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Minimizing Arbitrary Earliness/Tardiness Penalties with Common Due Date in Single-Machine Scheduling Problem Using a Tabu-Geno-Simulated Annealing
Materials and Manufacturing Processes
Abstract
In this paper, the single machine scheduling problem for a common due date with arbitrary earliness/tardiness penalties is discussed. The objective
is to determine the common due date and processing sequence of new jobs together with the re-sequencing of old jobs to minimize the sum of
total earliness/tardiness (E/T), completion time, and due date (dd) related penalties. We propose a new approach Tabu-Geno-Simulated Annealing
(TGSA) by hybridization of three well-known metaheuristics, which have proven to be effective for this non deterministic polynomial time (NP)
hard scheduling problem, namely, genetic algorithms (GA), tabu search, and simulated annealing (SA). Computational results have shown the
effectiveness of the proposed approach in comparison with the ad-hoc heuristics on various single-machine scheduling problems. The assessment
of the proposed hybridization indicates the efficiency in both the result and the time versus the other methods.
... They emphasized that hybrid metaheuristic algorithms can be more efficient than the general ones. Combining algorithms to a hybrid one leads an intelligence search engine for performing the exploration and exploitation phases more efficiently (Shirazi et al., 2010 andLi et al., 2017). ...
Growing environmental concerns and social legislations enforce decision makers to design their supply chains considering environmental and social impacts as well as economical objectives. Degradation difficulties and recovering profits lead to recycle scraped tires regarding the sustainability factors. This paper firstly develops a multi-objective mixed integer linear programming model for designing sustainable tire closed-loop supply chain network. The proposed model aims to optimize total cost, environmental impacts of establishment of facilities, processing of tires and transportation between each level as well as social impacts including job opportunities and work's damages. To alleviate the drawbacks of existing metaheuristic algorithms when solving the large-scale networks, four new hybrid metaheuristic algorithms based on the advantages of recent and old ones are developed. To evaluate the quality of the proposed algorithms, extensive computational experiments, comparison, and sensitivity analyses are conducted with different criteria. Results reveal that hybrid algorithms are effective approaches to solve the underlying problem in large-scale networks.
... In the solution phase, global search is made by simulated annealing, global search is made by genetic algorithm according to the results in the tabu list. The number of jobs considered was between the range of 15 and 25 (Shirazi, et al., 2010). ...
... The objective of this problem is to minimize the total amount of earliness and tardiness of jobs, which are assigned to a single machine. Shirazi et al. (2010) proposed a new approach called Tabu-Geno-Simulated Annealing (TGSA) by hybridization of three well-known metaheuristics for solving single machine scheduling problem for a common due date with arbitrary E/T penalties. The objective is to determine the common due date and processing sequence of new jobs together with the re-sequencing of old jobs to minimize the sum of total E/T, completion time, and due date related penalties. ...
This paper considers preemption and idle time are allowed in a single machine scheduling problem with just-in-time (JIT) approach. It incorporates Earliness/Tardiness (E/T) penalties, interruption penalties and holding cost of jobs which are waiting to be processed as work-in-process (WIP). Generally in non-preemptive problems, E/T penalties are a function of the completion time of the jobs. Then, we introduce a non-linear preemptive scheduling model where the earliness penalty depends on the starting time of a job. The model is liberalized by an elaborately–designed procedure to reach the optimum solution. To validate and verify the performance of proposed model, computational results are presented by solving a number of numerical examples.
This study considers some significant parameters in the manufacturing systems, such as work in process, cut of works, number of earliness, and tardiness in just-in-time systems simultaneously. Discussing these assumptions could play a vital role in creating a competitive advantage as well as managing and improving the performance of the manufacturing system elements, such as bottlenecks. We also suppose the probable breakdown and repair times for each machine. In order to solve the mathematical model, a hybrid genetic algorithm is proposed and as the efficiency of algorithm is really dependent on its parameters, we tuned the parameters using Taguchi method.
Advanced automated manufacturing systems are widely used in industrial companies where productivity objectives have to be met. These systems often being costly, they must be designed to be as efficient as possible. Here, we focus on automated manufacturing systems in a job shop layout considering automated guided vehicle as a material handling resource. The key issue in manufacturing operations is how to produce high quality products at low costs in such a way that the diversified demand are met. Hence, modern manufacturing companies should become as responsive as possible in order to satisfy customer demands.
This paper, in addition to earliness and tardiness cost parameters which are common in literature review, considers other parameters such as WIP, job interruption, and number of tardiness and earliness for a single machine scheduling problem in a JIT production system. Consideration of these features in a production model cause to resolving bottleneck challenge, increasing production rate, improving system performance and bringing competitive advantage. The goal of this scheduling problem is minimizing total costs including earliness and tardiness cost, interruption cost and WIP holding. Also, the number of earliness and tardiness is minimized to keep all customers satisfied as much as possible. Several numerical examples are solved by the GAMS software to illustrate the promising results obtained by the incorporated features.
The paper considers the due-date assignment problem with a non-linear deterioration in which the due dates are determined by the equal slack method. Here, the processing time of a job is defined by a non-linear function of total normal processing time of jobs in front of it in the sequence. The objective is to minimize the total tardiness penalties. According to the needs from the real world, the problem is divided into two cases, i.e., allowing with early jobs and no early jobs respectively. The related lemma, corollary and theorems for the problems are proposed and proved. At the same time, it shows that the problems in this paper can be solved in the polynomial times.
Store Steel Ltd. faces the problem of producing a huge amount (approximately 1400) of different steel compositions in relatively small quantities (approximately 15 tons). This production is performed in batches of predetermined quantities (50-53 tons). The purpose of this article is to present the methodology for optimizing the production of predetermined steel grades in predetermined quantities before a customer's set deadline in such a way as to reduce the non-planned and ordered quantities with the date ahead of the deadline and to minimize the number of batches. The genetic algorithm method was used for optimization. The results of the genetic algorithm-based batch filling scheduling have been used in practice since 2006. The non-planned and ordered steel quantities with the date ahead of the deadline have been reduced from 17.17% to 10.12% since then.
Štore Steel Ltd. is a small flexible steel plant in Slovenia. In 2010, the new continuous rolling mill, which has a technical capacity of 250,000 tons per year, was installed. The new continuous rolling mill, which entailed a corresponding reduction in space, required an urgent relocation of machinery. The genetic algorithm was used for the optimal rearranging of the machinery. Two-dimensional or three-dimensional representation of the machines without any kind of geometrical restrictions can be used in the proposed genetic algorithm. The layout efficiency after machinery relocation could be increased by 58.1%, but due to spatial, financial, and practical constraints, the layout efficiency is only 13.58% higher.
We propose and investigate a genetic algorithm for scheduling jobs about an unrestricted common due date on a single machine. The objective is to minimize total earliness and tardiness cost where early and tardy penalty rates are allowed to be arbitrary for each job. Jobs are classified into families and a family setup time is required between jobs from two different families. Results from a computational study are promising with close to optimal solutions obtained rather easily and quickly.
Scheduling jobs with different processing times and distinct known due dates on parallel machines (which may be idle) so as to minimise the total weighted earliness and tardiness is NP-hard. It occurs frequently in industrial settings with a just-in-time production environment. Here, small instances of this problem are tackled via an exact mixed-integer program, whereas larger instances are approximately solved using hybrid algorithms. The computational investigation discerns what makes a difficult instance, and demonstrates the efficiency of the approach.
Tabu search, also called adaptive memory programming, is a method for solving challenging problems in the field of optimization. The goal is to identify the best decisions or actions in order to maximize some measure of merit (such as maximizing profit, effectiveness, quality, and social or scientific benefit) or to minimize some measure of demerit (cost, inefficiency, waste, and social or scientific loss).
Practical applications in optimization addressed by tabu search are exceedingly challenging and pervade the fields of business, engineering, economics, and science. Everyday examples include problems in resource management, financial and investment planning, healthcare systems, energy and environmental policy, pattern classification, biotechnology, and a host of other areas. The complexity and importance of such problems has motivated a wealth of academic and practical research throughout the past several decades, in an effort to discover methods that are able to find solutions of higher quality than many found in the past and capable of producing such solutions within feasible time limits or at reduced computational cost.
Tabu search has emerged as one of the leading technologies for handling optimization problems that have proved difficult or impossible to solve with classical procedures that dominated the attention of textbooks and were considered the mainstays of available alternatives until recent times. A key feature of tabu search, underscored by its adaptive memory programming alias, is the use of special strategies designed to exploit adaptive memory. The idea is that an effective search for optimal solutions should involve a process of flexibly responding to the solution landscape in a manner that permits it to learn appropriate directions to take along with appropriate departures to explore new terrain. The adaptive memory feature of tabu search allows the implementation of procedures that are capable of searching this terrain economically and effectively.
Traditional scheduling and due-date determination models assume that the production system is operating in a static and deterministic environment and that the system carries no workload at each scheduling epoch. In this research we consider a due-date determination model where the scheduler wishes to update the existing schedule when some new jobs have: arrived into the system. In this model, jobs are categorized as either "old" or "new" jobs, where the due-dates of the old jobs are treated as given parameters and those of the new jobs are decision variables. The objective is to minimize the maximum weighted tardiness penalty and the due-date assignment cost. The computational complexity of this model is analyzed, and an efficient algorithm is developed for an important special case.
The authors 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 total penalty function. This penalty function is based on the due date value and on the earliness or the lateness of each job in the selected sequence. A presentation is made of a polynomial bound scheduling algorithm for the solution of this problem along with the proof of optimality, a numerical example and discuss some extensions.
We consider the NP-hard problem of scheduling jobs on a single machine about an unrestricted due date to minimize total weighted earliness and tardiness cost. Jobs are grouped into families where jobs in the same family share a setup; a setup time is required between the processing of two jobs from different families. Each job has an earliness penalty rate and a tardiness penalty rate that are allowed to be arbitrary. These rates are assessed on a per-period basis when the completion time deviates from its due date. In this paper, we generalize properties from the literature that characterize the structure of an optimal schedule, present a lower bound, propose a branch and bound algorithm and a beam search procedure, and report results from a computational experiment. We find that optimal solutions can be quickly obtained for smaller problem instances. For large problems, we find high quality solutions within a few minutes of CPU time.
This article uses tabu search to solve the restricted, common-due-date, early/tardy machine scheduling problem generalised earliness and tardiness penalties. Different forms of the tabu search are tested, including one based on a sequence of jobs solution space and another based on an early/tardy solution space. Results show that a search which uses an early/tardy solution space with a neighbourhood scheme which eliminates infeasible areas of the solution space is the most efficient and effective solution method.
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.
This paper and its companion (Part II) concern the scheduling of jobs with cost penalties for both early and late completion. In Part I, we consider the problem of minimizing the weighted sum of earliness and tardiness of jobs scheduled on a single processor around a common due date, d. We assume that d is not early enough to constrain the scheduling decision. The weight of a job does not depend on whether the job is early or late, but weights may vary between jobs. We prove that the recognition version of this problem is NP-complete in the ordinary sense. We describe optimality conditions, and present a computationally efficient dynamic programming algorithm. When the weights are bounded by a polynomial function of the number of jobs, a fully polynomial approximation scheme is given. We also describe four special cases for which the problem is polynomially solvable. Part II provides similar results for the unweighted version of this problem, where d is arbitrary.
We consider the problem of rescheduling a facility modeled as a single machine in the face of newly arrived jobs with part-type
dependent setup times. The facility contains a number of jobs that have been assigned due dates and scheduled so as to meet
them. We wish to insert the new jobs into the existing schedule in a manner that will minimize the disruption of the jobs
in the system and minimize the total weighted completion time or the maximum completion time of the new jobs. We provide a
polynomial-time algorithm for the maximum completion time problem, prove that the total weighted completion time problem is
NP-hard in the strong sense and study several of its special cases. In particular, we show that the case with reverse-agreeable
weights (of which the unit weight problem is a special case) can be solved in polynomial time when the number of part types
is fixed. We also present two heuristics for the problem with arbitrary weights and develop data-dependent worst-case error
bounds. Extensive computational experiments show that the heuristics consistently obtain near-optimal solutions in very reasonable
CPU times.
W.-X. Zheng, H. Nagasawa and N. Nishiyama [Int. J. Prod. Res. 31, 1611-1620 (1993)] introduced the problem of scheduling non-preemptive, independent jobs with zero ready times and an unrestrictive common due date on a single machine so as to minimize the total cost of flowtime, earliness and tardiness (FET), where the cost function is identical for all jobs. They derived several dominance properties that have to be satisfied for an optimal schedule. These dominance properties were then exploited to develop a branch-and-bound (B&B) algorithm for finding an optimal schedule. Unfortunately, two key dominance properties do not necessarily hold for an optimal schedule. The aim here is to show why the two dominance properties may not hold and to provide a modification which guarantees the validity of the two dominance properties. We also show that if all those dominance properties hold, the B&B algorithm proposed by Zheng et al., in general, still fails to find an optimal schedule to the FET problem. In addition, we present another optimality property that can be used to accelerate the B&B algorithm.
We consider scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates. For identical processors, the secondary criteria of minimizing makespan and machine occupancy are addressed. The extension to different, uniform processors is also solved.
This paper considers a single-machine scheduling problem in which penalities occur when a job is completed early or late. The objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions for jobs. A procedure is presented for finding an optimal schedule.
We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.
This paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time. The scheduling objective is to minimize mean squared deviation (MSD) of job completion times about the due date. This nonregular measure of performance is appropriate when earliness and tardiness are both penalized, and when large deviations of completion time from the due date are undesirable. A special case of the MSD problem, referred to as the unconstrained MSD problem, is shown to be equivalent to the completion time variance problem (CTV) studied by Merten and Muller (Merten, A. G., M. E. Muller. 1972. Variance minimization in single machine sequencing problems. Management Sci. 18(September) 518--528.) and Schrage (Schrage, L. 1975. Minimizing the time-in-system variance for a finite jobset. Management Sci. 21(May) 540--543.). Strong results for this latter problem are combined with several new propositions to develop a reasonably efficient procedure for solving the unconstrained MSD problem. This enables us to improve the existing procedures for the CTV problem. We also propose a branching procedure for the constrained MSD problem and present computational results.
Traditional scheduling and due-date determination models assume that the production system is operating in a static and deterministic environment and that the system carries no workload at each scheduling epoch. In this research we consider a due-date determination model where the scheduler wishes to update the existing schedule when some new jobs have arrived into the system. In this model, jobs are categorized as either old or new jobs, where the due-dates of the old jobs are treated as given parameters and those of the new jobs are decision variables. The objective is to minimize the maximum weighted tardiness penalty and the due-date assignment cost. The computational complexity of this model is analyzed, and an efficient algorithm is developed for an important special case.
We attempt to present in this paper a critical review of a particular segment of scheduling research in which the due to date assignment decision is of primary interest. The literature is classified into the static and dynamic job shop situations. The static job shop is analyzed from two different perspectives: the due date is constrained to be greater than or equal to makespan, and the optimal due date and optimal sequence are to be determined when the method of assigning due dates is specified. The literature on dynamic job shops is also reviewed under two broad categories. First, we discuss all the literature concerned with comparative and investigative studies to identify the most desirable due date assignment method. Second, we discuss the literature dealing with determination of optimal due dates. We note that computer simulation and analytical methods are two common approaches for the second type of problems. We observe that while the static single-machine problem with constant or common due dates has been well researched, very little or no work has been done on the dynamic multi-machine problem with sophisticated due date assignment methods. Finally, we identify and suggest some worthwhile areas for future research.
The single machine early/tardy job scheduling problem (SMETP) consists of determining the best processing sequence for a set of jobs in order to minimize total costs. Minimizing both earliness and tardiness costs pushes the completion of each job to as close to its due date as possible in accordance with the just-in-time philosophy of production planning. As the problem is NP-hard and local optimality conditions may be well away from global optimality conditions new methods are needed to generate near optimal solutions. We propose a new heuristic for the SMETP that alternates search techniques performed at different neighborhood ranges using its own results to guide the alternation in a dynamic way. The computational results we obtained on randomly generated test problems compared very favorably with the results obtained with tabu search and simulated annealing algorithms.The single machine early/tardy job scheduling problem (SMETP) is a NP-hard problem for which most properties of optimal solutions for single machine problems with regular objective function do not hold. In this paper we present a new composite heuristic for the SMETP that combines tabu search, simulated annealing and steepest descent techniques to generate near optimal schedules. Computational experience is reported for a set of randomly generated test problems.
We discuss the one-machine-model with deterministic processing times. In the first part we restrict the model to the common due date case. In the second part an equivalence between this model and the ‘Equal Slack Due Date’ model is shown. As a penalty function F we use the sum of identical functions f of the lateness (both earliness and tardiness). The function f must be monotonous with respect to the absolute lateness. No other restrictions are necessary. Several special cases are known in the literature and summarized here to show the generality of our approach. This idea of penalizing jobs whose completion times deviate from their due date arises in some scheduling models for ‘just-in-time’ production. We give two structural results for an optimal schedule: An optimal schedule works without idle times except eventually one at time 0 and is ‘v-shaped’. Using these two structural results we construct an optimal schedule with a pseudopolynomial algorithm. This algorithm has a complexity bound of O(nP), where P denotes the sum of the given processing times. For a subclass of penalty functions, we extend the pseudopolynomial algorithm to a fully polynomial approximation scheme. The complexity bound for this approximation scheme is of the order O(n3·(1/ε)), where ε denotes the relative precision of the approximate solution. As mentioned above we show the equivalence of the ‘common due date’ problem and the ‘equal slack due date’ problem. Mathematically these two problems can be expressed as:Common Due Date Rule: d(i) := d for all jobs i, and Equal Slack Rule: d(i) := d + p(i) for all jobs i, where p(i) denotess the given processing time of job i and d is a constant value.
Scheduling problems involving both earliness and tardiness costs have received significant attention in recent years. This type of problem became important with the advent of the just-in-time (JIT) concept, where early or tardy deliveries are highly discouraged. In this paper we examine the single-machine scheduling problem with a common due date. Performance is measured by the minimization of the sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, we propose a tabu search-based heuristic and a genetic algorithm which exploit specific properties of the optimal solution. Hybrid strategies are also analyzed to improve the performance of these methods. The proposed approaches are examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs.
We consider the problem of scheduling a number of jobs on a single machine against a restrictive common due date. The paper consists of two parts: firstly a new and appropriate problem representation is developed. As the restrictive common due date problem is known to be intractable we decided, secondly, to apply meta-heuristics, namely evolutionary strategies, simulated annealing and threshold accepting. We demonstrate that our application of these meta-heuristics is efficient in obtaining near-optimal solutions by solving 140 benchmark problems with up to 1000 jobs. Furthermore, we compare their solution quality and find that a new variant of threshold accepting is superior to the other approaches.
A set of n jobs has to be scheduled on a single machine which can handle only one job at a time. Each job requires a given positive uninterrupted processing time and has a positive weight. The problem is to find a schedule that minimizes the sum of weighted deviations of the job completion times from a given common due date d, which is smaller than the sum of the processing times. We prove that this problem is NP-hard even if all job weights are equal. In addition, we present a pseudopolynomial algorithm that requires O(n2d) time and O(nd) space.
The purpose of this paper is to develop parallel genetic algorithms for a job scheduling problem on a single machine. The objective of the scheduling is to minimize the total generally weighted earliness and tardiness penalties from a common due date. A binary representation scheme is employed for coding job schedules into chromosomes. Parallel subpopulations are constructed by considering only jobs that can be processed first in the schedule. Three important genetic algorithm operators; reproduction, crossover and mutation are implemented by reflecting the problem-specific properties. The efficiency of the parallel genetic algorithm is illustrated with computational results.
This paper studies the problem of scheduling a set of n jobs on a single machine to minimize weighted absolute deviation of completion times from a common due date. It is assumed that weights of jobs are proportional to their processing times. It has been shown by other researchers that the problem can be solved efficiently for a sufficiently large due date. In the present paper we solve the problem for any given due date.
Estimation and modelling problems as they arise in many fields often turn out to be intractable by standard numerical methods. One way to deal with such a situation consists in simplifying models and procedures. However, the solutions to these simplified problems might not be satisfying. A different approach consists in applying optimization heuristics such as evolutionary algorithms (simulated annealing, threshold accepting), neural networks, genetic algorithms, tabu search, hybrid methods, etc., which have been developed over the last two decades. Although the use of these methods became more standard in several fields of sciences, their use in estimation and modelling in statistics appears to be still limited.A brief introduction to the computational complexity of problems encountered in the fields of statistical modelling and econometrics as well as an overview and classification of the optimization heuristics used is provided. Given the applications presented and the growing availability of optimization heuristics, it is expected that their use will become more frequent in statistics in the near future.
We consider the problem of scheduling n jobs on m parallel and identical machines. The goal is to find an optimal permutation of the jobs and an optimal due date which jointly minimize an objective function consisting of earliness tardiness and completion time penalties. We show that the problem is NP-hard and present a polynomially solvable case. Furthermore a heuristic is developed and computationally demonstrated to be efficient in obtaining near-optimal solutions.Scope and purposeThis study deals with the problem of scheduling a number of jobs on parallel machines. We assume that companies are mainly interested in two objectives, namely achieving small deviations from a common due date and short flowtimes. Therefore earliness tardiness and completion time penalties for the jobs are introduced. We are able to show that the problem is intractable and consequently develop an efficient heuristic to obtain near-optimal solutions.
In the recent years, theory of constraints (TOC) has emerged as an effective management philosophy for solving decision making problems with the aim of profit maximization by considering the bottleneck in traditional as well as modern manufacturing plants. One of the key components of TOC application is to enumerate quantity of the various products to be manufactured keeping in view the system constraints. Problem of this kind is termed as TOC product mix decision problem. It is a well-known computationally complex problem and thus warrants the application of heuristics techniques or AI based optimization tools to achieve optimal or near optimal solution in real time. In this research, a hybrid algorithm named tabu-simulated annealing is proposed. It exploits the beauty of tabu search and simulated annealing (SA) to ensure the convergence at faster rate. It is found that the performance of hybrid tabu-SA algorithm on a well known data set of product mix optimization problem is superior as compared to tabu search, SA, TOC heuristic, Revised-TOC (R-TOC) heuristic, and Integer Linear Programming (ILP) based approaches.
Genetic algorithms have been used in science and engineering as adaptive algorithms for solving practical problems and as computational models of natural evolutionary systems. This brief, accessible introduction describes some of the most interesting research in the field and also enables readers to implement and experiment with genetic algorithms on their own. It focuses in depth on a small set of important and interesting topics—particularly in machine learning, scientific modeling, and artificial life—and reviews a broad span of research, including the work of Mitchell and her colleagues.
The descriptions of applications and modeling projects stretch beyond the strict boundaries of computer science to include dynamical systems theory, game theory, molecular biology, ecology, evolutionary biology, and population genetics, underscoring the exciting "general purpose" nature of genetic algorithms as search methods that can be employed across disciplines.
An Introduction to Genetic Algorithms is accessible to students and researchers in any scientific discipline. It includes many thought and computer exercises that build on and reinforce the reader's understanding of the text. The first chapter introduces genetic algorithms and their terminology and describes two provocative applications in detail. The second and third chapters look at the use of genetic algorithms in machine learning (computer programs, data analysis and prediction, neural networks) and in scientific models (interactions among learning, evolution, and culture; sexual selection; ecosystems; evolutionary activity). Several approaches to the theory of genetic algorithms are discussed in depth in the fourth chapter. The fifth chapter takes up implementation, and the last chapter poses some currently unanswered questions and surveys prospects for the future of evolutionary computation.
Bradford Books imprint
This paper is concerned with the optimal due dates and the optimal sequence to a set of jobs on a single-machine. The common due date assignment method is used, in which all jobs are assigned a common flow allowance. The objective is to find the optimal common due date and the optimal sequence to minimize an objective function of the sum of the Earliness/Tardiness (E/T) penalties and the additional penalties (including two dimensions, namely due date penalties and completion times penalties). It is assumed that E/T penalties will not occur if a job is completed within the due window. However, E/T penalties will occur if a job is completed outside the due window. Five lemmas and a polynomial-time algorithm are presented to determine the optimal common due date and the optimal sequence, a numerical example is provided to illustrate our algorithm.
This paper focuses on scheduling jobs with different processing times and distinct due dates on a single machine with no inserted idle time as to minimize the sum of total earliness and tardiness. This scheduling problem is a very important and frequent industrial problem that is common to most just-in-time production environments. This NP hard scheduling problem is herein solved using a hybrid heuristic which combines local search heuristics (dispatching rules, hill climbing and simulated annealing) and an evolutionary algorithm based on genetic algorithms. The heuristic involves low and high, relay and teamwork hybridization. Computational results reflect the sizeable solution quality improvement induced by hybridization, and assess the impact of each type of hybridization on the efficiency of the hybrid heuristic.
The just-in-time production philosophy has led to a growing interest in schedulingproblems considering both earliness and tardiness penalties. Most publications considering these so-called nonregular objective functions are devoted to single machine problems. In the case of multimachine problems, there are some papers dealing with parallel machine problems. However, for multi-operation scheduling problems such as shop scheduling problems, investigations have begun only recently. In this paper, inspired by recent own work (partly yet unpublished), we survey some results on multimachine scheduling problems with a given common due date, where the focus is on possible approaches for shop scheduling problems.
In the daily activity of workshops the problem of minimizing delay in dispatching is one of the most interesting among those of scheduling. Throughout this article a mixed application of simulated annealing (which allows TS to be started from a better initial solution) and tabu search is studied.
- F W Glover
- M Tabu Laguna
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Glover, F.W.; Laguna, M. Tabu Search, Kluwer Academic
Publishers: Boston 1998; 408 pp.