Blocking Job Shop Research Articles

Generating Dispatching Rules for the Interrupting Swap-Allowed Blocking Job Shop Problem Using Graph Neural Network and Reinforcement Learning

Abstract The interrupting swap-allowed blocking job shop problem (ISBJSSP) is a complex scheduling problem that is able to model many manufacturing planning and logistics applications realistically by addressing both the lack of storage capacity and unforeseen production interruptions. Subjected to random disruptions due to machine malfunction or maintenance, industry production settings often choose to adopt dispatching rules to enable adaptive, real-time re-scheduling, rather than traditional methods that require costly re-computation on the new configuration every time the problem condition changes dynamically. To generate dispatching rules for the ISBJSSP problem, we introduce a dynamic disjunctive graph formulation characterized by nodes and edges subjected to continuous deletions and additions. This formulation enables the training of an adaptive scheduler utilizing graph neural networks and reinforcement learning. Furthermore, a simulator is developed to simulate interruption, swapping, and blocking in the ISBJSSP setting. By employing a set of reported benchmark instances, we conduct a detailed experimental study on ISBJSSP instances with a range of machine shutdown probabilities to show that the scheduling policies generated can outperform or are at least as competitive as existing dispatching rules with predetermined priority. This study shows that the ISBJSSP, which requires real-time adaptive solutions, can be scheduled efficiently with the proposed method when production interruptions occur with random machine shutdowns.

Efficient primal heuristic updates for the blocking job shop problem

The blocking job shop problem is a variant of the classical job shop problem, where a job continues to block a machine after being serviced, until the downstream machine needed by the job becomes available. Many real world problems have been modeled as blocking job shop problems, and local search heuristics have been shown to produce good quality solutions. Existing literature shows that the computational complexity of these local search algorithms is very high, severely limiting their practical performance. In this work, we present new theoretical results for blocking job shop and show how these results can be used to significantly improve the computational efficiency of existing local search procedures. We empirically evaluate the proposed algorithm updates on existing benchmarks. The results demonstrate that our approach outperforms the current state-of-the-art, by consistently matching or improving previous best known results, usually within a fraction of the time reported for blocking job shop benchmarks. Due to the efficiency in neighborhood computations, our approach scales up to larger size problems than have been considered in prior studies. In particular, for the first time for blocking job shop, we show results for the 100 x 20 instances in Taillard’s benchmark.

Multi-objective invasive weeds optimisation algorithm for solving simultaneous scheduling of machines and multi-mode automated guided vehicles

In this paper, a novel model is presented for machines and automated guided vehicles' simultaneous scheduling, which addresses an extension of the blocking job shop scheduling problem, considering the transferring of jobs between different machines using a limited number of multi-mode automated guided vehicles. Since the model is strictly NP-hard, and because objectives contradict each other, a meta-heuristic algorithm called 'multi-objective invasive weeds optimisation algorithm' with a new chromosome structure which guarantees the feasibility of solutions is developed to solve the proposed problem. Two other meta-heuristic algorithms namely 'non-dominated sorting genetic algorithm' and 'multi-objective particle swarm optimisation algorithm' are applied to validate the solutions obtained by the developed multi-objective invasive weeds optimisation algorithm. A certain method was applied to select the algorithm with the best performance. The result of ranking the algorithms indicated that the developed multi-objective invasive weeds optimisation algorithm had the best performance in terms of solving the mentioned problems. [Received: 7 January 2017; Revised: 30 December 2017; Revised: 17 August 2018; Revised: 22 January 2019; Accepted: 26 July 2019]

On Neighborhood Structures and Repair Techniques for Blocking Job Shop Scheduling Problems

The job shop scheduling problem with blocking constraints and total tardiness minimization represents a challenging combinatorial optimization problem of high relevance in production planning and logistics. Since general-purpose solution approaches struggle with finding even feasible solutions, a permutation-based heuristic method is proposed here, and the applicability of basic scheduling-tailored mechanisms is discussed. The problem is tackled by a local search framework, which relies on interchange- and shift-based operators. Redundancy and feasibility issues require advanced transformation and repairing schemes. An analysis of the embedded neighborhoods shows beneficial modes of implementation on the one hand and structural difficulties caused by the blocking constraints on the other hand. The applied simulated annealing algorithm generates good solutions for a wide set of benchmark instances. The computational results especially highlight the capability of the permutation-based method in constructing feasible schedules of valuable quality for instances of critical size and support future research on hybrid solution techniques.

Efficient parallel tabu search for the blocking job shop scheduling problem

The Blocking Job Shop Scheduling (BJSS) is an NP-hard scheduling problem. It is obtained from the classical job shop scheduling problem by replacing the infinite buffer capacity constraint by a zero buffer capacity which introduces the blocking constraint. This constraint affects deeply the ability of meta-heuristics to find good solutions due to the low ratio of feasible to explored solutions. In this paper, we discuss the parallelization of the Tabu Search algorithm (TS) which represents one of the most widely used heuristics. Applying the classical TS neighborhood to the BJSS problem produces infeasible solutions in 98% of cases which leads to waste a valuable time in exploring infeasible solutions. For this reason, the use of a feasibility recovery strategy is unavoidable; however, the recovery step slows down considerably the TS algorithm. Therefore, incurring a huge time to explore a small area in the search space. To overcome this drawback and to accelerate the TS algorithm, we propose in this paper parallel multi-start TS approaches where several processes explore simultaneously the search space. Our parallelization exploits a cluster-based architecture with 512 CPU-cores. The obtained results show the positive impact of our proposed parallelization on the solution quality. Moreover, combining both the parallelism and the recovery strategy allowed us to improve the best result in the literature for a large number of known benchmarks.

A Permutation-Based Heuristic Method for the Blocking Job Shop Scheduling Problem

In the manufacturing of highly customized goods and the operation of automatic logistics systems, efficient schedules constitute an everyday challenge. Therefore, the job shop problem is established as a standard model in scheduling research. While classical variants are well studied, the involvement of practically relevant conditions, such as the absence of intermediate buffers and customer-oriented optimization criteria, shows a lack of theoretical understanding. This work provides a study in this research direction by examining the applicability of a scheduling-tailored heuristic search method to the blocking job shop problem with total tardiness minimization. Permutation-based encodings are used to represent a schedule. Appearing redundancy and feasibility issues are discussed. Two well-known neighborhood structures for sequencing problems are applied and an advanced repairing technique to construct feasible blocking job shop schedules is proposed. The computational results obtained by embedding the components in a simulated annealing framework highlight advantages of the heuristic solution approach against existing general-purpose methods.

Hybrid multi-core CPU and GPU-based B&B approaches for the blocking job shop scheduling problem

The Branch and Bound algorithm (B&B) is a well known method for solving optimally Combinatorial Optimization Problems. This method is based on intelligent enumeration of all feasible solutions which reduce considerably the search space. Nevertheless, it remains inefficient when using the sequential approach to deal with large problem instances due to its huge resolutions time. However, the execution time can be reduced considerably by using parallel computing architectures. With the huge evolution of the multi-cores CPUs and GPUs, it is quite hard to design schemes that efficiently exploit the different hardware architectures simultaneously. As a result, most of the existing works focus on exploiting one hardware architecture at a time. In this paper, we propose five parallel approaches to accelerate the B&B execution time using Multi and Many-core systems. Our goal is to solve optimally the Blocking Job Shop Scheduling problem (BJSS) which is one of the hardest scheduling problem. The first proposed approach is a multi-search parallelization based on master/worker paradigm, exploiting the multi-Core CPU-processors. The second and the third approaches represent a GPU-based parallelization schemes having different level of parallelism and GPU occupancy. The fourth and fifth approaches represent a hybridization between the Multi-core approach and the GPU-based parallelization approaches. The goal of this hybridization is to benefit from the power of both the CPU-cores and the GPU at the same time. This hybridization is based on concurrent kernels execution provided by Nvidia Multi process Service (MPS) that allows multiple host processes (Master and workers) to use simultaneously the GPU to launch their kernels in order to accelerate the bounding of one or several nodes at a time. Experiments using the well known Taillard instances confirm the efficiency of our proposals and show a relative speedup of 160x as compared to an optimized sequential B&B algorithm.

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.

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.

An efficient Tabu Search neighborhood based on reconstruction strategy to solve the blocking job shop scheduling problem

The blocking job shop scheduling problem (BJSS) is a version of the classical job shop scheduling with no intermediate buffer between machines. The BJSS is known to be NP-hard in the strong sense. A known way to solve such a problem is to use the Tabu Search algorithm (TS) which is a higher level heuristic procedure for solving optimization problems, designed to guide other methods to escape the trap of local optimality. However, the use of the classical TS neighborhood on BJSS problem produces infeasible solutions in most cases (98% of cases). This leads to waste valuable time in exploring infeasible solutions. To overcome this drawback, we propose a new tabu search neighborhood based on reconstruction strategy. This neighborhood consists to remove arcs causing the infeasibility and rebuild the neighbor solutions by using heuristics. Experiments on the reference benchmark instances show that the TS algorithm using the proposed neighborhood improves most of the known results in the literature and gives new upper bounds for more than 52 benchmarks in both BJSS cases (BJSS with Swap and BJSS no-Swap). Moreover, the proposed approach reaches much faster the optimal solution for most of the optimally solved benchmarks.

A hybrid metaheuristic algorithm to optimise a real-world robotic cell

In this paper, a real-world robotic cell is investigated by transforming it into a special job shop with a set of stationary robots for manufacturing the parts of a product (i.e., operations of a job) at multiple operational stages. In addition, this robotic cell contains a particular mobile robot to transport the parts among stationary robots inside the cell as well as a depot (for initialising the production) and a stockpile (for stocking the complete products) outside the cell. Thus, a new scheduling problem called Blocking Job Shop Scheduling problem with Robotic Transportation (BJSSRT) is proposed. A numerical example is presented to illustrate the characteristics and complexity of BJSSRT. According to the problem properties, four types of robotic movements are defined for a mobile robot in an operation’s execution: processing-purpose, depot-purpose, return-purpose and stocking-purpose. By satisfying complex feasibility conditions, an innovative graph-based constructive algorithm is developed to produce a good feasible BJSSRT schedule. Embedded with the constructive algorithm, a hybrid Tabu Search and Threshold Accepting metaheuristic algorithm is developed to find a near-optimal solution in an efficient way. The proposed BJSSRT methodology has practical benefits in modelling the automated production system using stationary and mobile robots, especially in manufacturing and mining industries.

An iterated greedy metaheuristic for the blocking job shop scheduling problem

In this paper we consider a job shop scheduling problem with blocking (BJSS) constraints. Blocking constraints model the absence of buffers (zero buffer), whereas in the traditional job shop scheduling model buffers have infinite capacity. There are two known variants of this problem, namely the blocking job shop scheduling with swap allowed (BWS) and the one with no swap allowed (BNS). This scheduling problem is receiving an increasing interest in the recent literature, and we propose an Iterated Greedy (IG) algorithm to solve both variants of the problem. IG is a metaheuristic based on the repetition of a destruction phase, which removes part of the solution, and a construction phase, in which a new solution is obtained by applying an underlying greedy algorithm starting from the partial solution. A comparison with recent published results shows that the iterated greedy algorithm outperforms other state-of-the-art algorithms on benchmark instances. Moreover it is conceptually easy to implement and has a broad applicability to other constrained scheduling problems.

Scheduling of no buffer job shop cells with blocking constraints and automated guided vehicles

The blocking job shop (BJS) problem is an extension of a job shop problem with no buffer constraints. It means that after a job is completed on the current machine, it remains on that machine until the next machine becomes available. This paper addresses an extension of the BJS problem, which takes into account transferring jobs between different machines using a limited number of automated guided vehicles (AGV), called a BJS–AGV problem. Two integer non-linear programming (INLP) models are proposed. A two-stage heuristic algorithm that combines an improving timetabling method and a local search is proposed to solve the BJS–AGV problem. A neighborhood structure in the local search is proposed based on a disjunctive graph model. According to the characteristics of the BJS–AGV problem, four principles are proposed to guarantee the feasibility of the search neighborhood. Computation results are presented for a set of benchmarking tests, some of which are enlarged by transportation times between different machines. The numerical results show the effectiveness of the proposed two-stage algorithm.

The blocking job shop with rail-bound transportation

The blocking job shop with rail-bound transportation (BJS-RT) considered here is a version of the job shop scheduling problem characterized by the absence of buffers and the use of a rail-bound transportation system. The jobs are processed on machines and are transported from one machine to the next by mobile devices (called robots) that move on a single rail. The robots cannot pass each other, must maintain a minimum distance from each other, but can also "move out of the way". The objective of the BJS-RT is to determine for each machining operation its starting time and for each transport operation its assigned robot and starting time, as well as the trajectory of each robot, in order to minimize the makespan. Building on previous work of the authors on the flexible blocking job shop and an analysis of the feasible trajectory problem, a formulation of the BJS-RT in a disjunctive graph is derived. Based on the framework of job insertion in this graph, a local search heuristic generating consistently feasible neighbor solutions is proposed. Computational results are presented, supporting the value of the approach.

Iterative Improvement Algorithms for the Blocking Job Shop

This paper provides an analysis of the efficacy of a known iterative improvement meta-heuristic approach from the AI area in solving the Blocking Job Shop Scheduling Problem (BJSSP) class of problems. The BJSSP is known to have significant fallouts on practical domains, and differs from the classical Job Shop Scheduling Problem (JSSP) in that it assumes that there are no intermediate buffers for storing a job as it moves from one machine to another; according to the BJSSP definition, each job has to wait on a machine until it can be processed on the next machine. In our analysis, two specific variants of the iterative improvement meta-heuristic are evaluated: (1) an adaptation of an existing scheduling algorithm based on the Iterative Flattening Search and (2) an off-the-shelf optimization tool, the IBM ILOG CP Optimizer, which implements Self-Adapting Large Neighborhood Search. Both are applied to a reference benchmark problem set and comparative performance results are presented. The results confirm the effectiveness of the iterative improvement approach in solving the BJSSP; both variants perform well individually and together succeed in improving the entire set of benchmark instances.

A job-shop scheduling approach for optimising sugarcane rail operations

The sugarcane transport system is very complex and uses a daily schedule, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Producing efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. In this paper, the sugarcane rail operations are formulated as a blocking job shop scheduling problem. A mixed integer programming approach is used to formulate the shop job scheduling problem. Mixed integer programming and constraint programming search techniques are integrated for solving the problem. A case study is solved to test the approach.

The flexible blocking job shop with transfer and set-up times

The Flexible Blocking Job Shop (FBJS) considered here is a job shop scheduling problem characterized by the availability of alternative machines for each operation and the absence of buffers. The latter implies that a job, after completing an operation, has to remain on the machine until its next operation starts. Additional features are sequence-dependent transfer and set-up times, the first for passing a job from a machine to the next, the second for change-over on a machine from an operation to the next. The objective is to assign machines and schedule the operations in order to minimize the makespan. We give a problem formulation in a disjunctive graph and develop a heuristic local search approach. A feasible neighborhood is constructed, where typically a critical operation is moved (keeping or changing its machine) together with some other operations whose moves are "implied". For this purpose, we develop the theoretical framework of job insertion with local flexibility, based on earlier work of Groflin and Klinkert on insertion. A tabu search that consistently generates feasible neighbor solutions is then proposed and tested on a larger test set. Numerical results support the validity of our approach and establish first benchmarks for the FBJS.

A new neighborhood and tabu search for the Blocking Job Shop

The Blocking Job Shop is a version of the job shop scheduling problem with no intermediate buffers, where a job has to wait on a machine until being processed on the next machine. We study a generalization of this problem which takes into account transfer operations between machines and sequence-dependent setup times. After formulating the problem in a generalized disjunctive graph, we develop a neighborhood for local search. In contrast to the classical job shop, there is no easy mechanism for generating feasible neighbor solutions. We establish two structural properties of the underlying disjunctive graph, the concept of closures and a key result on short cycles, which enable us to construct feasible neighbors by exchanging critical arcs together with some other arcs. Based on this neighborhood, we devise a tabu search algorithm and report on extensive computational experience, showing that our solutions improve most of the benchmark results found in the literature.

Surgical case scheduling as a generalized job shop scheduling problem

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.

Feasible insertions in job shop scheduling, short cycles and stable sets

Insertion problems arise in scheduling when additional activities have to be inserted into a given schedule. This paper investigates insertion problems in a general disjunctive scheduling framework capturing a variety of job shop scheduling problems and insertion types. First, a class of scheduling problems is introduced, characterized by disjunctive graphs with the so-called short cycle property, and it is shown that in such problems, the feasible selections correspond to the stable sets of maximum cardinality in an associated conflict graph. Two types of insertion problems are then identified where the underlying disjunctive graph is through- or bi-connected. For these cases, it is shown that the short cycle property holds and the conflict graph is bipartite, allowing to derive a polyhedral characterization of all feasible insertions. An efficient method for deciding whether there exists a feasible insertion, and a lower and upper bound procedure for the minimum makespan insertion problem are developed. For bi-connected graphs, this procedure solves the insertion problem to optimality. The obtained results are applied to three extensions of the classical Job Shop, the Multi-Processor Task, Blocking and No-Wait Job Shop, and two types of insertions, job and block insertion.