Classical Job Shop Scheduling Problem Research Articles

Solving flexible job shop scheduling problems using a hybrid lion optimisation algorithm

This paper addresses the flexible job shop scheduling problem (FJSP) with makespan criterion. The FJSP has been proved to be strongly NP-hard. The FJSP is a generalisation and extension of the classical job shop scheduling problem (JSP). As the problem is NP-hard, exact solution techniques cannot be used to tackle the problem. Researchers have proposed several heuristics and meta-heuristics to solve the problem. The lion optimisation algorithm is one of the recently developed meta-heuristic algorithms. A hybrid lion optimisation algorithm (HLOA) is proposed in the present work to solve the FJSP. A heuristic is hybridised with the LOA to improve the solution quality. To the best of our knowledge this is the first reported application of the LOA to solve the scheduling problems. The performance of the proposed algorithm is tested with two different sets of benchmark problems addressed in the literature. Computational results substantiate the effectiveness of the proposed algorithm.

Multi-agent model based on combination of chemical reaction optimisation metaheuristic with Tabu search for flexible job shop scheduling problem

Scheduling in production systems consists in assigning operations on a set of available resources in order to achieve defined objectives. The flexible job shop scheduling problem (FJSP) is one of the scheduling problems and also an extension of classical job shop scheduling problem such that each operation can be processed on different machine and its processing time depends on the used machine. This paper proposes a multi-agent model based on combination of chemical reaction optimisation metaheuristic with Tabu search to solve the FJSP in order to minimise the maximum completion time (makespan). To evaluate the performance of our model, experiments are performed on well known benchmark instances proposed in the literature and comparisons are made with other approaches in literature.

Solving flexible job shop scheduling problems using a hybrid lion optimisation algorithm

This paper addresses the flexible job shop scheduling problem (FJSP) with makespan criterion. The FJSP has been proved to be strongly NP-hard. The FJSP is a generalisation and extension of the classical job shop scheduling problem (JSP). As the problem is NP-hard, exact solution techniques cannot be used to tackle the problem. Researchers have proposed several heuristics and meta-heuristics to solve the problem. The lion optimisation algorithm is one of the recently developed meta-heuristic algorithms. A hybrid lion optimisation algorithm (HLOA) is proposed in the present work to solve the FJSP. A heuristic is hybridised with the LOA to improve the solution quality. To the best of our knowledge this is the first reported application of the LOA to solve the scheduling problems. The performance of the proposed algorithm is tested with two different sets of benchmark problems addressed in the literature. Computational results substantiate the effectiveness of the proposed algorithm.

Optimizing the Low-Carbon Flexible Job Shop Scheduling Problem Considering Energy Consumption

Flexible job shop scheduling problem (FJSP) is a typical discrete combinatorial optimization problem, which can be viewed as an extended version of the classical job shop scheduling problem. In previous researches, the scheduling problem has historically emphasized the production efficiency. Recently, scheduling problems with green criterion have been paid great attention by researchers. In this paper, the mathematical model of the low-carbon flexible job shop scheduling problem is established with the objective of minimizing the sum of the energy consumption cost and the earliness/tardiness cost. For solving the model, a kind of bi-population based discrete cat swarm optimization algorithm (BDCSO) is presented to obtain the optimal scheduling scheme in the workshop. In the framework of the BDCSO, two sub-populations are used to adjust the machine assignment and operation sequence respectively. At the initialization stage, a two-component discrete encoding mechanism is first employed to represent each individual, and then a heuristic method is adopted to generate the initial solutions with good quality and diversity. By considering the discrete characteristics of the scheduling problem, the modified updating methods are developed for the seeking and tracing modes to ensure the algorithm work directly in a discrete domain. To coordinate the global and local search in each sub-population, six adjustment curves are used to change the number of cats in the seeking and tracing modes, based on which six algorithms are developed, i.e., LBDCSO, SinBDCSO, CosBDCSO, TanBDCSO, LnBDCSO, and SquareBDCSO. In addition, the information exchanging strategy is introduced to implement the cooperation of the two sub-populations. Finally, extensive simulation based on random instances and benchmark instances is carried out. The comparisons results demonstrate the effectiveness of the proposed algorithms in solving the FJSP under study.

Dual-Resource Constraints in Classical and Flexible Job Shop Problems: A State-of-the-Art Review

The Job shop Scheduling Problem (JSP) is one of the most known problems in the domain of the production task scheduling. The Dual-Resource Constrained Job shop Scheduling Problem (DRCJSP) and the Dual-Resource Constrained Flexible Job shop Scheduling Problem (DRCFJSP) are two extensions of the classical JSP consisting of three sub-problems: (i) Assigning operations to resources of machines, (ii) Assigning operations to resources of workers; (iii) Sequencing the operations on the machines considering workers in order to optimize the performance measure. In this paper, we make a state-of-the-art review of the different works proposed for the DRCJSP and DRCFJSP, where we present a new classification schema according to six criteria such as the used method, the machine flexibility, the worker flexibility, the optimization criteria, the implemented approaches, and the structure of the approach.

A neighborhood for complex job shop scheduling problems with regular objectives

Due to the limited applicability in practice of the classical job shop scheduling problem, many researchers have addressed more complex versions of this problem by including additional process features, such as time lags, setup times, and buffer limitations, and have pursued objectives that are more practically relevant than the makespan, such as total flow time and total weighted tardiness. However, most proposed solution approaches are tailored to the specific scheduling problem studied and are not applicable to more general settings. This article proposes a neighborhood that can be applied for a large class of job shop scheduling problems with regular objectives. Feasible neighbor solutions are generated by extracting a job from a given solution and reinserting it into a neighbor position. This neighbor generation in a sense extends the simple swapping of critical arcs, a mechanism that is widely used in the classical job shop but that is not applicable in more complex job shop problems. The neighborhood is embedded in a tabu search, and its performance is evaluated with an extensive experimental study using three standard job shop scheduling problems: the (classical) job shop, the job shop with sequence-dependent setup times, and the blocking job shop, combined with the following five regular objectives: makespan, total flow time, total squared flow time, total tardiness, and total weighted tardiness. The obtained results support the validity of the approach.

Solving the flexible job shop problem by hybrid metaheuristics-based multiagent model

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop scheduling problem that allows to process operations on one machine out of a set of alternative machines. The FJSP is an NP-hard problem consisting of two sub-problems, which are the assignment and the scheduling problems. In this paper, we propose how to solve the FJSP by hybrid metaheuristics-based clustered holonic multiagent model. First, a neighborhood-based genetic algorithm (NGA) is applied by a scheduler agent for a global exploration of the search space. Second, a local search technique is used by a set of cluster agents to guide the research in promising regions of the search space and to improve the quality of the NGA final population. The efficiency of our approach is explained by the flexible selection of the promising parts of the search space by the clustering operator after the genetic algorithm process, and by applying the intensification technique of the tabu search allowing to restart the search from a set of elite solutions to attain new dominant scheduling solutions. Computational results are presented using four sets of well-known benchmark literature instances. New upper bounds are found, showing the effectiveness of the presented approach.

Flexible Job Shop Scheduling Problem Using an Improved Ant Colony Optimization

As an extension of the classical job shop scheduling problem, the flexible job shop scheduling problem (FJSP) plays an important role in real production systems. In FJSP, an operation is allowed to be processed on more than one alternative machine. It has been proven to be a strongly NP-hard problem. Ant colony optimization (ACO) has been proven to be an efficient approach for dealing with FJSP. However, the basic ACO has two main disadvantages including low computational efficiency and local optimum. In order to overcome these two disadvantages, an improved ant colony optimization (IACO) is proposed to optimize the makespan for FJSP. The following aspects are done on our improved ant colony optimization algorithm: select machine rule problems, initialize uniform distributed mechanism for ants, change pheromone’s guiding mechanism, select node method, and update pheromone’s mechanism. An actual production instance and two sets of well-known benchmark instances are tested and comparisons with some other approaches verify the effectiveness of the proposed IACO. The results reveal that our proposed IACO can provide better solution in a reasonable computational time.

A metaheuristic technique for energy-efficiency in job-shop scheduling

AbstractMany real life problems can be modeled as a scheduling problem. The main objective of these problems is to obtain optimal solutions in terms of processing time, cost and quality. Nowadays, energy-efficiency is also taken into consideration. However, these problems are NP-hard, so many search techniques are not able to obtain a solution in a reasonable time. In this paper, a genetic algorithm is developed to solve an extended version of the classical job-shop scheduling problem. In the extended version, each operation has to be executed by one machine and this machine can work at different speed rates. The machines consume different amounts of energy to process tasks at different rates. The evaluation section shows that a powerful commercial tools for solving scheduling problems was not able to solve large instances in a reasonable time, meanwhile our genetic algorithm was able to solve all instances with a good solution quality.

Esnek atölye tipi çizelgeleme problemlerinin meta sezgisel yöntemler ile çözümüne yönelik bir inceleme

Flexible job shop scheduling (FJSS) problems which are parts of real life applications are the extended case of classical job shop scheduling (JSS) problems. There are no parallel machines at JSS problems. FJSS Problems arise when works need to be done on parallel machines in the workshop. In FJSS problems, jobs have different routes and each job is consisted of at least one operation. These operations are processed by any of the machine sets which are parallel to each other. In literature; the number of studies on FJSS problems are more limited than the one on JSS problems. In this paper, recent studies in the literature on the topic of FJSS problems are reviewed. The findings and recommendations on the solution of this kind of problems by using meta-heuristic methods are presented.

Mixed Integer Programming models for job shop scheduling: A computational analysis

In both industry and the research literature, Mixed Integer Programming (MIP) is often the default approach for solving scheduling problems. In this paper we present and evaluate four MIP formulations for the classical job shop scheduling problem (JSP). While MIP formulations for the JSP have existed since the 1960s, it appears that comprehensive computational studies have not been performed since then. Due to substantial improvements in MIP technology in recent years, it is of interest to compare the standard JSP models using modern optimization software. We perform a fully crossed empirical study of four MIP models using CPLEX, GUROBI and SCIP, focusing on both the number of instances that can be proved optimal and the solution quality over time. Our results demonstrate that modern MIP solvers are able to prove optimality for moderate-sized problems very quickly. Comparing the four MIP models, the disjunctive formulation proposed by Manne performs best on both performance measures. We also investigate the performance of MIP with multi-threading and parameter tuning using CPLEX. Noticeable performance gain is observed when compared to the results using only single thread and default parameter settings. Our results serve as a snapshot of the performance of modern MIP solvers for an important, well-studied scheduling problem. Finally, the results of MIP is compared to constraint programming (CP), another common approach for scheduling, and the best known complete algorithm to provide a broad view among different approaches.

An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem

Flexible job shop scheduling problem (FJSP) which is an extension of the classical job shop scheduling problem is a very important problem in the modern manufacturing system. It allows an operation to be processed by any machine from a given set. It has been proved to be a NP-hard problem. In this paper, an effective hybrid algorithm (HA) which hybridizes the genetic algorithm (GA) and tabu search (TS) has been proposed for the FJSP with the objective to minimize the makespan. The GA which has powerful global searching ability is utilized to perform exploration, and TS which has good local searching ability is applied to perform exploitation. Therefore, the proposed HA has very good searching ability and can balance the intensification and diversification very well. In order to solve the FJSP effectively, effective encoding method, genetic operators and neighborhood structure are used in this method. Six famous benchmark instances (including 201 open problems) of FJSP have been used to evaluate the performance of the proposed HA. Comparisons among proposed HA and other state-of-the-art reported algorithms are also provided to show the effectiveness and efficiency of proposed method. The computational time of proposed HA also has been compared with other algorithms. The experimental results demonstrate that the proposed HA has achieved significant improvement for solving FJSP regardless of the solution accuracy and the computational time. And, the proposed method obtains the new best solutions for several benchmark problems.

A genetic algorithm for energy-efficiency in job-shop scheduling

Many real-world scheduling problems are solved to obtain optimal solutions in term of processing time, cost, and quality as optimization objectives. Currently, energy-efficiency is also taken into consideration in these problems. However, this problem is NP-hard, so many search techniques are not able to obtain a solution in a reasonable time. In this paper, a genetic algorithm is developed to solve an extended version of the Job-shop Scheduling Problem in which machines can consume different amounts of energy to process tasks at different rates (speed scaling). This problem represents an extension of the classical job-shop scheduling problem, where each operation has to be executed by one machine and this machine can work at different speeds. The evaluation section shows that a powerful commercial tool for solving scheduling problems was not able to solve large instances in a reasonable time, meanwhile our genetic algorithm was able to solve all instances with a good solution quality.

Hybrid approach using simulation-based optimisation for job shop scheduling problems

In this paper, we present a hybrid modelling approach and formulation using simulation-based optimisation (SbO) for solving complex problems, viz., job shop scheduling. The classical job shop scheduling problem is NP-Hard. Traditionally, the problem is modelled as a Mixed-Integer Programming (MIP) model and solved using exact algorithms (branch-and-bound, branch-and-cut, etc) or using meta-heuristics (Genetic Algorithm, Particle Swarm Optimisation, etc). In our hybrid SbO approach, we propose a modified formulation of the scheduling problem where the operational aspects of the job shop are captured only in the simulation model. Two new decision variables, controller delays and queue priorities, are introduced. The performances of the MIP-based approach and the proposed hybrid approach are compared through the number of decision variables, run time and the objective values for select deterministic benchmark problem instances. The results clearly indicate that the hybrid approach outperforms the traditional MIP for all large-scale problems, resulting in solutions closer to optimum in a much lesser computational time. Interestingly, it is also observed that the introduction of an ‘error’ term in the objective of the deterministic problem improves performance. Finally, the performance of the proposed SbO approach is analysed for stochastic job shops.

Configuration and the advantages of the shifting bottleneck procedure for optimizing the job shop total weighted tardiness scheduling problem

This paper answers two fundamental questions concerning the usage of the shifting bottleneck (SB) procedure to optimize the criterion total weighted tardiness for the classical job shop scheduling problem. The first question is how to configure the SB procedure, as it is a divide-and-conquer method and consists of diverse subsolutions for each procedure phase. The second question is what the advantages of the SB procedure are, in comparison with other state-of-the-art approaches. To answer the first question, we evaluate the performance (i.e. the scheduling quality) and the efficiency (i.e. the computational time) of various SB variants using computational experiments and present guidelines for configuring the SB procedure. To respond to the second question, extensive computational experiments were conducted on various benchmark instances (up to 100 jobs $$\times $$× 20 machines). Results show the superior performance/efficiency trade-off of the SB variants with certain configuration to local search methods. This excellent trade-off between performance and efficiency makes the SB procedure particularly promising for solving practical production scheduling problems.

Energy efficiency, robustness, and makespan optimality in job-shop scheduling problems

AbstractMany real-world problems are known as planning and scheduling problems, where resources must be allocated so as to optimize overall performance objectives. The traditional scheduling models consider performance indicators such as processing time, cost, and quality as optimization objectives. However, most of them do not take into account energy consumption and robustness. We focus our attention in a job-shop scheduling problem where machines can work at different speeds. It represents an extension of the classical job-shop scheduling problem, where each operation has to be executed by one machine and this machine can work at different speeds. The main goal of the paper is focused on the analysis of three important objectives (energy efficiency, robustness, and makespan) and the relationship among them. We present some analytical formulas to estimate the ratio/relationship between these parameters. It can be observed that there exists a clear relationship between robustness and energy efficiency and a clear trade-off between robustness/energy efficiency and makespan. It represents an advance in the state of the art of production scheduling, so obtaining energy-efficient solutions also supposes obtaining robust solutions, and vice versa.

A new genetic algorithm for flexible job-shop scheduling problems

Flexible job-shop scheduling problem (FJSP), which is proved to be NP-hard, is an extension of the classical job-shop scheduling problem. In this paper, we propose a new genetic algorithm (NGA) to solve FJSP to minimize makespan. This new algorithm uses a new chromosome representation and adopts different strategies for crossover and mutation. The proposed algorithm is validated on a series of benchmark data sets and tested on data from a drug manufacturing company. Experimental results prove that the NGA is more efficient and competitive than some other existing algorithms.

A hybrid discrete firefly algorithm for solving multi-objective flexible job shop scheduling problems

Firefly algorithm (FA) is a nature-inspired optimisation algorithm that can be successfully applied to continuous optimisation problems. However, lot of practical problems are formulated as discrete optimisation problems. In this paper a hybrid discrete firefly algorithm (HDFA) is proposed to solve the multi-objective flexible job shop scheduling problem (FJSP). FJSP is an extension of the classical job shop scheduling problem that allows an operation to be processed by any machine from a given set along different routes. Three minimisation objectives - the maximum completion time, the workload of the critical machine and the total workload of all machines are considered simultaneously. This paper also proposes firefly algorithms discretisation which consists of constructing a suitable conversion of the continuous functions as attractiveness, distance and movement, into new discrete functions. In the proposed algorithm discrete firefly algorithm (DFA) is combined with local search (LS) method to enhance the searching accuracy and information sharing among fireflies. The experimental results on the well-known benchmark instances and comparison with other recently published algorithms shows that the proposed algorithm is feasible and an effective approach for the multi-objective flexible job shop scheduling problems.

Towards an Embedded Distributed Implementations of PSO Solutions for the Flexible Job Shop Problem

Abstract The Flexible Job Shop Problem (FJSP) is an extension of the classical job shop scheduling problem which allows an operation to be processed by any machine from a given set. The particle swarm optimization (PSO) is an evolutionary algorithm that uses a population of candidate solutions to develop an optimal solution to the problem. This paper aims to study the performance of centralized and distributed PSO solutions to solve the FJSP. It presents various implementations of PSO: serial, centralized parallel, distributed and multi agent. Then, it compares the performances obtained on a workstation against the Raspberry B+ credit-card sized computer, both running Java SE embedded virtual machine.

A Modified Biogeography-Based Optimization for the Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSSP) is a practical extension of classical job shop scheduling problem that is known to be NP-hard. In this paper, an effective modified biogeography-based optimization (MBBO) algorithm with machine-based shifting is proposed to solve FJSSP with makespan minimization. The MBBO attaches great importance to the balance between exploration and exploitation. At the initialization stage, different strategies which correspond to two-vector representation are proposed to generate the initial habitats. At global phase, different migration and mutation operators are properly designed. At local phase, a machine-based shifting decoding strategy and a local search based on insertion to the habitat with best makespan are introduced to enhance the exploitation ability. A series of experiments on two well-known benchmark instances are performed. The comparisons between MBBO and other famous algorithms as well as BBO variants prove the effectiveness and efficiency of MBBO in solving FJSSP.