We consider the problem of scheduling n jobs to minimize the total earliness and tardiness penalty. We review the literature on this topic, providing a framework to show how results have been generalized starting with a basic model that contains symmetric penalties, one machine and a common due date. To this base we add such features as parallel machines, complex penalty functions and distinct due dates. We also consolidate many of the existing results by proving general forms of two key properties of earliness/tardiness models.

Sequencing with Earliness and Tardiness Penalties: A Review

This paper reviews recent studies of dispatching rules. A dispatching rule is used to select the next job to be processed from a set of jobs awaiting service. The paper has two objectives. The first is to discuss the state of the art in the study of dispatching rules. The discussion includes analytical approaches, simulation techniques and evaluation criteria. The second objective of the paper is to compare several of the dispatching rules listed in the Appendix using the results of recently published studies. It is impossible to identify any single rule as the best in all circumstances. However, several rules have been identified as exhibiting good performance in general.

A state-of-the-art survey of dispatching rules for manufacturing job shop operations.

Survey of scheduling research involving due date determination decisions

Recent research studies of job shop scheduling have begun to examine the interaction between sequencing priorities and the method of assigning due-dates. This paper surveys the tactical aspects of this interaction, focusing primarily on average tardiness as a measure of scheduling effectiveness. The discussion highlights several factors that can affect the performance of dispatching rules, such as the average flow allowance, the due-date assignment method, and the use of progress milestones. A set of simulation experiments illuminates how these factors interact with the dispatching rule, and the experimental results suggest which combinations are most effective in a scheduling system.

Sequencing Rules and Due-Date Assignments in a Job Shop

In this paper, we survey the literature on heuristic priority rule-based job shop scheduling. Priority rules have been intensively investigated over the last 30 years by means of simulation experiments. They are also used in Shop Floor Control software systems. We present a classification, a characterization, and an evaluation of elementary priority rules. Some priority rule-related model extensions are discussed.

A Survey of Priority Rule-Based Scheduling

Much of job-shop scheduling research is based on the assumption that due dates are outside the control of the scheduler. The paper examines several procedures for specifying due dates, largely dependent on the expected processing time for jobs and on the level of congestion in the shop. The effect of these procedures is examined in the case of three loading rules (FIFO, St and SI∗) On waiting times, on missing due dates and on notional cost functions. The study is based on numerous simulations of a given shop operating at various levels of load ratio and the case of a fluctuating load is briefly examined.

Due dates in job shop scheduling

The paper considers the problem of n given jobs to be processed on a single machine where it is desirable to minimise the variance of job waiting times. A theorem is presented to the effect that the optimal sequence must be V-shaped i.e., the jobs must be arranged in descending order of processing times if they are placed before the shortest job, but in ascending order of processing times if placed after it, and an algorithm for determining the optimal solution is given. A heuristic method is proposed for solving the problem where n is large; this method requires very little computing and was found to produce very good results for a sample of problems of varying size. The concept of the “efficient set” is examined and heuristic methods for generating this set are given.

Minimising Waiting Time Variance in the Single Machine Problem

This paper reports on the results of various experi ments with the loading rule SIx for scheduling jobs and compares its performance with two other, general ly more popular, methods. Several advantages of the SIx rule are discussed.

Experiments with the SIX rule in job-shop scheduling:

The effectiveness of various scheduling or loading rules in a job shop has been widely studied through simulation, where a given shop can be subjected to alternative patterns of arrivals and processing. This study is particularly concerned with the case when arrivals are in batches, either of regular size or where the batch size is Poisson distributed, and when the batches arrive at regular time intervals, and certain empirical relationships between three loading rules are investigated. Two types of operational flexibility are examined, the first where more than one machine may perform a given operation and the second where changes in the sequence of operations are allowed, and the effect of such flexibilities on the expected job waiting time is determined. Finally, the effect of different procedures for determining due-dates for arriving jobs is investigated.

Studies in a Simulated Job Shop

Most queueing models are based on assumptions of steady-state conditions, and most solutions of mathematical models in this field are almost entirely concerned with steady-state conditions. Elaborate queueing models (such as job-shop models) are not amenable to analytical solutions, and investigators have therefore to resort to simulation. The main objective, however, is still to derive values for such variables as the average waiting time and the average queue length that may be expected in the long run. In practice, obtaining this information may require long simulation exercises.

I. G. Chowdhury

Papers

Due dates in job shop scheduling

Minimising Waiting Time Variance in the Single Machine Problem

Experiments with the SIX rule in job-shop scheduling:

Studies in a Simulated Job Shop

A note on steady-state results in queueing and job-shop scheduling: