In a general flow-shop situation, where all the jobs must pass through all the machines in the same order, certain heuristic algorithms propose that the jobs with higher total process time should be given higher priority than the jobs with less total process time. Based on this premise, a simple algorithm is presented in this paper, which produces very good sequences in comparison with existing heuristics. The results of the proposed algorithm have been compared with the results from 15 other algorithms in an independent study by Park [13], who shows that the proposed algorithm performs especially well on large flow-shop problems in both the static and dynamic sequencing environments.

A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem

/pdf/sequencing-and-scheduling-algorithms-and-complexity-lnutyrr3kz.pdf

Sequencing and scheduling: algorithms and complexity

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

We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems.

A multi-objective genetic local search algorithm and its application to flowshop scheduling

A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem

This paper describes a simple algorithm for the solution of very large sequence problems without the use of a computer. It produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time. Up to m-1 sequences may be found.

http://www1.ximb.ac.in/users/fac/surya/surya.nsf/23e5e39594c064ee852564ae004fa010/0f776dc7f3fe2550652574e2002240df/$file/n jobs and m- machine problem.pdf

A Heuristic Algorithm for the n Job, m Machine Sequencing Problem

We consider an n job, one machine scheduling problem in which all jobs have a common due date. The objective is to determine the optimal value of this due date and an optimal sequence to minimize a...

Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem

This paper reviews the flowshop-sequencing research since 1954 that has been devoted to the static deterministic case in which n jobs are to be processed through a shop in which the processing times at each stage are fixed. The paper then comments on NP-completeness, the selection of criteria for optimization, and the lack of applications of this work in industry. Finally, it draws some conclusions about the possible future of sequencing research and the lessons that this area's work has to teach the rest of operations research.

The Lessons of Flowshop Scheduling Research

Given processing times of n jobs on a single machine with penalties for earliness and tardiness and penalties associated with assignment of due-dates, the objective is to select optimal due-dates and optimal sequence. Scheduling procedure for the solution of this problem is presented along with proof of optimality and illustrative numerical examples.

Optimal assignment of due-dates for a single processor scheduling problem

Types of industrial scheduling problems were investigated by personal visits to plants and by questionnaires mailed to scheduling departments. Information on problem sizes, job flow, optimization criteria and job similarity was obtained. Results indicate that most of the present procedures in theoretical research cannot handle average industrial problems. Also most commonly used objective criteria differ from industrial goals. There is a definite need for better communication between sequencing researchers and scheduling practioners.

Milton L. Smith

Papers

A Heuristic Algorithm for the n Job, m Machine Sequencing Problem

Common Due Date Assignment to Minimize Total Penalty for the One Machine Scheduling Problem

The Lessons of Flowshop Scheduling Research

Optimal assignment of due-dates for a single processor scheduling problem

Sequencing Research and the Industrial Scheduling Problem