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Showing papers on "Job shop published in 2012"


Journal ArticleDOI
TL;DR: The robustness on the relative ranking of the performance quality is checked for the various priority rules when applied on larger problem instances, on the extension of multiple machines possibilities per job as well as on the introduction of sequence-dependent setup times.
Abstract: In this paper, a comparison and validation of various priority rules for the job shop scheduling problem under different objective functions is made. In a first computational experiment, 30 priority rules from the literature are used to schedule job shop problems under two flow time-related and three tardiness-related objectives. Based on this comparative study, the priority rules are extended to 13 combined scheduling rules in order to improve the performance of the currently best-known rules from the literature. Moreover, the best-performing priority rules on each of these five objective functions are combined into hybrid priority rules in order to be able to optimise various objectives at the same time. In a second part of the computational experiment, the robustness on the relative ranking of the performance quality is checked for the various priority rules when applied on larger problem instances, on the extension of multiple machines possibilities per job as well as on the introduction of sequence-dependent setup times. Moreover, the influence of dynamic arrivals of jobs has also been investigated to check the robustness on the relative ranking of the performance quality between static and dynamic job arrivals. The results of the computational experiments are presented and critical remarks and future research avenues are suggested.

115 citations


Journal ArticleDOI
01 Aug 2012
TL;DR: An effective co-evolutionary genetic algorithm (CGA) is developed for the minimization of fuzzy makespan and Computational results show that CGA outperforms those algorithms compared.
Abstract: Fuzzy flexible job shop scheduling problem (FfJSP) is the combination of fuzzy scheduling and flexible scheduling in job shop environment, which is seldom investigated for its high complexity. We developed an effective co-evolutionary genetic algorithm (CGA) for the minimization of fuzzy makespan. In CGA, the chromosome of a novel representation consists of ordered operation list and machine assignment string, a new crossover operator and a modified tournament selection are proposed, and the population of job sequencing and the population of machine assignment independently evolve and cooperate for converging to the best solutions of the problem. CGA is finally applied and compared with other algorithms. Computational results show that CGA outperforms those algorithms compared.

111 citations


Journal ArticleDOI
TL;DR: In this article, four multiobjective, Pareto-based, meta-heuristic optimisation methods, namely NSGA-II, non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm, MOGA, and PAREto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal PareTO front.
Abstract: This paper deals with a problem of partial flexible job shop with the objective of minimising makespan and minimising total operation costs. This problem is a kind of flexible job shop problem that is known to be NP-hard. Hence four multi-objective, Pareto-based, meta-heuristic optimisation methods, namely non-dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), multi-objective genetic algorithm (MOGA) and Pareto archive evolutionary strategy (PAES) are proposed to solve the problem with the aim of finding approximations of optimal Pareto front. A new solution representation is introduced with the aim of solving the addressed problem. For the purpose of performance evaluation of our proposed algorithms, we generate some instances and use some benchmarks which have been applied in the literature. Also a comprehensive computational and statistical analysis is conducted in order to analyse the performance of the applied algorithms in five metrics including non-dominat...

106 citations


Journal ArticleDOI
TL;DR: Comparisons of WLC order release methods against the best-performing purely periodic and continuous release rules across a range of flow directions demonstrate that LUMS COR and the continuous WLC release methods consistently outperform purely periodic release and Constant WIP.
Abstract: Protecting throughput from variance is the key to achieving lean. Workload control (WLC) accomplishes this in complex make-to-order job shops by controlling lead times, capacity, and work-in-process (WIP). However, the concept has been dismissed by many authors who believe its order release mechanism reduces the effectiveness of shop floor dispatching and increases work center idleness, thereby also increasing job tardiness results. We show that these problems have been overcome. A WLC order release method known as “LUMS OR” (Lancaster University Management School order release) combines continuous with periodic release, allowing the release of work to be triggered between periodic releases if a work center is starving. This paper refines the method based on the literature (creating “LUMS COR” [Lancaster University Management School corrected order release]) before comparing its performance against the best-performing purely periodic and continuous release rules across a range of flow directions, from the pure job shop to the general flow shop. Results demonstrate that LUMS COR and the continuous WLC release methods consistently outperform purely periodic release and Constant WIP. LUMS COR is considered the best solution in practice due to its excellent performance and ease of implementation. Findings have significant implications for research and practice: throughput times and job tardiness results can be improved simultaneously and order release and dispatching rules can complement each other. Thus, WLC represents an effective means of implementing lean principles in a make-to-order context.

101 citations


05 Nov 2012
TL;DR: The application of a recent developed metaheuristic called Firefly Algorithm for solving JSSP is presented, the parameter setting of the proposed algorithm is investigated, and the performance of the FA performance is compared using various parameter settings.
Abstract: Job shop scheduling problem (JSSP) is one of the most famous scheduling problems, most of which are categorised into Non-deterministic Polynomial (NP) hard problem. The objectives of this paper are to i) present the application of a recent developed metaheuristic called Firefly Algorithm (FA) for solving JSSP; ii) investigate the parameter setting of the proposed algorithm; and iii) compare the FA performance using various parameter settings. The computational experiment was designed and conducted using five benchmarking JSSP datasets from a classical OR-Library. The analysis of the experimental results on the FA performance comparison between with and without using optimised parameter settings was carried out. The FA with appropriate parameters setting that got from the experiment analysis produced the best-so-far schedule better than the FA without adopting parameter settings. Keywords : Scheduling, Job shop, Metaheuristics, Firefly Algorithm, Experimental design, Parameter setting (Selected from 1st Symposium on Hands-on Research and Development, Chiang Mai)

91 citations


Journal ArticleDOI
TL;DR: The hybrid model proposed here surpasses most similar systems in solving many more traditional benchmark problems and real-life problems and achieves by the combined impact of several small but important features such as powerful chromosome representation, effective genetic operators, restricted neighbourhood strategies and efficient search strategies along with innovative initial solutions.
Abstract: In recent decades many attempts have been made at the solution of Job Shop Scheduling Problem using a varied range of tools and techniques such as Branch and Bound at one end of the spectrum and Heuristics at the other end However, the literature reviews suggest that none of these techniques are sufficient on their own to solve this stubborn NP-hard problem Hence, it is postulated that a suitable solution method will have to exploit the key features of several strategies We present here one such solution method incorporating Genetic Algorithm and Tabu Search The rationale behind using such a hybrid method as in the case of other systems which use GA and TS is to combine the diversified global search and intensified local search capabilities of GA and TS respectively The hybrid model proposed here surpasses most similar systems in solving many more traditional benchmark problems and real-life problems This, the system achieves by the combined impact of several small but important features such as powerful chromosome representation, effective genetic operators, restricted neighbourhood strategies and efficient search strategies along with innovative initial solutions These features combined with the hybrid strategy employed enabled the system to solve several benchmark problems optimally, which has been discussed elsewhere in Meeran and Morshed (8th Asia Pacific industrial engineering and management science conference, Kaohsiung, Taiwan, 2007) In this paper we bring out the system's practical usage aspect and demonstrate that the system is equally capable of solving real life Job Shop problems

86 citations


Journal ArticleDOI
TL;DR: This paper addresses the serial batch scheduling problem embedded in a job shop environment to minimize makespan with a tabu search algorithm which consists of various neighborhood functions, multiple tabu lists and a sophisticated diversification structure.

76 citations


Journal ArticleDOI
TL;DR: A dynamic opportunistic preventive maintenance model is developed for a multi-component system with considering changes in job shop schedule and is more efficient than the ones based on two other commonly used preventive maintenance models.

68 citations


Journal ArticleDOI
TL;DR: This work proposes a comprehensive real-time PPC system for arbitrary capacitated job-shop manufacturing by integrating production ordering and batch sizing control mechanisms into a dynamic model, and adopts a system dynamics (SD) approach which is proved to be appropriate for studying the dynamic behavior of complex manufacturing systems.

63 citations


Journal ArticleDOI
TL;DR: EQNML enhances interoperability between a wide range of analytical solvers and simulation tools dealing with systems performance evaluation and based on the extended queuing theory, and provides a starting point for the development of a standard inter-change format.
Abstract: This paper focuses on the development of EQNML which is an extended queuing modelling and markup language. We discuss the DSML metamodel and its XML-based exchange format which represent the cornerstone of the development process. EQNML enhances interoperability between a wide range of analytical solvers and simulation tools dealing with systems performance evaluation and based on the extended queuing theory. Furthermore, the Model Driven Engineering approach allows automatic generation of modelling environments and simulation/analytical codes which improve productivity and quality. Our aim is to induce discussion on and contributions for elaborating the whole metamodel and providing a starting point for the development of a standard inter-change format. 19 refs. (Received in February 2011, accepted in April 2012. This paper was with the authors 2 months for 2 revisions.)

62 citations


Journal ArticleDOI
TL;DR: A new approach for the organization of the ‘control’ function in a Job Shop having the characteristics of working with small series relies on the use of the holonic paradigm on an isoarchic architecture and on a decision-making capacity based on a multicriteria analysis.
Abstract: Faced with international competition, industrial production increasingly requires implementation conditions which, in some cases, lead to seek new techniques for workshop control. This is the case when it is asked to establish Just in Time management in a Job Shop having the characteristics of working with small series. A new approach for the organization of the `control' function in such a context is presented here. This approach relies on the use of the holonic paradigm on an isoarchic architecture and on a decision-making capacity based on a multicriteria analysis. The various concepts of this approach are addressed first. Then, the multicriteria decision mechanisms that are used are detailed, as well as the implementation and instrumentation phases. The first results that were obtained are presented.

Journal ArticleDOI
TL;DR: A data mining based approach to discover previously unknown priority dispatching rules for job shop scheduling problem is presented and implemented for a job shop problem with maximum lateness as the scheduling objective.

Journal ArticleDOI
TL;DR: A stochastic model is presented, which concerns uncertain processing times in proactive scheduling stage on the basis of analyzing the deficiencies of a classical scheduling model for a production schedule in practice.
Abstract: Multi-agent-based proactive–reactive scheduling for job shops is presented, aiming to hedge against the uncertainties of dynamic manufacturing environments. This scheduling mechanism consists of two stages, including proactive scheduling stage and reactive scheduling stage. In the proactive scheduling stage, the objective is to generate a robust predictive schedule against known uncertainties; in the reactive scheduling stage, the objective is to dynamically rectify the predictive schedule to adapt to unknown uncertainties, viz. the reactive scheduling stage is actually complementary to the proactive scheduling stage. A stochastic model is presented, which concerns uncertain processing times in proactive scheduling stage on the basis of analyzing the deficiencies of a classical scheduling model for a production schedule in practice. For the stochastic scheduling problem, a multi-agent-based architecture is proposed and a distributed scheduling algorithm is used to solve this stochastic problem. Finally, the repair strategies are introduced to maintain the original proactive schedule when unexpected events occur. Case study examples show that this scheduling mechanism generates more robust schedules than the classical scheduling mechanism.

Journal ArticleDOI
TL;DR: In this paper, a hybrid genetic algorithm (GA) was proposed to solve the integrated process planning and scheduling problem in a modern manufacturing system, where problem-specific GA operators were designed to enhance the global search power of GA and a local search procedure was incorporated into the GA to improve the performance.
Abstract: Process planning and scheduling are two important functions in a modern manufacturing system. Although integrating decisions related to these functions gives rise to a hard combinatorial problem, due to the impressive improvement in system performance which is resulted through this integration, developing effective methods to solve this problem is of great theoretical and practical importance. In this research, after formulating the integrated process planning and scheduling problem as a mathematical program, we propose a hybrid genetic algorithm (GA) for the problem. In the proposed algorithm, problem-specific genetic operators are designed to enhance the global search power of GA. Also, a local search procedure has been incorporated into the GA to improve the performance of the algorithm. The model considers precedence relations among job operations, based on which feasible process plans for each job can be represented implicitly. A novel neighborhood function, considering the constraints of a flexible job shop environment and nonlinear precedence relations among operations, is presented to speed up the local search process. In experimental study, the performance of the proposed algorithm has been evaluated based on a number of problems adopted from the literature. The experimental results demonstrate the efficiency of the proposed algorithm to find optimal or near-optimal solutions.

Journal ArticleDOI
TL;DR: In this article, the authors argue that job shop designed ORR systems are not the best ones for non-repetitive production and that a significant number of production systems are better modelled as flow shops, rather than as job shops.
Abstract: Lean implementations are no longer limited to high-volume production and are becoming increasingly common in low-volume, high-variety non-repetitive companies. Such companies, usually with make-to-order or engineer-to-order production, have normally been modelled with a job shop production system, but many of them actually have a dominant flow in production. Moreover, one of the main characteristics of lean implementation is that it streamlines production flow, makes it unidirectional and reduces setup and lot size. Consequently, a significant number of production systems are better modelled as flow shops, rather than as job shops. This has an impact on production management approaches, and in particular on order review and release systems. In fact, ORR systems have been designed with job shops in mind, because they are the most complex systems to manage, and because they are considered the optimal system for non-repetitive production. We believe that job shop designed ORR systems are not the best ones fo...

Journal ArticleDOI
TL;DR: In this article, the authors developed two heuristic rescheduling procedures, AWIJ and AWI-O, to minimise mean tardiness of jobs in a job shop.
Abstract: Rescheduling is a procedure to repair a production plan affected by unexpected disruptions. It is important because a production schedule released to a shop floor is subject to unexpected disruptions. This paper develops two novel heuristic rescheduling procedures, AWI-J and AWI-O, to minimise mean tardiness of jobs in a job shop. The procedures are based on an active schedule-generation procedure and Wilkerson–Irwin algorithm, which is well known for minimising mean tardiness of a schedule. The performances of the new procedures are compared with those of the Affected Operations Rescheduling (AOR) procedure, which is popular in the rescheduling literature. Efficiency measures such as mean tardiness, mean flowtime, and makespan, and a stability measure, deviation of new operation start times from the original start times, are used for comparison. Test results show that AWI-J improves efficiency over AOR, and AWI-O improves efficiency and stability as well.

Journal ArticleDOI
TL;DR: In this article, a two-stage ant colony optimisation (ACO) algorithm is implemented in a multi-agent system (MAS) to accomplish integrated process planning and scheduling (IPPS) in the job shop type flexible manufacturing environments.
Abstract: In this paper, a two-stage ant colony optimisation (ACO) algorithm is implemented in a multi-agent system (MAS) to accomplish integrated process planning and scheduling (IPPS) in the job shop type flexible manufacturing environments. Traditionally, process planning and scheduling functions are performed sequentially and the actual status of the production facilities is not considered in either process planning or scheduling. IPPS is to combine both the process planning and scheduling problems in the consideration, that is, the actual process plan and the schedule are determined dynamically in accordance with the order details and the status of the manufacturing system. The ACO algorithm can be applied to solve IPPS problems. An innovative two-stage ACO algorithm is introduced in this paper. In the first stage of the algorithm, instead of depositing pheromones on graph edges as in common ant algorithms, ants are directed to deposit pheromones at the nodes to select a set of more favourable processes. In th...

Journal ArticleDOI
TL;DR: Based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search (TS) metaheuristic algorithm is developed to deal with the PMJSS problem.
Abstract: In practice, parallel-machine job-shop scheduling (PMJSS) is very useful in the development of standard modelling approaches and generic solution techniques for many real-world scheduling problems. In this paper, based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version SBP algorithm for the job-shop scheduling (JSS) has been significantly improved to solve the PMJSS problem with four novelties: i) a topological-sequence algorithm is proposed to decompose the PMJSS problem into a set of single-machine scheduling (SMS) and/or parallel-machine scheduling (PMS) subproblems; ii) a modified Carlier algorithm based on the proposed lemmas and the proofs is developed to solve the SMS subproblem; iii) the Jackson rule is extended to solve the PMS subproblem; iv) a Tabu Search metaheuristic algorithm is embedded under the framework of SBP to optimise the JSS and PMJSS cases. The computational experiments show that the proposed HSBP is very efficient in solving the JSS and PMJSS problems.

Journal ArticleDOI
TL;DR: In this article, the authors proposed two new differential evolution algorithms (DE) for solving the job shop scheduling problem (JSP) that minimises two single objective functions: makespan and total weighted tardiness.
Abstract: This paper proposes two new differential evolution algorithms (DE) for solving the job shop scheduling problem (JSP) that minimises two single objective functions: makespan and total weighted tardiness. The proposed algorithms aim to enhance the efficiency of the search by dynamically balancing exploration and exploitation ability in DE and avoiding the problem of premature convergence. The first algorithm allows DE population to simultaneously perform different mutation strategies in order to extract the strengths of various strategies and compensate for the weaknesses of each individual strategy to enhance the overall performance. The second algorithm allows the whole DE population to change the search behaviour whenever the solutions do not improve. This study also introduces a modified local mutation operation embedded in the two proposed DE algorithms to promote exploitation in different areas of the search space. In addition, a local search technique, called Critical Block (CB) neighbourhood, is app...

Journal ArticleDOI
TL;DR: A relative good and efficient genetic algorithm is proposed for the problem with normal processing time, resumable jobs and the objective of minimizing makespan, and computational results show the GA performs better than PSO and SA for stochastic job shop scheduling problems considered.

Journal ArticleDOI
TL;DR: This work proposes a proactive approach to generate efficient and stable schedules for a job shop subject to processing time variability and random machine breakdowns; a surrogate stability measure is developed and a branch-and-bound algorithm is developed for this problem variant.
Abstract: The ability to cope with uncertainty in dynamic scheduling environments is becoming an increasingly important issue. In such environments, any disruption in the production schedule will translate into a disturbance of the plans for several external activities as well. Hence, from a practical point of view, deviations between the planned and realized schedules are to be avoided as much as possible. The term stability refers to this concern. We propose a proactive approach to generate efficient and stable schedules for a job shop subject to processing time variability and random machine breakdowns. In our approach, efficiency is measured by the makespan, and the stability measure is the sum of the variances of the realized completion times. Because the calculation of the original measure is mathematically intractable, we develop a surrogate stability measure. The version of the problem with the surrogate stability measure is proven to be NP-hard, even without machine breakdowns; a branch-and-bound algorithm is developed for this problem variant. A tabu search algorithm is proposed to handle larger instances of the problem with machine breakdowns. The results of extensive computational experiments indicate that the proposed algorithms are quite promising in performance. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Journal ArticleDOI
TL;DR: A survey of dispatching rules that explicitly take into account setup times in their decision making is provided in this article, where the most promising rules from the three categories are identified from the literature and compared empirically on various job shop problems with sequence-dependent setup times.
Abstract: This paper provides a survey of dispatching rules that explicitly take into account setup times in their decision making. Rules are classified into the categories of purely setup-oriented, composite and family-based rules, and the most promising rules from the three categories are identified from the literature. These rules are then compared empirically on various job shop problems with sequence-dependent setup times for their performance regarding mean setup time, mean flow time, mean tardiness and proportion of tardy jobs. The setup times are modelled using setup time matrices, and five different types of matrices are applied to assess the influence of this factor on the relative performance of a setup-oriented dispatching rule. Experimental results indicate that the choice of the best rule is often dependent on the setup time matrix structure. While good family-based rules exist for reducing the mean setup time and mean flow time, they are clearly outperformed by effective composite rules for due date-...

Journal ArticleDOI
TL;DR: In this article, a case study research approach is used to investigate the decisions of five manufacturing companies that satisfy the characteristics of job production system and identify process specific decisions for job shop and non-process specific decisions that are influenced by other contextual factors.
Abstract: Purpose – The purpose of this paper is to understand the configuration of a job production system with reference to manufacturing decision areas. The aim is to identify the process specific decisions for job shop and the non‐process specific decisions that are influenced by other contextual factors.Design/methodology/approach – A case study research approach is used in the present paper to investigate the decisions of five manufacturing companies that satisfy the characteristics of job production system. Data are collected from case company's products, order winners and choices made in manufacturing decision areas. The paper uses within case and cross‐case analysis to identify various patterns in the data, with a view to meeting the required research objectives.Findings – The present paper identifies a number of decisions specific to job shop. Further, many non‐process specific decisions are seen to be influenced by competitive priorities (order winner), strategic orientation of manufacturing (stages in H...

Journal ArticleDOI
TL;DR: The proposed method combines mathematical programming for selecting the best routing alternatives and tabu search for finding the best assignment of machines to operations along with the routings for balancing the load on machines of a flexible job shop.
Abstract: In workshops of CNC machines, jobs may have alternative sequences of operations, where each operation must be performed on one of a pre-specified subset of machines. The key to solving to this extremely hard scheduling problem is balancing the load on machines of a flexible job shop. The proposed method combines mathematical programming for selecting the best routing alternatives and tabu search for finding the best assignment of machines to operations along with the routings. Experiments in an industrial case study refer to the primary role of optimized load balancing that proved to be computationally tractable on large-scale problem instances.

Journal ArticleDOI
TL;DR: A new integer programming formulation is presented and it is shown that it outperforms an existing model from the literature in the problem of minimising the cycle time (maximising the throughput) in a job-shop environment.

Proceedings ArticleDOI
10 Jun 2012
TL;DR: Novel multi-objective genetic programming based hyper-heuristic methods for automatic design of SPs including dispatching rules (DRs) and due-date assignment rules (DDARs) in job shop environments and the proposed Diversified Multi-Objective Cooperative Coevolution (DMOCC) method can effectively evolve Pareto fronts.
Abstract: A scheduling policy (SP) strongly influences the performance of a manufacturing system. However, the design of an effective SP is complicated and time-consuming due to the complexity of each scheduling decision as well as the interactions between these decisions. This paper proposes novel multi-objective genetic programming based hyper-heuristic methods for automatic design of SPs including dispatching rules (DRs) and due-date assignment rules (DDARs) in job shop environments. The experimental results show that the evolved Pareto front contains effective SPs that can dominate various SPs from combinations of existing DRs with dynamic and regression-based DDARs. The evolved SPs also show promising performance on unseen simulation scenarios with different shop settings. On the other hand, the proposed Diversified Multi-Objective Cooperative Coevolution (DMOCC) method can effectively evolve Pareto fronts of SPs compared to NSGA-II and SPEA2 while the uniformity of SPs obtained by DMOCC is better than those evolved by NSGA-II and SPEA2.

Journal ArticleDOI
TL;DR: An efficient Shift Penalty-Based Timetabling method is proposed, which constructs two initial timetables from time difference-based sets and improves them by an investigated timetable tightening method.
Abstract: The no-wait job shop problem that exists with makespan minimization is well known to be a strongly NP-hard problem. In this paper, the properties of the problem are analyzed according to its characteristics. The problem is remodeled based on the introduced time difference. A traditional framework is adopted by decomposing the problem into two subproblems: the sequencing and the timetabling problems. An efficient Shift Penalty-Based Timetabling method is proposed, which constructs two initial timetables from time difference-based sets and improves them by an investigated timetable tightening method. A modified complete local search with memory is presented for the sequencing problem. The whole algorithm is tested on benchmark instances and compared with the two best existing algorithms. Computational results show that the proposed algorithm performs well on both effectiveness and efficiency.

Journal ArticleDOI
TL;DR: In this paper, a tabu search-based algorithm is proposed for the job shop scheduling problem with makespan criterion, which takes advantage of both N1 and N6 neighborhoods and is tested on standard benchmark sets, outperformed all previous approaches (including i-TSAB) and found six new upper bounds.
Abstract: The job shop scheduling problem with makespan criterion is valuable from both practical and theoretical points of view. This problem has been attacked by most of the well-known meta-heuristic algorithms. Among them, tabu search has emerged as the most effective approach. The proposed algorithm takes advantages of both N1 and N6 neighborhoods. N1 neighborhood is used as a path relinking procedure while N6 neighborhood with its guideposts is applied in a tabu search framework. In addition, a method is presented for updating the topological order, heads and tails in N6 neighborhood. The algorithm is tested on standard benchmark sets, outperformed all previous approaches (include i-TSAB) and found six new upper bounds among the unsolved problems. Furthermore, we have tried to collect the newest upper bounds for the other problems.

Journal ArticleDOI
TL;DR: A pseudo-polynomial time algorithm is provided to solve the problem of maximizing the weighted number of just-in-time jobs in a two-machine flow shop scheduling system, proving that it is $\mathcal{NP}$-hard in the ordinary sense.
Abstract: The problem of maximizing the weighted number of just-in-time jobs in a two-machine flow shop scheduling system is known to be $\mathcal {NP}$ -hard (Choi and Yoon in J Shed 10:237---243, 2007) However, the question of whether this problem is strongly or ordinarily $\mathcal{NP}$ -hard remains an open question We provide a pseudo-polynomial time algorithm to solve this problem, proving that it is $\mathcal{NP}$ -hard in the ordinary sense Moreover, we show how the pseudo-polynomial algorithm can be converted to a fully polynomial time approximation scheme (FPTAS) In addition, we prove that the same problem is strongly $\mathcal{NP}$ -hard for both a two-machine job shop scheduling system and a two-machine open shop scheduling system

Journal ArticleDOI
TL;DR: Workload control is a production planning and control concept developed to meet the needs of small and medium-sized make-to-order companies, where a job shop configuration is common as discussed by the authors.
Abstract: Workload control (WLC) is a production planning and control concept developed to meet the needs of small- and medium-sized make-to-order companies, where a job shop configuration is common. Although simulation has shown WLC can improve job shop performance, field researchers have encountered significant implementation challenges. One of the most notable challenges is the presence of ‘assembly job shops’ where product structures are more complex than typically modelled in simulation and where the final product consists of several sub-assemblies (or work orders) which have to be co-ordinated. WLC theory has not been developed sufficiently to handle such contexts, and the available literature on assembly job shops is limited. In response, this paper extends the applicability of WLC to assembly job shops by determining the best combination of: (i) WLC due date (DD) setting policy, (ii) release method and (iii) policy for coordinating the progress of work orders. When DDs are predominantly set by the company, ...