Job Sequencing Problem Research Articles

Exploiting symmetry for the job sequencing and tool switching problem

The Job Sequencing and Tool Switching Problem (SSP), a well-known combinatorial optimization problem in the domain of Flexible Manufacturing Systems (FMS), is studied in this article. The aim of this research is to improve the currently known exact solution methodology for this NP-hard problem. We propose a new integer linear programming approach with symmetry-breaking and tightening cuts that provably outperformed the existing methodology described in the literature. The computational study conducted on a data set with 1,050 instances showed that the developed method can solve hard instances that were not solvable with the state-of-the-art methods presented in the literature.

Biased random-key genetic algorithm for the job sequencing and tool switching problem with non-identical parallel machines

We address the job sequencing and tool switching problem associated with non-identical parallel machines – a variation of the well-known sequencing and switching problem (SSP) better adapted to reflect the challenges in modern production environments. The NP-hard problem is approached by considering two isolated objective functions: the minimization of the makespan and the minimization of the total flow time. We present two versions of a parallel biased random-key genetic algorithm hybridized with tailored local search procedures that are organized using variable neighborhood descent. The proposed methods are compared with state-of-the-art methods by considering 640 benchmark instances from literature. For both objective functions considered, the proposed methods consistently outperform the compared methods. All known optimal values for both objectives are achieved, and a substantial gap is reported for all instance groups when compared with the best previously published solution values.

Hybridizing local searching with genetic algorithms for the job sequencing and tool switching problem with non-identical parallel machines

The job sequencing and tool switching problem (SSP) is an old and highly studied problem. However, the SSP with non-identical parallel machines (SSP-NPM) is a new generalization of this problem. Since the SSP-NPM has been very recently introduced, the number of solution methods for this problem is low. Additionally, exact solution methods are mostly insufficient to find a good solution within a reasonable computational time since this problem is NP-hard. Therefore, heuristic approaches are more appropriate, especially when solving large-size problems. Thus, this study presents a new hybrid algorithm that is a combination of a genetic algorithm (GA) and a local search (LS) technique. Both of these methods are greatly preferred by authors for solving job scheduling problems. Thereby, this study combines their strengths to solve the SSP-NPM. Two versions of the proposed method are tested with benchmark instances. These versions differ in terms of their tool optimization policies: the first uses the well-known “keep tool needed soonest” (KTNS) policy, while the second uses the “randomly remove tool” (RRT) policy. Computational experiments showed that combining some of the features of GA and LS methods for the SSP-NPM contributed greatly to the quality of the solution. Two versions of the proposed hybrid method were compared to a mixed-integer programming model and several schemes of an iterated local search algorithm. Our computational results show that both versions of the proposed hybrid method were significantly better than the other methods, and were able to find the solutions within a reasonable computational time.

Multiobjective Sequence-Dependent Job Sequencing and Tool Switching Problem

This article considers the extension of the job sequencing and tool switching problem with sequence-dependent setup times (SDSSP) and with the requirement to comply with the due date of the processed jobs. This extension is motivated by the practical application in manufacturing environment where the products manufactured may be subjected to a specific due date. This study develops a multiobjective SDSSP model (MO-SDSSP) to simultaneously minimize the total setup time of tool switches and the tardiness of the machining process. Then, a two-stage Multiobjective Adaptive Large Neighborhood Search (MOALNS) and Simulated Annealing (SA) is presented as a heuristic algorithm for the MO-SDSSP, in which the MOALNS is proposed to solve the job sequencing subproblem while the SA is used to solve the tool switching subproblem. Subsequently, the performance of MOALNS-SA is compared to several popular multiobjective optimization algorithms. Comparison on four performance criteria has shown the applicability of the MOALNS. Finally, managerial analysis is performed to analyze the relationship between the total tool setup time and the compliance of due dates.

New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources

We study the prize-collecting job sequencing problem with one common and multiple secondary resources. In this problem, a set of jobs is given, each with a profit, multiple time windows for its execution, and a duration during which it requires the main resource. Each job also requires a preassigned secondary resource before, during, and after its use of the main resource. The goal is to select and schedule the subset of jobs that maximize the total profit. We present a new mixed integer linear programming formulation of the problem and a branch-cut-and-price algorithm as an exact solution method. We also introduce a heuristic algorithm to tackle larger instances. Extensive numerical experiments show that our exact algorithm can solve to optimality literature instances with up to 500 jobs for a particular dataset and up to 250 jobs for another dataset with different characteristics. Our heuristic builds high-quality solutions in a small computational time. It computes new best-known solutions for most of the larger instances.

Hybrid metaheuristic to solve job sequencing problem

<p>In this article, the job shop scheduling problem was solved, which is considered as an NP - Hard problem, so it is difficult to solve. The proposed algorithm consists in the combination and adaptation of the nearest neighbor meta heuristics and iterated local search (ILS) to find optimal solutions. The proposed algorithm was evaluated by comparing the results with those presented in different instances and sizes of the literature. The results of the proposed method were close in high percentages to the best re sults and averages obtained by other methods in the literature and in some cases, they were improved. The above represents the feasibility of a new combination of efficient methods in solving task scheduling problems.</p>

A comparison of different mathematical models for the job sequencing and tool switching problem with non-identical parallel machines

This paper addresses the generalisation of the NP-hard job sequencing and tool switching problem with non-identical parallel machines and sequence-dependent setup times where a set of jobs is to be scheduled on unrelated parallel machines with machine-dependent processing and tool switching times. Three different mathematical models for two different objectives are presented and applied to newly generated test instances. The instances are compared and analysed using a commercial solver and an iterated local search heuristic. Overall, it is shown that the solution quality obtained by the mathematical models depends on the size of the problem instance as well as the tool requirements. The precedence-based formulation is superior in general to the position-based and time-index-based formulation for dense problem instances while the position-based formulation works well for sparse problems. With an increasing problem size, the metaheuristic requires significantly less time to find near-optimal solutions than the mathematical models.

A two-stage heuristic for the sequence-dependent job sequencing and tool switching problem

The job sequencing and tool switching problem is a combinatorial optimization problem that commonly happens in a flexible manufacturing system environment. In this type of environment, a set of flexible manufacturing machines can be configured with various tools to process different jobs and the requirement to switch tools may correspond to a reduction of productivity. Consequently, research on the job sequencing and tool switching problem has been concentrated on minimizing the number of tools switches. This paper discusses the sequence-dependent job sequencing and tool switching problem. The sequence-dependent job sequencing and tool switching problem extends the standard model by considering non-uniform setup times since industrial applications indicate that a tool setup time might be influenced by the previously installed tool at the same magazine slot. A two-stage heuristic procedure is developed here. In the first stage, an adaptive large neighborhood search is deployed for finding the near-optimal job sequence. Then, in the second stage, a combination of the Keep Tool Needed Soonest policy and simulated annealing is proposed for the tooling sub-problem. Comprehensive computational experiments are carried out to demonstrate the efficacy and robustness of the proposed method for solving the sequence-dependent job sequencing and tool switching problem.

An iterated local search procedure for the job sequencing and tool switching problem with non-identical parallel machines

In this paper, a new generalization of the uniform job sequencing and tool switching problem is presented. It considers non-identical parallel machines, which differ in tool magazine capacity and setup times. Applications of the problem can be found in the metal working or semiconductor manufacturing industries when the jobs require different tool sets for processing. The paper provides a Mixed Integer Programming formulation for the job sequencing and tool switching problem with machine-dependent processing and tool switching times under the consideration of three conflicting objectives (minimizing the total flowtime, minimizing the makespan and minimizing the total number of tool switches). Different efficient construction heuristics and Iterated Local Search methods are proposed and evaluated, using 640 new and publicly available instances. The results of the construction heuristics, the Iterated Local Search schemes and a Mixed Integer Programming Solver are discussed. The extensive computational experiments show the merit of the perturbation strategy in order to overcome local optima. It is shown that certain methods are more or less suitable depending on the objective function.

The job sequencing and tool switching problem with sequence-dependent set-up time

Job sequencing and tool switching (SSP) is a well-known combinatorial optimization problem that aims to minimize the number of tool switches. The problem mainly arises in a flexible manufacturing system, in which machines can be configured with various tools to process different jobs and tool switches will reduce productivity. While the general studies assume uniform set-up time for tool switching, applications in the industries indicate that the set-up time of a tool might depend on the previously installed tool of the same slot. Therefore, this article proposes two integer linear programming models for the sequence-dependent SSP, namely, the five-index formulation and the multicommodity flow formulation. Experimental tests are executed to compare the sequence-dependent SSP with the uniform SSP, and the results show the effectiveness of multicommodity flow formulation. Finally, several managerial discussions are derived from the results.

A job-sequencing problem using modified score function in PNN environment

Pentagonal neutrosophic number (PNN) is an extension of general established triangular and trapezoidal neutrosophic number. In this article, the structural form of PNN has been applied on operation...

A job-sequencing problem using modified score function in PNN environment

A job-sequencing problem using modified score function in PNN environment

Different linear and non-linear form of trapezoidal neutrosophic numbers, de-neutrosophication techniques and its application in time-cost optimization technique, sequencing problem

In this research article, we envisage the neutrosophic number from various distinct rational perspectives & viewpoints to give it a look of a conundrum. We focused & analysed various types of linear and non-linear generalized trapezoidal neutrosophic numbers which serves an indispensable role for uncertainty concept related problem. We also introduce the idea of de-neutrosofication for trapezoidal neutrosophic number using an influx of different logical & innovative methods by which we move with a manifesto to convert a neutrosophic number into a crisp number. Using this concept of de-neutrosophication, we analyze some real-life problem like networking Crash model problem and job-sequencing problem of operation research field when the numbers are in trapezoidal neutrosophic ambience. We also compare our specified result with previously defined score and accuracy function and try to present some interesting and better result without any possible fiasco. This noble thought will help us to solve a plethora of daily life problems in neutrosophic arena.

A simple and effective hybrid genetic search for the job sequencing and tool switching problem

The job Sequencing and tool Switching Problem (SSP) has been extensively studied in the field of operations research, due to its practical relevance and methodological interest. Given a machine that can load a limited amount of tools simultaneously and a number of jobs that require a subset of the available tools, the SSP seeks a job sequence that minimizes the number of tool switches in the machine. To solve this problem, we propose a simple and efficient hybrid genetic search based on a generic solution representation, a tailored decoding operator, efficient local searches and diversity management techniques. To guide the search, we introduce a secondary objective designed to break ties. These techniques allow to explore structurally different solutions and escape local optima. As shown in our computational experiments on classical benchmark instances, our algorithm significantly outperforms all previous approaches while remaining simple to apprehend and easy to implement. We finally report results on a new set of larger instances to stimulate future research and comparative analyses.

A∗-based construction of decision diagrams for a prize-collecting scheduling problem

Decision diagrams (DDs) have proven to be useful tools in combinatorial optimization. Relaxed DDs represent discrete relaxations of problems, can encode essential structural information in a compact form, and may yield strong dual bounds. We propose a novel construction scheme for relaxed multi-valued DDs for a scheduling problem in which a subset of elements has to be selected from a ground set and the selected elements need to be sequenced. The proposed construction scheme builds upon A* search guided by a fast-to-calculate problem-specific dual bound heuristic. In contrast to traditional DD compilation methods, the new approach does not rely on a correspondence of DD layers to decision variables. For the considered kind of problem, this implies that multiple nodes representing the same state at different layers can be avoided, and consequently also many redundant isomorphic substructures. For keeping the relaxed DD compact, a new mechanism for merging nodes in a layer-independent way is suggested. For our prize-collecting job sequencing problem, experimental results show that the DDs from our A*-based approach provide substantially better bounds while frequently being an order-of-magnitude smaller than DDs obtained from traditional compilation methods, given about the same time. To obtain a heuristic solution and a corresponding lower bound, we further propose to construct a restricted DD based on the relaxed one, thereby substantially exploiting already gained information. This approach outperforms a standalone restricted DD construction, basic constraint programming and mixed integer linear programming approaches, and a variable neighborhood search in terms of solution quality on most of our benchmark instances.

JOHNSONS ALGORITHM IN FUZZY ENVIRONMENT

Adv. Math. Sci. J. Vol. 9, No. 4 Open Access JOHNSONS ALGORITHM IN FUZZY ENVIRONMENT K. K. Mishra DOI: https://doi.org/10.37418/amsj.9.4.94 Full Text Abstract Abstract Classical Johnson algorithm is extended to find fuzzy number job sequencing problem. The processing time is represented by trapezoidal fuzzy number. The trapezoidal fuzzy numbers are defuzzified by … page AMSJ9-N4-94 Read More »

A new multicommodity flow model for the job sequencing and tool switching problem

In this paper a new multicommodity flow mathematical model for the Job Sequencing and Tool Switching Problem (SSP) is presented. The proposed model has an LP relaxation lower bound equal to the number of tools minus the tool machine's capacity. Computational tests were performed comparing the new model with the models of the literature. The proposed model performed better, both in execution time and in the number of instances solved to optimality.

A Job Sequencing Problem of an Overhead Shuttle Crane in a Rail-Based Automated Container Terminal

This study proposes a job scheduling model and its heuristics for an automated container terminal with an overhead shuttle crane (OS) to reduce the total tardiness time of flatcars and external trucks by considering the separation of each job into a main job, and a premarshaling or remarshaling job. The OS is busy or idle according to the fluctuations in the processing times of different pieces of equipment. We identify the OS job sequencing problem considering job separation (OSJSPS) as a mixed-integer programming (MIP) model, which simultaneously sequences a set of jobs and searches for their possible separation into premarshaling and remarshaling jobs. We present a two-stage genetic algorithm (TGA) based on two local improvement procedures: an iterative local search procedure and an opportunistic job separation procedure. We conclude that the two-stage genetic algorithm reduces the total tardiness time of the container terminal’s flatcars and external trucks as the number of OS jobs increases.

Solving Sequencing Problems Under Fuzzy Environment

A sequencing problem is to select the order in which the vital tasks are to be done to minimize the total elapsed time taken for all the tasks. Generally, in job sequencing problems, the processing times are precisely valued. But in reality, it is observed that the processing times during the performance of the job are indefinite. For that reason, the conception of fuzzy job sequencing problem make available for use an effective outline which is useful for real-life situations with fuzzy processing times. Here, we suggest a new technique for solution of fuzzy sequencing problems involving triangular fuzzy numbers (TFN) without transforming them into equivalent crisp sequencing problem.

Continuous process improvement implementation framework using multi-objective genetic algorithms and discrete event simulation

PurposeContinuous process improvement is a hard problem, especially in high variety/low volume environments due to the complex interrelationships between processes. The purpose of this paper is to address the process improvement issues by simultaneously investigating the job sequencing and buffer size optimization problems.Design/methodology/approachThis paper proposes a continuous process improvement implementation framework using a modified genetic algorithm (GA) and discrete event simulation to achieve multi-objective optimization. The proposed combinatorial optimization module combines the problem of job sequencing and buffer size optimization under a generic process improvement framework, where lead time and total inventory holding cost are used as two combinatorial optimization objectives. The proposed approach uses the discrete event simulation to mimic the manufacturing environment, the constraints imposed by the real environment and the different levels of variability associated with the resources.FindingsCompared to existing evolutionary algorithm-based methods, the proposed framework considers the interrelationship between succeeding and preceding processes and the variability induced by both job sequence and buffer size problems on each other. A computational analysis shows significant improvement by applying the proposed framework.Originality/valueSignificant body of work exists in the area of continuous process improvement, discrete event simulation and GAs, a little work has been found where GAs and discrete event simulation are used together to implement continuous process improvement as an iterative approach. Also, a modified GA simultaneously addresses the job sequencing and buffer size optimization problems by considering the interrelationships and the effect of variability due to both on each other.