dependency will open a new avenue for more integrated models, and result in significant savings in operational cost and improved efficiency for any production system. This paper reviews the literature on models addressing different aspects of integration in these areas. This integration is treated in two different ways in the literature. The first way is to present models where a model is considered for one function taking into account the other. These models are referred to as interrelated models. The second way is to simultaneously model two or more elements of the production system. These models are referred to as integrated models. The objective of this paper is to review research in both interrelated and integrated modelling of production planning, scheduling, maintenance and quality to identify possible future directions.

Integrated models in production planning and scheduling, maintenance and quality: a review

Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity

Game theory based real-time multi-objective flexible job shop scheduling considering environmental impact

Scheduling a maintenance activity and due-window assignment on a single machine

We study a single machine scheduling problem. The processor needs to go through a maintenance activity, which has to be completed prior to a given deadline. The objective function is minimum total weighted completion time. The problem is proved to be NP-hard, and an introduction of a pseudo-polynomial dynamic programming algorithm indicates that it is NP-hard in the ordinary sense. We also present an efficient heuristic, which is shown numerically to perform well.

Scheduling a maintenance activity to minimize total weighted completion-time

We extend a classical single-machine due-window assignment problem to the case of position-dependent processing times. In addition to the standard job scheduling decisions, one has to assign a time interval (due-window), such that jobs completed within this interval are assumed to be on time and not penalized. The cost components are: total earliness, total tardiness and due-window location and size. We introduce an O(n
3) solution algorithm, where n is the number of jobs. We also investigate several special cases, and examine numerically the sensitivity of the solution (schedule and due-window) to the different cost parameters.

https://link.springer.com/content/pdf/10.1057%2Fpalgrave.jors.2602439.pdf

A due-window assignment problem with position-dependent processing times

Due-date assignment on uniform machines

We study a problem of scheduling a maintenance activity on parallel identical machines, under the assumption that all the machines must be maintained simultaneously. One example for this setting is a situation where the entire system must be stopped for maintenance because of a required electricity shut-down. The objective is minimum flow-time. The problem is shown to be NP-hard, and moreover impossible to approximate unless P = NP. We introduce a pseudo-polynomial dynamic programming algorithm, and show how to convert it into a bicriteria FPTAS for this problem. We also present an efficient heuristic and a lower bound. Our numerical tests indicate that the heuristic provides in most cases very close-to-optimal schedules. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009

Assaf Sarig

Papers

Scheduling a maintenance activity and due-window assignment on a single machine

Scheduling a maintenance activity to minimize total weighted completion-time

A due-window assignment problem with position-dependent processing times

Due-date assignment on uniform machines

Scheduling a maintenance activity on parallel identical machines