Approximative procedures for no-wait job shop scheduling

In this article we consider the no-wait job shop problem with makespan objective. Based on a decomposition of the problem into a sequencing and a timetabling problem, we propose two local search algorithms. Extensive computational tests in which the algorithms compare favorably to the best existing strategies are reported. Although not specifically designed for that purpose, our algorithms also outperform one of the best no-wait flow shop algorithms in literature.     

The two-machine no-wait general and proportionate open shop makespan problem

We consider the two-machine no-wait open shop minimum makespan problem in which the determination of an optimal solution requires an optimal pairing of the jobs followed by the optimal sequencing of the job pairs. We show that the required enumeration can be curtailed by reducing the pair sequencing problem for a given pair set to a traveling salesman problem which is equivalent to a two-machine no-wait flow shop problem solvable in O(n log n) time. We then propose an optimal O(n log n) algorithm for the proportionate problem with equal machine speeds in which each job has the same processing time on both machines. We show that our O(n log n) algorithm also applies to the more general proportionate problem with equal machine speeds and machine-specific setup times. We also analyze the proportionate problem with unequal machine speeds and conclude that the required enumeration can be further curtailed (compared to the problem with arbitrary job processing times) by eliminating certain job pairs from consideration.     

Complete local search with limited memory algorithm for no-wait job shops to minimize makespan

In this paper, no-wait job shop problems with makespan minimization are considered. It is well known that these problems are strongly NP-hard. The problem is decomposed into the sequencing and the timetabling components. Shift timetabling is developed for the timetabling component. An effective method, CLLM (complete local search with limited memory), is presented by integrating with shift timetabling for the sequencing component. Experimental results show that CLLM outperforms all the existing effective algorithms for the considered problem with a little more computation time.     

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.     

A survey of scheduling problems with setup times or costs

The first comprehensive survey paper on scheduling problems with separate setup times or costs was conducted by [Allahverdi, A., Gupta, J.N.D., Aldowaisan, T., 1999. A review of scheduling research involving setup considerations. OMEGA The International Journal of Management Sciences 27, 219–239], who reviewed the literature since the mid-1960s. Since the appearance of that survey paper, there has been an increasing interest in scheduling problems with setup times (costs) with an average of more than 40 papers per year being added to the literature. The objective of this paper is to provide an extensive review of the scheduling literature on models with setup times (costs) from then to date covering more than 300 papers. Given that so many papers have appeared in a short time, there are cases where different researchers addressed the same problem independently, and sometimes by using even the same technique, e.g., genetic algorithm. Throughout the paper we identify such areas where independently developed techniques need to be compared. The paper classifies scheduling problems into those with batching and non-batching considerations, and with sequence-independent and sequence-dependent setup times. It further categorizes the literature according to shop environments, including single-machine, parallel machines, flow shop, no-wait flow shop, flexible flow shop, job shop, open shop, and others.     

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.     

Two-machine flow shop scheduling problems with no-wait jobs

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a -approximation algorithm.     

On no-wait and no-idle flow shops with makespan criterion

The paper deals with the NP-hard problems of minimizing the makespan in m-machine no-wait and no-idle permutation flow shops. We identify networks whose longest path lengths represent the makespans. These networks reveal the duality between the two problems, and show graphical explanations of the fact that under no-wait and no-idle conditions the makespan can be a decreasing function of some job processing times. Moreover, they also lead to a natural reduction of the no-wait flow shop problem to the traveling salesman problem, some lower bounds on the shortest makespan, and new efficiently solvable special cases.     

Open shop problems with unit time operations

We show that them-machine open shop problem in which all operations have unit processing times can be polynomially transformed to a special preemptive scheduling problem onm identical parallel machines. Many results published recently as well as some new results are derived by using this transformation. The new results include solutions of open problems mentioned in a recent paper by Kubiak et al. p]A similar relationship is derived between no-wait open shop problems with unit time operations andm-machine problems with jobs having unit processing times.This work was supported by Deutsche Forschungsgemeinschaft (Project JoPTAG).     

Polynomial time algorithms for two special classes of the proportionate multiprocessor open shop

This paper describes a complex scheduling problem taken from a hospital diagnostic testing center that schedules hundreds of patients in an open shop environment consisting of multiple facilities and multiple processors. This scheduling problem, known as the multiprocessor open shop (MPOS) problem, is strongly NP-hard with few published results. Realizing that in many MPOS environments processing times are stage-dependent, not both job and stage-dependent, this paper examines a new class of problems for the MPOS—proportionate ones. This paper exploits the structural nature of the proportionate MPOS and defines new terms. Despite the enormous complexity of the MPOS problem, this work demonstrates that polynomial time algorithms exist for two special cases. Since other applications of this problem exist in service and manufacturing environments, solving the proportionate MPOS problem is not only significant in the theory of optimization, but also in many real-world applications.     

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.     

Solving the serial batching problem in job shop manufacturing systems

This paper addresses the serial batch scheduling problem embedded in a job shop environment to minimize makespan. Sequence dependent family setup times and a job availability assumption are also taken into account. In consideration of batching decisions, we propose a tabu search algorithm which consists of various neighborhood functions, multiple tabu lists and a sophisticated diversification structure. Computational experiments show that our algorithm outperforms a well-known tabu search approach which is developed for solving the traditional job shop problem. These results also confirm the benefits of batching.     

安装、加工和拆卸时间分离的两台机器混合作业问题

混合作业是经典的自由作业和异序作业的一种综合,其中一些工件可以按任意的机器顺序进行处理,而另一些工件必须遵守预先指定的机器顺序.本文研究安装、加工和拆卸时间分离的两台机器混合作业排序问题,该问题已经被知道是强NP困难的,本文把流水作业中的同顺序作业概念推广到混合作业,并得到这个混合作业问题在同顺序意义下的最优解,这个解对于一般情形是3/2近似解,但对于一些有意义的特殊情形是整体最优的.     

Two-machine flow shop no-wait scheduling with machine maintenance

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is subject to mandatory maintenance. The length of the maintenance period is defined by a non-decreasing function that depends on the starting time of that maintenance. The objective is to minimize the completion time of all activities. We present a polynomial-time approximation scheme for this problem. Received: November 2004 / Received version: March 2005 AMS classification: 90B35, 90B30, 90C59 The research was partly supported by INTAS (Project 03-51-5501) All correspondence to: Vitali A. Strusevich     

Complexity of shop-scheduling problems with fixed number of jobs: a survey

The paper surveys the complexity results for job shop, flow shop, open shop and mixed shop scheduling problems when the number n of jobs is fixed while the number r of operations per job is not restricted. In such cases, the asymptotical complexity of scheduling algorithms depends on the number m of machines for a flow shop and an open shop problem, and on the numbers m and r for a job shop problem. It is shown that almost all shop-scheduling problems with two jobs can be solved in polynomial time for any regular criterion, while those with three jobs are NP-hard. The only exceptions are the two-job, m-machine mixed shop problem without operation preemptions (which is NP-hard for any non-trivial regular criterion) and the n-job, m-machine open shop problem with allowed operation preemptions (which is polynomially solvable for minimizing makespan).     

Cyclic job shop scheduling problems with blocking

A tabu search algorithm for a cyclic job shop problem with blocking is presented. Operations are blocking if they must stay on a machine after finishing when the next machine is occupied by another job. During this stay the machine is blocked for other jobs. For this problem traditional tabu search moves often lead to infeasible solutions. Recovering procedures are developed which construct nearby feasible solutions. Computational results are presented for the approach.     

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.     

Optimal Configurations of General Job Shops

In this paper we study the problem of minimizing the expected number of jobs in a single class general open queueing network model of a job shop. This problem was originally posed by Buzacott and Shanthikumar [2] and solved by them for a special case. We extend their work in this paper. We derive feasibility conditions that simplify the analysis of the problem. We show that the optimal configuration can be completely characterized when both the utilizations of the machine centers are high and there are a large number of servers at each machine center. We also derive conditions under which the optimization problem reduces to solving a concave or a convex program and provide conditions under which the uniform flow line and the symmetric job shop (or variants of these) are optimal configurations for the job shop.     

Hybrid Rollout Approaches for the Job Shop Scheduling Problem

In this paper, we focus on heuristic approaches for solving the deterministic job shop scheduling problem. More specifically, a new priority dispatch rule and hybrid rollout algorithms are developed for approaching the problem under consideration. The proposed solution algorithms are tested on a set of instances taken from the literature and compared with other methods. The computational results validate the effectiveness of the developed solution approaches and show that the proposed rollout algorithms are competitive with respect to several state-of-art heuristics for solving the job shop scheduling problem. The author thanks Dr. Marco Mancini and Dr. Alessandro Tarasio for valuable suggestions about computational issues.