A Rollout Metaheuristic for Job Shop Scheduling Problems

In this paper we deal with solution algorithms for a general formulation of the job shop problem, called alternative graph. We study in particular the job shop scheduling problem with blocking and/or no-wait constraints. Most of the key properties developed for solving the job shop problem with infinite capacity buffer do not hold in the more general alternative graph model. In this paper we report on an extensive study on the applicability of a metaheuristic approach, called rollout or pilot method. Its basic idea is a look-ahead strategy, guided by one or more subheuristics, called pilot heuristics. Our results indicate that this method is competitive and very promising for solving complex scheduling problems.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

A genetic approach to solving the problem of cyclic job shop scheduling with linear constraints

This study concerns the domain of cyclic scheduling. More precisely we consider the cyclic job shop scheduling problem with linear constraints. The main characteristic of this problem is that the tasks of each job are cyclic and are subjected to linear precedence constraints. First we review some approaches in the field of cyclic scheduling and present the cyclic job shop scheduling problem definition, which has an open complexity. Then we present a general approach for solving it, based on the coupling of a genetic algorithm and a scheduler. This scheduler utilises a Petri-net modelling the linear precedence constraints between cyclic tasks. The goal of this genetic algorithm is to propose an order of priority for jobs on the machines, to be used by the scheduler for solving resource conflicts. Finally a benchmark and some preliminary results of this approach are presented.     

A contribution to the stochastic flow shop scheduling problem

This paper deals with performance evaluation and scheduling problems in m machine stochastic flow shop with unlimited buffers. The processing time of each job on each machine is a random variable exponentially distributed with a known rate. We consider permutation flow shop. The objective is to find a job schedule which minimizes the expected makespan. A classification of works about stochastic flow shop with random processing times is first given. In order to solve the performance evaluation problem, we propose a recursive algorithm based on a Markov chain to compute the expected makespan and a discrete event simulation model to evaluate the expected makespan. The recursive algorithm is a generalization of a method proposed in the literature for the two machine flow shop problem to the m machine flow shop problem with unlimited buffers. In deterministic context, heuristics (like CDS [Management Science 16 (10) (1970) B630] and Rapid Access [Management Science 23 (11) (1977) 1174]) and metaheuristics (like simulated annealing) provide good results. We propose to adapt and to test this kind of methods for the stochastic scheduling problem. Combinations between heuristics or metaheuristics and the performance evaluation models are proposed. One of the objectives of this paper is to compare the methods together. Our methods are tested on problems from the OR-Library and give good results: for the two machine problems, we obtain the optimal solution and for the m machine problems, the methods are mutually validated.     

Maximization of solution flexibility for robust shop scheduling

We consider the problem of introducing flexibility in the schedule determination phase, for shop scheduling problems with release dates and deadlines. The flexibility is provided by generating a family of schedules, instead of a unique one. We represent a family of schedules by an ordered group assignment defining for each machine a sequence of groups where the operations within a group are totally permutable. We propose a polynomial time algorithm to evaluate the worst case completion time of operations in an ordered group assignment. We then consider the single machine problem with heads and deadlines associated to operations, as a sub-problem of the job shop problem. We propose polynomial time dynamic programming algorithms for minimizing the number of groups and for maximizing the number of characterized sequences, under specific constraints. Finally, computational experiences on job shop benchmarks, show the impact of grouping operations on the solution makespan value.     

Constraint Propagation and Problem Decomposition: A Preprocessing Procedure for the Job Shop Problem

In recent years, constraint propagation techniques have been shown to be highly effective for solving difficult scheduling problems. In this paper, we present an algorithm which combines constraint propagation with a problem decomposition approach in order to simplify the solution of the job shop scheduling problem. This is mainly guided by the observation that constraint propagation is more effective for small problem instances. Roughly speaking, the algorithm consists of deducing operation sequences that are likely to occur in an optimal solution of the job shop scheduling problem (JSP).The algorithm for which the name edge-guessing procedure has been chosen – since with respect to the job shop scheduling problem (JSP) the deduction of machine sequences is mainly equivalent to orienting edges in a disjunctive graph – can be applied in a preprocessing step, reducing the solution space, thus speeding up the overall solution process. In spite of the heuristic nature of edge-guessing, it still leads to near-optimal solutions. If combined with a heuristic algorithm, we will demonstrate that given the same amount of computation time, the additional application of edge-guessing leads to better solutions. This has been tested on a set of well-known JSP benchmark problem instances.     

Two machine preemptive scheduling problem with release dates,equal processing times and precedence constraints

We consider a scheduling problem with two identical parallel machines and n jobs. For each job we are given its release date when job becomes available for processing. All jobs have equal processing times. Preemptions are allowed. There are precedence constraints between jobs which are given by a (di)graph consisting of a set of outtrees and a number of isolated vertices. The objective is to find a schedule minimizing mean flow time. We suggest an O(n²) algorithm to solve this problem.The suggested algorithm also can be used to solve the related two-machine open shop problem with integer release dates, unit processing times and analogous precedence constraints.     

A computational study of constraint satisfaction for multiple capacitated job shop scheduling

We introduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously. We present an algorithm based on constraint satisfaction techniques to handle the problem effectively. The most important novel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a well-known set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.     

An Ant Colony Optimization Algorithm for Shop Scheduling Problems

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure derived by Nowicki and Smutnicki for the job shop scheduling problem. Then, we develop an ant colony optimization approach, which uses a strong non-delay guidance for constructing solutions and which employs black-box local search procedures to improve the constructed solutions. We compare this algorithm to an adaptation of the tabu search by Nowicki and Smutnicki to group shop scheduling. Despite its general nature, our algorithm works particularly well when applied to open shop scheduling instances, where it improves the best known solutions for 15 of the 28 tested instances. Moreover, our algorithm is the first competitive ant colony optimization approach for job shop scheduling instances.     

On-line two-machine open shop scheduling with time lags

We analyze the performance of the greedy algorithm for the on-line two-machine open shop scheduling problem of minimizing makespan, in which time lags exist between the completion time of the first and the start time of the second operation of any job. The competitive ratio for the greedy algorithm is 2, and it can be reduced to 5/3 if the maximum time lag is less than the minimum positive processing time of any operation. These ratios are tight. We also prove that no on-line non-delay algorithm can have a better competitive ratio.     

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.     

A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem

This paper deals with a general job shop scheduling problem with multiple constraints, coming from printing and boarding industry. The objective is the minimization of two criteria, the makespan and the maximum lateness, and we are interested in finding an approximation of the Pareto frontier. We propose a fast and elitist genetic algorithm based on NSGA-II for solving the problem. The initial population of this algorithm is either randomly generated or partially generated by using a tabu search algorithm, that minimizes a linear combination of the two criteria. Both the genetic and the tabu search algorithms are tested on benchmark instances from flexible job shop literature and computational results show the interest of both methods to obtain an efficient and effective resolution method.     

A branch and bound algorithm for scheduling trains in a railway network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.     

Games,Critical Paths and Assignment Problems in Permutation Flow Shops and Cyclic Scheduling Flow Line Environments

In this paper we address the non-pre-emptive flow shop scheduling problem for makespan minimization in a new modelling framework. A lower bound generation scheme is developed by using appropriately defined linear assignment problems and, based on this new approach, a special class of permutation flow shop problems is identified. We present a game theoretic interpretation of our modelling approach which leads to an integer programming formulation of the scheduling problem. A new branch and bound scheme is developed based on these results. The major advantage of our modelling framework and branch-and- bound approach is that it can be easily extended to address a general class of cyclic scheduling problems for production flow lines with blocking. After a discussion of this extension, we report on computational experience that indicates the very satisfactory performance of the new optimal solution procedure for cyclic scheduling problems with finite capacity buffers.     

基于遗传算法的多目标柔性工作车间调度问题求解

本文针对柔性工作车间调度问题给出了一个有意义的综合目标尽可能缩短制造周期的同时尽可能的减少机器负荷。由于传统遗传算法在多目标柔性工作车间调度问题上的局限性，我们提出了一种改进遗传算法：首先，我们给出了针对综合目标的工序调度算法获得初始集合；接着，针对柔性工作车间调度问题的特点，我们在常用的基于工序顺序的编码方法上融入了基于机器分配的编码方法，并据此设计了相应的交叉变异操作；最后借鉴了物种进化现象中的环境迁移思想设计了解决多目标优化问题的迁移操作。实验结果表明，改进的遗传算法在多目标柔性工作车间调度问题的解决上要优于传统遗传算法。     

Bilevel programming approach applied to the flow shop scheduling problem under fuzziness

This paper presents a fuzzy bilevel programming approach to solve the flow shop scheduling problem. The problem considered here differs from the standard form in that operators are assigned to the machines and imposing a hierarchy of two decision makers with fuzzy processing times. The shop owner considered higher level and assigns the jobs to the machines in order to minimize the flow time while the customer is the lower level and decides on a job schedule in order to minimize the makespan. In this paper, we use the concepts of tolerance membership function at each level to define a fuzzy decision model for generating optimal (satisfactory) solution for bilevel flow shop scheduling problem. A solution algorithm for solving this problem is given. Mathematics Subject Classification: 90C70, 90B36, 90C99     

有使用限制的二台机器流水作业问题

本文研究了机器有使用限制的二台机器流水作业排序问题,目标为最小化最大完工时间,工件加工可以被机器的不可用时间段中断。我们讨论了两台机器上均有使用限制离线问题的可近似情形,并给出了性能比为3/2的近似算法。同时我们还考虑了在第二台机器上存在一个不可用时间段情况下的半在线问题,给出了一个竞争比为3/2的半在线算法。     

Constraint-Based Job Shop Scheduling with IILOG SCHEDULER

We introduce constraint-based scheduling and discuss its main principles. An approximation algorithm based on tree search is developed for the job shop scheduling problem using ILOG SCHEDULER. A new way of calculating lower bounds on the makespan of the job shop scheduling problem is presented and we show how such results can be used within a constraint-based approach. An empirical performance analysis shows that the algorithm we developed performs well. Finally, taking the job shop scheduling problem as a start point, we discuss how constraint-based scheduling can be used to solve more general scheduling problems.     

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.     

Nested partitions for the large-scale extended job shop scheduling problem

This paper addresses the large-scale extended job shop scheduling problem while considering the bill of material and the working shifts constraints. We propose two approaches for the problem. One is based on dispatching rules (DR), and the other is an application of the Nested Partitions (NP) Framework. A sampling approach for the exact feasible subregion is developed to complete the NP method. Furthermore, to efficiently search each subregion, a weighted sampling approach is also presented. Computational experiments show that the NP method with weighted sampling can find good solutions for most large-scale extended job shop scheduling problems.