scispace - formally typeset
Search or ask a question

Showing papers on "Job shop scheduling published in 1980"


Journal ArticleDOI
TL;DR: It is shown that all the intermediate (finite capacity) cases of the flowshop scheduling problem with 4 machines is NP-complete, and exact bounds for the relative improvement of execution times when a given buffer capacity is used are proved.
Abstract: We examine the problem of scheduling 2-machine flowshops in order to minimize makespan, using a limited amount of intermediate storage buffers. Although there are efficient algorithms for the extreme cases of zero and infinite buffer capacities, we show that all the intermediate (finite capacity) cases are NP-complete. We prove exact bounds for the relative improvement of execution times when a given buffer capacity is used. We also analyze an efficient heuristic for solving the 1-buffer problem, showing that it has a 3/2 worst-case performance. Furthermore, we show that the "no-wait" (i.e., zero buffer) flowshop scheduling problem with 4 machines is NP-complete. This partly settles a well-known open question, although the 3-machine case is left open here.

244 citations


Journal ArticleDOI
TL;DR: A pseudo-polynomial algorithm is given to enumerate all these efficient points to minimize the holding cost and the maximum tardiness of n jobs to be sequenced on a single machine.

227 citations


Journal ArticleDOI
TL;DR: New heuristic scheduling rules are determined which give high performance for flow-shop scheduling where there is (i) no job-passing and (ii) noJob-waiting.
Abstract: Existing methods are reviewed and new heuristics examined and developed for the flow-shop scheduling problem. Comparative tests are carried out using simulation methods on different sizes of problem and with different variability of processing time data. New heuristic scheduling rules are determined which give high performance for flow-shop scheduling where there is (i) no job-passing and (ii) no job-waiting.

189 citations


Journal ArticleDOI
TL;DR: The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor available, 2nd shortest to the 2nd fastest etc., are examined, and shown to minimize expected values of various cost functions.
Abstract: : We consider preemptive scheduling of N tasks on m processors; processors have different speeds, tasks require amounts of work which are exponentially distributed, with different parameters. The policies of assigning at every moment the task with shortest (longest) expected processing time among those not yet completed to the fastest processor available, 2nd shortest (longest) to the 2nd fastest etc., are examined, and shown to minimize expected values of various cost functions. As special cases we obtain policies which minimize expected flowtime, expected makespan and expected lifetime of a series system with m component locations and N spares. (Author)

145 citations


Journal ArticleDOI
TL;DR: In this article, two experimental studies of design problem solving are presented: one of them isomorphic in structure: a schedule for stages in a manufacturing process or a layout for a business office.
Abstract: : Two experimental studies of design problem solving are presented. Eighty-one subjects worked on one of two design problems that were isomorphic in structure: a schedule for stages in a manufacturing process or a layout for a business office. In Experiment 1, a difference between problem isomorphs is obtained: the 'spatial' office layout problem obtains better performance and shorter solution times than the 'temporal' scheduling problem. In Experiment 2, this difference attenuates when subjects are provided with a graphic representation in both isomorph conditions. The availability of a graphic representation is discussed as an aid for procedural design. (Author)

122 citations


Journal ArticleDOI
TL;DR: In this article, the two duty period scheduling problem is reformulated as a one duty period problem with side constraints, and a Lagrangean relaxation is used to maximize the Lagrange.
Abstract: The two duty period scheduling problem is an integer programming problem with 0-1 constraint coefficients. It is recognized that the problem can be reformulated as a one duty period problem with side constraints. Since the one duty period problem can be solved as a minimal cost network flow problem, we dualize with respect to the side constraints, forming a Lagrangean relaxation which is easily solved. Subgradient optimization is used to maximize the Lagrangean. Computational results are reported for several large problems.

61 citations


Journal ArticleDOI
TL;DR: A heuristic method, based on a linear programming model, gives good integer solutions to the problem of finding a minimum cost set of schedules for railway locomotives to work a given set of trains.
Abstract: A method is described for finding a minimum cost set of schedules for railway locomotives to work a given set of trains. The times at which the trains start may be fixed or variable. A heuristic method, based on a linear programming model, is described. This gives good integer solutions to the problem.

49 citations


Journal ArticleDOI
TL;DR: A new heuristic is devised that, although the heuristic takes negligible time compared to the branch-and-bound procedure, on the average it is within 5 percent of the latter in the uniform case and within 1.3 percent in the general case.
Abstract: The problem of scheduling n independent jobs on m unequal parallel processors to minimize makespan is known to be very difficult for the nonpreemptive case. Until recently, research on this problem has consisted primarily of investigating the “worst case” behavior for simple approximation algorithms for the special cases of equal or uniform processors. Recently, Ibarra and Kim [10] have completed a similar analysis on five simple heuristics for general unequal processors. The approach in the present paper is to investigate the “average” behavior via large-scale computational testing. A new heuristic is devised. It is tested on a large number of problems (about 9,000) for both uniform and general processors, and the results are compared with the best solutions obtained from a truncated branch-and-bound procedure. It is observed that, although the heuristic takes negligible time compared to the branch-and-bound procedure, on the average it is within 5 percent of the latter in the uniform case and within 1.3 percent in the general case. It also performs better than a composite heuristic whose output, for any given problem, is the best of all previously suggested heuristics.

46 citations


Journal ArticleDOI
TL;DR: A node elimination procedure has been suggested in case the two sequences obtained by using Townsend's Townsend's method for solving the single machine quadratic penalty function scheduling problem contain a subset of r jobs in the first r positions.
Abstract: In this note, a node elimination procedure has been suggested in case the two sequences obtained by using Townsend's Townsend, W. 1978. The single machine problem with quadratic penalty function of completion times: A branch and bound solution. Management Sci.24 5 530-534. sufficient conditions for solving the single machine quadratic penalty function scheduling problem contain a subset Jr of r jobs in the first r positions. Numerical illustrations and computational experience has been given in the end.

44 citations


Journal ArticleDOI
TL;DR: Ease of implementation of the various procedures in a real world job shop environment is discussed, and a simple modification to remove the anomaly in ratio type dynamic priority rules is suggested.
Abstract: Dynamic priority dispatching rules in job shops require the computation of all job priorities in a work center queue every time a machine in the work center becomes idle. This is extremely costly. Alternative priority update procedures are studied and comparative results in terms of performance measures and costs are reported. Ease of implementation of the various procedures in a real world job shop environment is discussed. A second problem related to an anomaly in ratio type dynamic priority rules is also studied; a simple modification to remove the anomaly is suggested and the performances of the "old" and "modified" procedures are compared.

40 citations


Journal ArticleDOI
TL;DR: This article points out the analogy of the dynamic lot size problem to a certain vehicle scheduling problem and obtains by analogy a simple heuristic algorithm for the dynamic lots size problem.

Journal ArticleDOI
01 Feb 1980
TL;DR: For solving greater problems some modifications are discussed at the end of the paper, which are essentially based on the notion of “heuristic efficiency”.
Abstract: A mixed integer multiple criteria model is formulated for scheduling problems. Its solution is obtained by an interactive method based on the Tchebycheff-approximation. For solving greater problems some modifications are discussed at the end of the paper, which are essentially based on the notion of “heuristic efficiency”.

Journal ArticleDOI
TL;DR: It is found that EFTA rule is useful to solve the large-scale scheduling problems, and the makespan of the schedule is decreased and the efficiency of machine tools in increased by taking into account the alternative machine tools for the processes of the parts.

Journal ArticleDOI
TL;DR: The ordered flow shop sequencing problem with no in-processing waiting (OFSNW) is considered and it is shown that the sequence in which jobs are arranged according to the shortest processing time rule (SPT) represents an optimal sequence.
Abstract: The ordered flow shop sequencing problem with no in-processing waiting (OFSNW) is considered with respect to mean flow time criterion. It is shown that the sequence in which jobs are arranged according to the shortest processing time rule (SPT) represents an optimal sequence. Additional results for the makespan criterion are also discussed.

Journal ArticleDOI
TL;DR: In this paper, the problem of finding a minimum makespan permutation schedule in a deterministic flow-shop without intermediate queues is equivalent to the shortest distance routing traveling salesman problem, and an algorithm, having quadratic worstcase complexity in terms of the number of partial schedules explicitly enumerated, has been presented.
Abstract: The problem of finding a minimum makespan permutation schedule in a deterministic flow-shop without intermediate queues is equivalent to the shortest distance routing traveling salesman problem. If the task system is semi-ordered, the associated distance matrix of the corresponding traveling salesman problem is found to exhibit some peculiar characteristics. Consequently, we are able to derive some important results which help us to eliminate permutations in the search of the minimum makespan permutation schedule. The most important result is that the optimal permutation schedule is pyramidal. An algorithm, having quadratic worst-case complexity in terms of the number of partial schedules explicitly enumerated, has been presented. Some particular cases of the semi-ordered flow-shop are also discussed.

Journal ArticleDOI
TL;DR: This work proposes an iterative heuristic procedure based on the observation that a two-machine makespan problem is trivially reduced to a Knapsack problem and capitalize on the very special structure of the ILP to effect the reduction with small multipliers.
Abstract: In this paper we study the problem of scheduling n independent jobs available at time zero on m ≥ 2 parallel and identical processors with the objective of minimizing the makespanJWe propose two approaches, both are Knapsack-based. The first is analytical and depends on reducing the set of m occupancy constraints to a single Diophantine equation. We capitalize on the very special structure of the ILP to effect the reduction with small multipliers. The second approach is an iterative heuristic procedure that is based on the observation that a two-machine makespan problem is trivially reduced to a Knapsack problem. Computational experience indicates the superiority of this approach over other existing approaches. Realistic problems of up to 100 jobs on 10 machines are solved in a few seconds on the IBM 370/165.

Journal ArticleDOI
TL;DR: A heuristic algorithm developed to schedule a group of individuals such that every person performs each of the different activities they desire at some point during the time-frame of the schedule and the difference between the exogenously given number of people desired at each available location-activity-period position and those allocated to these positions is minimized.
Abstract: This paper describes a heuristic algorithm developed to schedule a group of individuals such that every person performs each of the different activities they desire at some point during the time-frame of the schedule and the difference between the exogenously given number of people desired at each available location-activity-period position and those allocated to these positions is minimized. The contribution of the present work is in the formulation of the problem, and the resulting ease with which good solutions to large-scale problems can be generated, rather than in the mechanics of the algorithm itself. The mathematic formulation of the scheduling problem is presented first, and subsequently, the solution strategy is elaborated. Experimental results on some reasonably large problems are also presented.

Journal ArticleDOI
TL;DR: In this paper, the effect of time-of-use electric rates for the Pacific Gas and Electric Company's largest customers on individual customer operations is discussed, and an estimate is made of their effect on the rate class load pattern.
Abstract: Time-of-use electric rates for the Pacific Gas and Electric Company's largest customers are examined. The effect of these rates on individual customer operations is discussed, and an estimate is made of their effect on the rate class load pattern. Limitations on the general use of these results are noted.

Journal ArticleDOI
TL;DR: A variety of modifications to this basic theme of scheduling tasks on a system consisting of two parallel processors in order that makespan be minimized are treated, including the cases of identical, proportional, and unrelated processors.
Abstract: This paper is concerned with the problem of scheduling tasks on a system consisting of two parallel processors in order that makespan be minimized. In particular, we treat a variety of modifications to this basic theme, including the cases of identical, proportional, and unrelated processors. In addition, a heuristic scheme is suggested when precedence constraints exist where such constraints may be assignment dependent. Substantial computational experience is reported in all cases where it would appear that relatively large problems can be handled routinely.

Journal ArticleDOI
TL;DR: It has been found that a suitable selection of a state vector reduces greatly the dimensionality of the problem and an algorithm to solve the scheduling problem by using the concept of state vectors of dynamic programming is described.
Abstract: The single facility multiple products scheduling problem is formulated into a multiperiod mathematical programming model with zero-one variables. An algorithm to solve the scheduling problem by using the concept of state vectors of dynamic programming is described. An example of application of the model and the algorithm is also presented. It has been found that a suitable selection of a state vector reduces greatly the dimensionality of the problem

Journal ArticleDOI
TL;DR: A heuristic, random number based computer program developed and implemented at the University of Pittsburgh's School of Medicine to solve linear scheduling problem of students through a clerkship program is described.
Abstract: A significant problem faced by the administration of a medical school is the scheduling of students through a clerkship program. This paper describes a heuristic, random number based computer program developed and implemented at the University of Pittsburgh's School of Medicine to solve this linear scheduling problem.

Journal ArticleDOI
TL;DR: A simulation approach to the comparative analysis of different job scheduling methods with regard to CPU efficiency, the job throughput, and the job waiting time is presented.

Journal ArticleDOI
TL;DR: In this article, the Weibull distribution is used as the limiting form of the frequency distribution of the smallest members of samples of feasible job-shop schedules, and estimates of the optimal solution are obtained by calculating the most likely value of the weibull location parameter, allowing a tight bracket for the optimal makespan value.
Abstract: The paper examines how the computational efficiency of tree search applied to job-shop scheduling problems may be improved by a statistical method which provides both a bound and stopping rule for the search process. The Weibull distribution is used as the limiting form of the frequency distribution of the smallest members of samples of feasible job-shop schedules. Estimates of the optimal solution are obtained by calculating the most likely value of the Weibull location parameter, allowing a tight bracket for the optimal makespan value to be established. Estimates of the optimal solution of sub-problems with fixed partial sequence are proposed as approximate lower bounds for a ‘best-bound’ search strategy.

Journal ArticleDOI
TL;DR: In this paper, a new approach to the hydro-thermal optimal active and reactive power scheduling problem is proposed, and the optimal schedules for a system with thermal and common-flow hydro-plants are obtained.
Abstract: A new approach to the hydro-thermal optimal active and reactive power scheduling problem is proposed. The optimal schedules for a system with thermal and common-flow hydro-plants are obtained. The active-reactive power balance model of the electric network is introduced. Although not as accurate as the load-flow model, the present model is simpler. The scheduling problem is solved by use of the minimum norm formulation of functional analytic optimization.

Journal Article
TL;DR: A heuristic method, based on a linear programming model, gives good integer solutions to the problem of finding a minimum cost set of schedules for railway locomotives to work a given set of trains.
Abstract: A method is described for finding a minimum cost set of schedules for railway locomotives to work a given set of trains. The times at which the trains start may be fixed or variable. A heuristic method, based on a linear programming model, is described. This gives good integer solutions to the problem.


Journal ArticleDOI
TL;DR: Once the classifier described herein has been determined, the pattern recognition approach may be exploited to overcome the dimensionality and computational requirements in such a massive dynamic scheduling problem.