Dynamic programming approach for solving the open shop problem

Scheduling two-machine preemptive open shops to minimize total completion time

An efficient tabu search approach for the two-machine preemptive open shop scheduling problem

Approximation algorithms for the multiprocessor open shop scheduling problem

The flexible open shop scheduling problem is the combination of two classical open shop and a parallel machine scheduling problems. Due to the computational complexity of solving the open shop scheduling problem, so far, limited research has considered the assumption of flexibility in this problem. In this study, a bi-objective flexible open shop scheduling with independent setup time is considered. The considered objective functions are to minimize the maximum completion time of jobs and total tardiness. Using the first objective function, an attempt is made to balance the amount of workloads on the machines so that the completion time of the last job is minimized, while using the second one, from the customers' point of view, an attempt is made to reduce the amount of tardiness in delivery of jobs to the customers. Here, firstly, a mixed-integer nonlinear programming model is proposed. Then, to deal with the multi-objective problem, the weighted Lp-metric method is used. Since, this problem is a non-deterministic polynomial-time hard problem (NP-hard), a scatter search algorithm is developed to obtain near-optimal solutions in a reasonable time. In this regard, for the first time, a novel solution representation method is also presented. To ensure the efficiency of the proposed algorithm, the results were compared with NSGA-II using several instances. After analyzing the results using four evaluation metrics, it is observed that the scatter search algorithm performs better than the NSGA-II.

In the real industrial scenario, the setup times and delivery times are two non-negligible factors, but only few studies have considered the open shop scheduling problem with sequence-dependent setup times and delivery times (OSSP-STDT). In this paper, a mixed integer linear programming model is formulated firstly to accurately solve small-size problems, but it will fail when the size of the problem increases. Then, a complex scheduling network model is developed to characterize OSSP-STDT. After comprehensively considering the local topological features and time attributes in the complex network model, an effective heuristic rule based on complex network is established for solving large-size problems. Finally, an actual warehouse scheduling problem is converted into the aforementioned problem and used as one typical application scenario. Experiments have been conducted and computational results show that compared with exact solutions and meta-heuristics, the proposed algorithm can solve the large-size open shop scheduling problem with sequence-dependent setup times and delivery times more effectively and efficiently.

Objectives: Scheduling is an optimization problem in computer science and operation research in which ideal jobs are assigned to particular times. Nowadays, the problem is presented as an online problem, that is, each job is presented and the online algorithm needs to make a decision about the job before the next job is presented. Methods and Statstical Analysis: The proposed approach is used to solve the open job scheduling problem in which any job can be connected with the available machine. That was implemented in matlab to available best results with hybrid evolutionary algorithm. Findings: In this paper, a hybrid algorithm based on the particle swarm optimization is proposed, for flexible, open shop scheduling problem, to minimize the make-span. First an effective new approach using two decisions based on parallel priories dispatching rules is applied. Next we develop a hybridizing HPSO, that presents new components for updating velocity and position using evolutionary operators, with an adaptive neighbourhood procedure based on the insert-interchange fitness function, selection, mutation, crossover. Application/Improvements: The performance of the proposed a new hybrid algorithm is compared to other benchmark problems. Keywords: Dispatching Rules, Evolutionary Operators, Flexible Open Shop Problem, Local Search, Particle Swarm Optimization

A genetic algorithm for scheduling open shops with sequence-dependent setup times

Flow shop and open shop scheduling with a critical machine and two operations per job

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence's benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

In this chapter, we consider the open shop scheduling problem which can be described as follows. A set of n jobs J1, J2, . . . , Jn has to be processed on a set of m machines M1,M2, . . . , Mm. The processing of job Ji on machine Mj is denoted as operation (i, j), and the sequence in which the operations of a job are processed on the machines is arbitrary. Moreover, each machine can process at most one job at a time and each job can be processed on at most one machine at a time. Such an open shop environment arises in many industrial applications. For example, consider a large aircraft garage with specialized work-centers. An airplane may require repairs on its engine and electrical circuit system. These two tasks may be carried out in any order but it is not possible to do these tasks on the same plane simultaneously. Further applications of open shop scheduling problems in automobile repair, quality control centers, semiconductor manufacturing, teacher-class assignments, examination scheduling, and satellite communications are described by Kubiak et al. (1991), Liu and Bulfin (1987) and Prins (1994). For each job Ji, i = 1, 2, . . . , n, there may be given a release date ri ≥ 0 which is the earliest possible time when the first operation of this job may start, a weight wi and a due date di ≥ 0 by which the job should be completed. The processing time of operation (i, j) is denoted as tij. It is assumed that the processing times of all operations are assumed to be given in advance. Let Ci be the completion time of job Ji, i.e. the time when the last operation of this job is completed. Traditional optimization criteria are basically partitioned into two types: either

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).

A self-tuning variable neighborhood search algorithm and an effective decoding scheme for open shop scheduling problems with travel/setup times

Open shop scheduling with maximal machines

It is known that in many real industrial settings, some setup is carried out before the process of a job. Usually, the magnitude of this setup depends on the order of two consecutive jobs. In this case, the setup is called sequence-dependent. This paper deals with open shop scheduling with sequence-dependent setup times to minimize the total completion time. The problem is formulated as an effective mixed integer linear programming model that best characterizes and solves to optimality small-sized instances of the problem under consideration. Since the electromagnetism-like metaheuristic (EM) is successfully applied to some NP-hard problems, we have been motivated to employ and assess the effectiveness of EM to solve the open shop with setup times. To further enhance EM, a local search engine in form of a fast and simple simulated annealing is incorporated. In order to evaluate the performance of the proposed algorithms, an experiment is designed where the proposed methods are compared against some algorithms in the literature. The related results are analyzed by statistical tools. The experimental results and statistical analyses demonstrate that the proposed model and EM are effective for the problem.

In this paper we study multiprocessor and open shop scheduling problems from several points of view. We explore a tight dependence of the polynomial solvability/intractability on the number of allowed preemptions. For an exhaustive interrelation, we address the geometry of problems by means of a novel graphical representation. We use the so-called preemption and machine-dependency graphs for preemptive multiprocessor and shop scheduling problems, respectively. In a natural manner, we call a scheduling problem acyclic if the corresponding graph is acyclic. There is a substantial interrelation between the structure of these graphs and the complexity of the problems. Acyclic scheduling problems are quite restrictive; at the same time, many of them still remain NP-hard. We believe that an exhaustive study of acyclic scheduling problems can lead to a better understanding and give a better insight of general scheduling problems.