Reentrant Job Shop Research Articles

Differential Evolution Algorithm Combined with Uncertainty Handling Techniques for Stochastic Reentrant Job Shop Scheduling Problem

This paper considers two kinds of stochastic reentrant job shop scheduling problems (SRJSSP), i.e., the SRJSSP with the maximum tardiness criterion and the SRJSSP with the makespan criterion. Owing to the NP-complete complexity of the considered RJSSPs, an effective differential evolutionary algorithm (DEA) combined with two uncertainty handling techniques, namely, DEA_UHT, is proposed to address these problems. Firstly, to reasonably control the computation cost, the optimal computing budget allocation technique (OCBAT) is applied for allocating limited computation budgets to assure reliable evaluation and identification for excellent solutions or individuals, and the hypothesis test technique (HTT) is added to execute a statistical comparison to reduce some unnecessary repeated evaluation. Secondly, a reentrant-largest-order-value rule is designed to convert the DEA’s individual (i.e., a continuous vector) to the SRJSSP’s solution (i.e., an operation permutation). Thirdly, a conventional active decoding scheme for the job shop scheduling problem is extended to decode the solution for obtaining the criterion value. Fourthly, an Insert-based exploitation strategy and an Interchange-based exploration strategy are devised to enhance DEA’s exploitation ability and exploration ability, respectively. Finally, the test results and comparisons manifest the effectiveness and robustness of the proposed DEA_UHT.

Digital twin application with horizontal coordination for reinforcement-learning-based production control in a re-entrant job shop

In a re-entrant job shop (RJS), an entity can visit the same resource type multiple times; this is called re-entrancy, which occurs frequently in actual industries. Re-entrancy causes an NP-hard problem and is dominated by heuristics-based production control. The stochastic arrivals due to re-entrancy require the design of an appropriate dispatching rule. Reinforcement learning (RL) is an efficient technique for establishing robust dispatching rules; however, only a few cases that coordinate RL-based production control with a digital twin (DT) have been reported. This study proposes a novel production control model that applies a DT and horizontal coordination with RL-based production control. The requirements for dispatching in the RJS and coordination between RL and the DT were defined. A suitable architectural framework, service composition, and systematic logic library schema were developed to exploit the advanced characteristics of the DT and improve the existing production control methods. This study is an early case of coordinating RL and DT, and the findings revealed that RL policy networks should be imported in the creation procedures rather than being synchronised to the DT. The results should be a valuable reference for research on other types of RL-based production control with regard to horizontal coordination.

Optimal Scheduling of AGVs in a Reentrant Blocking Job-shop

This work presents a mixed integer linear programming (MILP) formulation to find an optimal solution to a small instance of the complex scheduling problem in a make-to-order production. Minimizing the make span, the MILP generates the optimal schedule for the autonomous guided vehicles (AGVs) in a blocking reentrant job shop environment with different jobs. Feasible schedules for the machines and the AGVs are generated from different sized instances to evaluate the limits of the mathematical model. These results are compared to a priority rule based dispatching system, evaluated with a discrete event simulation. The comparison leads to the insight, that on the one hand optimal solutions cannot be calculated for most real world scenarios due to the complexity and on the other hand the application of a standard dispatching rule lead to poor performances neither of the technics are satisfying the need to generate an appropriate schedule. As a result possible solutions are presented.

Scheduling parallel machines with sequence dependent set-up times in job shop industries using GA and SA

ABSTRACTIn this paper, an unprecedented and practicable job shop scheduling problem (JSSP) is presented as the fuzzy hybrid reentrant job shop and parallel machines scheduling with sequence dependent set-up times. The JSSP is identified as a complicated optimisation situated in NP-hard (Non-deterministic polynomial) problems in turn. In addition, we have incorporated some applicative constraints such as: reentrant work flows, parallel machines and uncertainty as fuzzy processing times and fuzzy sequence dependent set-up times simultaneously. In a real-world job shop problem, determining exact values for the problem's factors is usually difficult, especially in human–dependent ones. Inserting uncertainty to the problem makes the job shop scheduling more practical and realistic. There is considerable work in the fuzzy job shop scheduling problem (FJSSP) but none of them has applied such complexity. A real-life work field has been studied for evaluating solving methodologies. Two distinguished metaheuristics – simulated annealing (SA) and genetic algorithm (GA) – are investigated and compared to achieve minimum of maximum fuzzy completion times (or fuzzy makespan Cmax ). The comparison results show the same performance of both proposed SA and GA in small-scale models. But in large-scale problems GA overcomes SA significantly.

Integrating Preventive Maintenance Planning and Production Scheduling under Reentrant Job Shop

This paper focuses on a preventive maintenance plan and production scheduling problem under reentrant Job Shop in semiconductor production. Previous researches discussed production scheduling and preventive maintenance plan independently, especially on reentrant Job Shop. Due to reentrancy, reentrant Job Shop scheduling is more complex than the standard Job Shop which belongs to NP-hard problems. Reentrancy is a typical characteristic of semiconductor production. What is more, the equipment of semiconductor production is very expensive. Equipment failure will affect the normal production plan. It is necessary to maintain it regularly. So, we establish an integrated and optimal mathematical model. In this paper, we use the hybrid particle swarm optimization algorithm to solve the problem for it is highly nonlinear and discrete. The proposed model is evaluated through some simple simulation experiments and the results show that the model works better than the independent decision-making model in terms of minimizing maximum completion time.

Scheduling of a hub reentrant job shop to minimize makespan

This paper focuses on a hub reentrant shop scheduling problem which is motivated by actual packing production line in the iron and steel industry. There are five operations for processing a job where three operations must be processed on a hub machine, and between any two consecutive operations on the hub machine, two operations must be processed on other two secondary machines, respectively. We mainly consider two types of the problem. The first is basic hub reentrant shop (BHRS) problem where only one machine in each secondary machine center. The second is hybrid hub reentrant shop (HHRS) problem where multiple machines in each secondary machine center. The objective is to minimize the makespan. For BHRS problem, we show that the problem is NP-hard in the strong sense. Some properties are derived for identifying an optimal schedule. Furthermore, a heuristic algorithm is proposed with the worst performance ratio 6:5, and this ratio is demonstrated tight. For HHRS problem, two well-solvable cases are proposed, respectively. Under a split condition, HHRS is equivalent to a two-stage hybrid flow shop problem. The worst case of a class of proposed algorithms is analyzed. The performance ratio is demonstrated relatively with the secondary machine numbers.

A modified shifting bottleneck heuristic for the reentrant job shop scheduling problem with makespan minimization

This paper proposes a modified shifting bottleneck heuristic (MSBH) for the reentrant job shop scheduling problem (RJSSP) with makespan minimization objective. Recently, the reentrant job shop has come into prominence as a new type of manufacturing shop. The principle characteristic of a reentrant job shop is that a job may visit certain machines more than once during the process flow, whereas in the classic job shop, each job visits a machine only once. The shifting bottleneck heuristic (SBH) is one of the most successful heuristic approaches for the classical job shop scheduling problem, which decomposes the problem into a number of single-machine subproblems. This paper adapts the SBH for the RJSSP and proposes a new sequencing heuristic for the single-machine maximum lateness subproblem considering the reentrant jobs in order to handle large-size RJSSPs. It also uses a subproblem criticality measure that further shortens the implementation time. The proposed MSBH is tested by using instances up to 20 machines and 100 jobs, and it is illustrated that good quality solutions can be obtained in reasonable computational times. A real-life application of the MSBH is also given as a case study to evaluate its performance.

Integer programming models for the re-entrant shop scheduling problems

A re-entrant shop describes a manufacturing environment in which a machine can process a job more than once. A re-entrant shop can be classified into a re-entrant job-shop (RJS) and a re-entrant flow-shop (RFS). This article presents the development of the mixed binary integer programming (BIP) technique for the RJS and the RFS scheduling problems. Eight mixed BIP models are proposed for solving re-entrant shop scheduling problems to minimize makespan. The models RJS-1, RJS-2, RJS-3, and RJS-4 are for the RJS problems, while the other four models (RFS-1, RFS-2, RFS-3, and RFS-4) are for the RFS problems. Computational results show that the RJS-4 model is the best of the RJS models, and the RFS-3 model is the best of the RFS models.

Modeling the reentrant job shop scheduling problem with setups for metaheuristic searches

We consider modeling the reentrant job shop scheduling problem with sequence dependent setup times in the context of metaheuristic search methods. We begin by investigating feasibility conditions when sequence dependent setups are incorporated into the traditional job shop scheduling problem. The investigation reveals that traditional methods of avoiding infeasible solutions for iterative search techniques do not suffice. The conditions under which these infeasible solutions occur are presented and an algorithm is presented to remove such infeasibilities. Reentrancy and its relationship to the traditional model are then illustrated, and the new features of the disjunctive graph are introduced. We conclude with a simple algorithm for obtaining an initial feasible solution, benefits of this research, and an application to the reentrant job shop scheduling problem with sequence dependent setups.

Mixed binary integer programming formulations for the reentrant job shop scheduling problem

This paper describes the development of mixed binary integer programming (BIP) formulations for the reentrant job shop scheduling problem. Based on an earlier classical job shop model developed by Manne and improved by Liao and You, this paper presents two extended BIP optimization formulations for the problem under consideration. In order to improve the solution speed of the BIP formulations, two layer division procedures are developed and incorporated in the corresponding models. Results of computational experiments, in which an average performance of these formulations is investigated, are also reported.

Matrix Controller Design and Deadlock Analysis of Automated Manufacturing Systems. Part 2: Deadlock Avoidance Policy

A matrix framework is offered that permits direct, fast design and reconfigures the rule-based controllers for automated manufacturing systems. The controller design is based on standard manufacturing techniques such as the bill of materials, task sequencing matrix, and resource requirement matrix that give the matrix equations. The result is a multiloop discrete event controller with outer loops for dispatching of shared resources. The equations of the closed-loop manufacturing system can be used to derive a Petri net for rigorous performance analysis. Combining the matrix controller state equation and the well-known Petri nets marking transition equation yields a complete dynamical description of a discrete event system. The matrix formulation allows a rigorous analysis of deadlock in terms of circular blockings, siphons, and the numbers of resources available. This allows efficient dispatching and routeing with deadlock avoidance. The matrix controller also allows both nonlinear activity level algorithms and logical discrete-event supervisory algorithms. Such a hybrid controller would potentially allow the optimisation of shared resource assignment and job sequencing between machines with fast and precise operation of each individual machine. A multiple-part-path re-entrant job shop is used to illustrate the concepts introduced.

Cyclic scheduling heuristics for a re-entrant job shop manufacturing environment

Two efficient cyclic scheduling heuristics for re-entrant job shop environments were developed. Each heuristic generated an efficient and feasible cyclic production schedule for a job shop in which a single product was produced repetitively on a set of machines was to determine an efficient and feasible cyclic schedule which simultaneously minimized flow time and cycle time. The first heuristic considered a repetitive production re-entrant job shop with a predetermined sequence of operations on a single product with known processing times, set-up and material handling times. The second heuristic was a specialization of the first heuristic where the set-up for an operation could commence even while the preceding operation was in progress. These heuristics have been extensively tested and computational results are provided. Also, extensive analysis of worst-case and trade-offs between cycle time and flow time are provided. The results indicate that the proposed heuristics are robust and yield efficient and superior cyclic schedules with modest computational effort.

Mean Flow Time Minimization in Reentrant Job Shops with a Hub

This paper considers a reentrant job shop with one hub machine which a job enters K times. Between any two consecutive entries into the hub, the job is processed on other machines. The objective is to minimize the total flow time. Under two key assumptions, the bottleneck assumption and the hereditary order (HO) assumption on the processing times of the entries, it is proved that there is an optimal schedule with the shortest processing time (SPT) job order and a dynamic programming algorithm is derived to find such a schedule. An approximation algorithm based on the shortest path algorithm and the SPT job order is also proposed to solve the problem. The approximation algorithm finds an optimal clustered schedule. In clustered schedules, jobs are scheduled in disjoint clusters; they resemble batch processing and seem to be of practical importance. Worst-case bounds for clustered schedules are proved with the HO assumption relaxed. Two special cases with the restriction that there are only two entries to the hub machine are further analyzed to offer more insight into the structure of optimal solutions.