:- Due to the stubborn nature of the deterministic job-shop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS:- Scheduling Theory; Job-Shop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...

: This paper proposes an extension of the constraint-based approach to job-shop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraint-satisfaction levels. Uncertainty is qualitatively described is terms of possibility distributions. The paper formulates a simple mathematical model of jobshop scheduling under preference and uncertainty, relating it to the formal framework of constraint-satisfaction problems in Artificial Intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of well-known look-ahead schemes. 1. Introduction There are traditionally three kinds of approaches to jobshop scheduling problems: priority rules, combinatorial optimization and constraint analysis. The first kind ...

A great deal of research has been focused on solving the job-shop problem (P J ), over the last forty years, resulting in a wide variety of approaches. Recently, much effort has been concentrated on hybrid methods to solve P J as a single technique cannot solve this stubborn problem. As a result much effort has recently been concentrated on techniques that combine myopic problem specific methods and a meta-strategy which guides the search out of local optima. These approaches currently provide the best results. Such hybrid techniques are known as iterated local search algorithms or meta-heuristics. In this paper we seek to assess the work done in the job-shop domain by providing a review of many of the techniques used. The impact of the major contributions is indicated by applying these techniques to a set of standard benchmark problems. It is established that methods such as Tabu Search, Genetic Algorithms, Simulated Annealing should be considered complementary rather than competitive...

Scheduling is concerned with allocating limited resources to tasks to optimize certain objective functions. Due to the popularity of the Total Quality Management concept, ontime delivery of jobs has become one of the crucial factors for customer satisfaction. Scheduling plays an important role in achieving this goal. Recent developments in scheduling theory have focused on extending the models to include more practical constraints. Furthermore, due to the complexity studies conducted during the last two decades, it is now widely understood that most practical problems are NP-hard. This is one of the reasons why local search methods have been studied so extensively during the last decade. In this paper, we review briefly some of the recent extensions of scheduling theory, the recent developments in local search techniques and the new developments of scheduling in practice. Particularly, we survey two recent extensions of theory: scheduling with a 1-job-on-r-machine pattern and machine scheduling with availability constraints. We also review several local search techniques, including simulated annealing, tabu search, genetic algorithms and constraint guided heuristic search. Finally, we study the robotic cell scheduling problem, the automated guided vehicles scheduling problem, and the hoist scheduling problem.

For large industrial applications the constraint-based formulation of scheduling problems fits better than mathematical representations from Operational Research, because the constraint approach is more flexible and can be adapted more easily to organizational changes in the production. However, the search for a good solution for realistic applications can be very expensive and furthermore, in scheduling one is not only interested in a feasible solution but also in an optimized solution. In this paper I present iterative improvement methods that can be used to optimize a schedule that is represented by constraints. These methods start with any schedule and try to optimize it by iterative modifications. The goal of the optimization method may be a minimization of the number of constraint violations or a maximization of a function that aggregates the satisfaction degrees of all involved soft constraints. Additionally, consistency techniques for constraints can be used to che...

In this paper we introduce a fuzzy based engine for the scheduling problem. We assume that a human planner is unable to determine the weights for a multi-objective system but is able only to compare between pairs of objectives according to a limited vocabulary. We convert this vocabulary to fuzzy terminology and apply a fuzzy based optimum search for a solution to the scheduling problem. We demonstrate our approach using a real world scheduling system. 1. INTRODUCTION Scheduling has been examined in the operations research literature since the early fifties. It can be defined as allocation of resources over time to perform a collection of tasks. In general, scheduling is the problem of sequencing a set of operations and allocating them to temporal slots without violating technical and capacitive constraints. These operations may be operations on machines in a factory, train or car movement in transportation, lessons at school, or computer processes performed on the CPU. By using an ...

Abstract — The purpose of this paper is to describe the implementation and testing of the tabu cycle method and two variants of the conditional probability method. These methods were originally described in Glover and Laguna (1997) but have been largely ignored in the tabu search literature. For the purpose of testing, we employ a singleattribute implementation of a short-term memory procedure for the solution of a single machine scheduling problem. Computational experiments that employ instances with up to 200 jobs reveal the usefulness of the tabu cycle and the conditional probability methods as viable alternatives for managing the short-term memory in a tabu search implementation. Tabu Cycle Method — 2 — Laguna 1.

Abstract — Researchers and practitioners frequently spend more time fine-tuning algorithms than designing and implementing them. This is particularly true when developing heuristics and metaheuristics, where the “right ” choice of values for search parameters has a considerable effect on the performance of the procedure. When testing metaheuristics, performance typically is measured considering both the quality of the solutions obtained and the time needed to find them. In this paper, we describe the development of CALIBRA, a procedure that attempts to find the best values for up to five search parameters associated with a procedure under study. Since CALIBRA uses Taguchi’s fractional factorial experimental designs coupled with a local search procedure, the best values found are not guaranteed to be optimal. We test CALIBRA on six existing heuristic-based procedures. These experiments show that CALIBRA is able to find parameter values that either match or improve the performance of the procedures resulting from using the parameter values suggested by their developers. The latest version of CALIBRA can be downloaded for free from

One simple way to schedule is to simply keep incrementally swapping and inserting batches until no more improvement is made. This greedy method works very quickly until it stops at one of the local optima. Tabu search is a means of using the quick greedy method while also escaping local optima. Refer to Glover [Jul-Aug 1990] and Glover [Winter 1990] for a tutorial on tabu search. Barnes [1991], Barnes and Chambers [1991], Barnes [1991 a], Barnes and Laguna [1991 b], Laguna, Barnes, and Glover [1991], and Widmer [1991] apply tabu search to scheduling. Punnen and Aneja [1995] and Laguna et al. apply tabu search to NP-Hard versions of assignment problems. There are three characteristics that must be present before a method can be said to be a tabu search. 1) A tabu: a temporary restriction excluding certain choices from the search. 2) Short-term memory: a list of tabus to prevent backtracking to previous steps for a period of time. 3) Aspiration level: a criteria for overriding the tabus. Indeed, a tabu search might use any ad hoc strategy to find local optima. The unique

Years of learning are not sufficient for one who wishes to prepare a dissertation; also necessary is an environment which encourages one to develop the talents which God has given and to become an intelligent person, a responsible person, a kind person, a successful person. For providing such a setting I thank my family. To many others am I indebted: to the chairman of my supervisory committee, Dr. Chung-Yee Lee, who has been an exceptional influence on my development as a researcher, teacher, and scholar, to department chairman Dr. Jack Elzinga, Dr. Boghos Sivazlian, and the members of my committee; to all who were involved in the Harris project and whose effort was critical to this work; and to the quality friends, classmates, and teachers whom I have known and who have all added something valuable to my life.