Multiprocessor Open Shop Research Articles

Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach

Bi-Objective, Dynamic, Multiprocessor Open-Shop Scheduling: A Hybrid Scatter Search–Tabu Search Approach

An ant colony optimization approach for the proportionate multiprocessor open shop

Multiprocessor open shop makes a generalization to classical open shop by allowing parallel machines for the same task. Scheduling of this shop environment to minimize the makespan is a strongly NP-Hard problem. Despite its wide application areas in industry, the research in the field is still limited. In this paper, the proportionate case is considered where a task requires a fixed processing time independent of the job identity. A novel highly efficient solution representation is developed for the problem. An ant colony optimization model based on this representation is proposed with makespan minimization objective. It carries out a random exploration of the solution space and allows to search for good solution characteristics in a less time-consuming way. The algorithm performs full exploitation of search knowledge, and it successfully incorporates problem knowledge. To increase solution quality, a local exploration approach analogous to a local search, is further employed on the solution constructed. The proposed algorithm is tested over 100 benchmark instances from the literature. It outperforms the current state-of-the-art algorithm both in terms of solution quality and computational time.

Solution Representation in Proportionate Multiprocessor Open Shop

Proportionate multiprocessor open shop is considered in this study. It is a shop model where a set of jobs follow no predefined route to visit several stages with at least one having two or more parallel machines to carry out the same task. Proportionality means that processing times depend only on stages and are independent of jobs, hence is defined as stage-wise. The shop model has various application areas in industry but the literature on the field is still limited. In this study, a novel solution representation scheme is proposed for the proportionate multiprocessor open shop. The scheme is based on permutation of stages and encodes the cumulative number of job assignments to a stage. The proposed scheme is shown to generate higher quality random solutions compared to the common operation permutation representation for the shop model. The approach proposed in this study to design a solution representation for a scheduling problem is a new and favorable approach that takes into account the specific machine environment, job characteristics and objective function of the problem under consideration. This way of designing solution representation schemes would increase the solution quality or decrease the computational time required in solution algorithms for scheduling problems.

Bi-objective dynamic multiprocessor open shop scheduling for maintenance and healthcare diagnostics

This paper addresses a bi-objective dynamic multiprocessor open shop scheduling problem in which the simultaneous objectives of minimizing both the mean weighted flow time and the makespan are considered. This problem is commonly encountered in maintenance and healthcare diagnostic systems. Since it is NP-hard for both objectives, efficient heuristics are needed to quickly generate a set of non-dominated solutions that a decision maker would choose from. For this sake, two metaheuristic approaches based on the non-dominated sorting genetic algorithm (NSGA-II) and the multi-objective grey wolf optimizer (MOGWO) are developed in this paper. Both metaheuristics are hybridized with simulated annealing (SA) local search. Parameter tuning computational experiments are conducted first on a set of 30 small instances from the literature for which Pareto optimal solutions are known. Then, computational experiments on large randomly generated instances are conducted. Computational results for small instances show that the NSGA-II is capable of generating non-dominated solutions that are very close to the optimal Pareto front. Results also reveal that the performance of the NSGA-II is better in most of the cases compared to the MOGWO under different settings of the studied problem for both small and large instances. However, for large instances with large number of workstations and jobs, low loading level and high percentage of busy machines at the beginning of the schedule, the difference in performance between both metaheuristics is minor.

Multiprocessor open shop problem: literature review and future directions

Multi-processor open shop (MPOS) is a combination of the classical open shop and parallel shop environments. Although there exist wide application areas of this shop environment in both production and service facilities, the research in the field is still limited. In this paper, we provided a detailed review of the research on MPOS problem. With this survey, we aimed to provide a helpful guide to those who are willing to contribute to this open field of study. We have reviewed the studies in MPOS literature under the following topics: mathematical formulations, polynomial-time optimum solution algorithms for few special cases, approximation algorithms, dispatching rules, heuristics and metaheuristics. We further presented test data used in the literature and investigated the ways researchers evaluated their results. Solution representation and parameter tuning in metaheuristic applications have been also covered in detail. There is considerable room for improvement, especially in terms of near-optimal solution approaches. We closely investigated research topics that need particular attention in future research. We believe the review here will be a good starting point to study MPOS problem, even for those who have no prior knowledge of the field.

Bi-Objective Dynamic Multiprocessor Open Shop Scheduling: An Exact Algorithm

An important element in the integration of the fourth industrial revolution is the development of efficient algorithms to deal with dynamic scheduling problems. In dynamic scheduling, jobs can be admitted during the execution of a given schedule, which necessitates appropriately planned rescheduling decisions for maintaining a high level of performance. In this paper, a dynamic case of the multiprocessor open shop scheduling problem is addressed. This problem appears in different contexts, particularly those involving diagnostic operations in maintenance and health care industries. Two objectives are considered simultaneously—the minimization of the makespan and the minimization of the mean weighted flow time. The former objective aims to sustain efficient utilization of the available resources, while the latter objective helps in maintaining a high customer satisfaction level. An exact algorithm is presented for generating optimal Pareto front solutions. Despite the fact that the studied problem is NP-hard for both objectives, the presented algorithm can be used to solve small instances. This is demonstrated through computational experiments on a testbed of 30 randomly generated instances. The presented algorithm can also be used to generate approximate Pareto front solutions in case computational time needed to find proven optimal solutions for generated sub-problems is found to be excessive. Furthermore, computational results are used to investigate the characteristics of the optimal Pareto front of the studied problem. Accordingly, some insights for future metaheuristic developments are drawn.

Scatter search with path relinking for multiprocessor open shop scheduling

Maintenance and health care diagnostic systems are generally composed of different workstations pertaining to technologically different processes. A workstation is composed of one or more parallel machines. In such systems, the multiprocessor open shop scheduling problem is commonly encountered. It is concerned with assigning processing intervals for each job on machines that need to be selected in each requested workstation. Meanwhile, jobs do not require a specific order for visiting workstations. This paper considers a static, deterministic version of the problem in which jobs do not have to visit all workstations, the workstations do not necessarily have identical machines, and the processing times depend on both the job and the machine. The objective is to minimize the maximum completion time (makespan) which is commensurate with maximizing the utilization of the available machines. To the best of our knowledge, this problem structure has not been considered in the literature before despite its existence in real-life applications. Since it is NP-hard problem, efficient heuristics are needed to generate near optimal solutions in practically acceptable computational times. In this paper, two neighborhood search functions and two solution combination functions are developed and used within a scatter search with path relinking metaheuristic, along with a new distance definition between solutions. Computational experiments are conducted first to select the best levels of the metaheuristic parameters. Then, computational experiments are conducted on specially designed instances that take into consideration different settings of the studied problem. This is followed by computational experiments on a set of benchmark instances of the proportionate multiprocessor open shop scheduling problem which is a special case of the studied problem for which other metaheuristics have been developed in the literature. Results show that the developed metaheuristic is capable of generating optimal or near-optimal solutions for different configurations of the studied problem. In addition, it generates competitive results for the proportionate case compared to the available metaheuristics with 18 new upper bounds; among them seven are optimal.

Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments

We study a scheduling environment that finds many real-world manufacturing applications, in which there is a close connection between a hybrid multiprocessor open shop and multiple parallel identical flow shops. In this environment, there is an extended two-stage open shop, where in one stage we have a set of parallel identical machines, while in the other we have a two-machine flow shop. Our objective is to minimize the makespan, that is, the latest completion time of all jobs. We pursue approximation algorithms with provable performance, and we achieve a 2-approximation when the number of parallel identical machines is constant or is part of the input; we also design a 5/3-approximation for the special case where there is only one machine in the multiprocessor stage, which remains weakly NP-hard. Our empirical experiments show that both approximation algorithms perform much better in simulated instances; their average ratios over the proposed lower bound are around 1.5 and 1.2, respectively.

Large-scale medical examination scheduling technology based on intelligent optimization

In recent years, the scale of the health examination business has increased rapidly, and research on the combinatorial optimization of medical examinations has become more important. In this context, a special large-scale flexible open shop scheduling problem (FOSP) is introduced based on the idea of the multi-processor open shop scheduling problem. A mixed integer programming model is developed for the FOSP, which regards client satisfaction as the most important objective. As the FOSP is particularly complex, three different intelligent optimization algorithms are examined, namely a genetic algorithm, hybrid particle swarm optimization, and simulated annealing. According to the medical examination preferences of the clients, a group of large-scale test problems are created on the basis of benchmark instances of the flexible job shop problem, and these are used to evaluate the performance of each algorithm. The experimental results show that the genetic algorithm outperforms both simulated annealing and hybrid particle swarm optimization, especially in large-scale problems.

A Particle Swarm Optimization to Minimize Makespan for a Four-Stage Multiprocessor Open Shop with Dynamic Job Release Time

This paper considers the scheduling problem observed in chip sorting operation of LED manufacturing, where each lot (job) with release time have four operations to be processed on a set of processing stages without pre-determined necessary route. Each stage has one and more identical sorting machines. The sorting machines scheduling problem can be treated as a four-stage multiprocessor open shop problem with dynamic job release, and the objective is minimizing the makespan in the paper. This problem is formulated into a mixed integer programming (MIP) model and empirically shows its computational intractability. Due to the computational intractability, a particle swarm optimization (PSO) algorithm is proposed. A series of computational experiments are conducted to evaluate the performance of the proposed PSO in comparison with exact solution on various small-size problem instances. The results show that the PSO algorithm could finds most optimal or better solutions in one second.

A tabu search approach for proportionate multiprocessor open shop scheduling

In the multiprocessor open shop scheduling problem, jobs are to be processed on a set of processing centers—each having one or more parallel identical machines, while jobs do not have a pre-specified obligatory route. A special case is the proportionate multiprocessor open shop scheduling problem (PMOSP) in which the processing time on a given center is not job-dependent. Applications of the PMOSP are evident in health care systems, maintenance and repair shops, and quality auditing and final inspection operations in industry. In this paper, a tabu search (TS) approach is presented for solving the PMOSP with the objective of minimizing the makespan. The TS approach utilizes a neighborhood search function that is defined over a network representation of feasible solutions. A set of 100 benchmark problems from the literature is used to evaluate the performance of the developed approach. Experimentations show that the developed approach outperforms a previously developed genetic algorithm as it produces solutions with an average of less than 5 % deviation from a lower bound, and 40 % of its solutions are provably optimal.

A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop

In this paper a new mixed-integer linear programming (MILP) model is proposed for the multi-processor open shop scheduling (MPOS) problems to minimize the makespan with considering independent setup time and sequence dependent removal time. A hybrid imperialist competitive algorithm (ICA) with genetic algorithm (GA) is presented to solve this problem. The parameters of the proposed algorithm are tuned by response surface methodology (RSM). The performance of the algorithm to solve small, medium and large sized instances of the problem is evaluated by introducing two performance metrics. The quality of obtained solutions is compared with that of the optimal solutions for small sized instances and with the lower bounds for medium sized instances. Also some computational results are presented for large sized instances.

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.

A Dispatching Rule Study of a LED Sorting System

The scheduling problem of LED chip sorting workstation is a multiprocessor open shop scheduling problem. In practice, this problem is usually solved with finding a dispatching rule to achieve certain performance indexes. Experimental design was applied to find a proper rule, and dispatching rule, wafer quantity, wafer mix type, and bottleneck location were chosen as independent variables. Maximum make-span and average queuing time were selected as dependent variables. Five dispatching rules were considered in the dispatching rule factor. Experimental results showed that all independent variables are significant on all dependent variables. While make-span as the performance index, three dispatching rules common in applying LPT in bottleneck machines obtained better results. A dispatching rule with applying SPT in non-bottleneck machines has least average queuing time among those three, and this rule is recommended for practical application.

A genetic algorithm for the proportionate multiprocessor open shop

The multiprocessor open shop (MPOS) scheduling problem is NP-complete, a category of hard combinatorial optimization problems that have not received much attention in the literature. In this work, a special MPOS—a proportionate one—is introduced for the first time. Two original mixed integer programming formulations for the proportionate MPOS are developed and their complexity is discussed. Due to the complexity of the MPOS, this paper develops a compu-search methodology (a genetic algorithm (GA)) to schedule the shop with the objective of minimizing the makespan. In this novel GA, a clever chromosome representation of a schedule is developed that succinctly encodes a schedule of jobs across multiple stages. The innovative design of this chromosome enables any permutation of its genes to yield a feasible solution. This simple representation of an otherwise very complex schedule enables the genetic operators of crossover and mutation to easily manipulate a schedule as the algorithm iteratively searches for better schedules. A testbed of difficult instances of the problem are created to evaluate the performance of the GA. The solution for each instance is compared with a derived lower bound. Computational results reveal that the algorithm performs extremely well, demonstrating its potential to efficiently schedule MPOS problems. More importantly, successful experiments on large-scale problem instances suggest the readiness of the GA for industrial use.

A linear time approximation scheme for makespan minimization in an open shop with release dates

In this paper, we demonstrate the existence of a linear time approximation scheme for makespan minimization in the multiprocessor open shop problem with release dates. Our approximation scheme is linear and does not require solving linear program.

Linear time approximation scheme for the multiprocessor open shop problem

For the r-stage open shop problem with identical parallel machines at each stage and the minimum makespan criterion, an approximation scheme is constructed with running time O( nrm+ C( m, ε)), where n is the number of jobs, m is the total number of machines, and C( m, ε) is a function independent of n.

Approximation algorithms for the multiprocessor open shop scheduling problem

We investigate the multiprocessor multi-stage open-shop scheduling problem. In this variant of the open-shop model, there are s stages, each consisting of a number of parallel identical machines. Each job consists of s operations, one for each stage, that can be executed in any order. The goal is to find a non-preemptive schedule that minimizes the makespan. We derive two approximation results for this NP -hard problem. First, we demonstrate the existence of a polynomial-time approximation algorithm with worst case ratio 2 for the case that the number s of stages is part of the input. This algorithm is based on Racsmány's concept of dense schedules. Secondly, for the multiprocessor two-stage open-shop problem we derive a family of polynomial-time approximation algorithms whose worst-case ratios can be made arbitrarily close to 3 2 .