Mixed Shop Scheduling Problem Research Articles

An adapted constraint‐programming formulation of the resource‐constrained project scheduling problem applied to the identical parallel machines group shop and mixed shop scheduling problems

AbstractIn this paper, we study the group shop and the mixed shop scheduling problems with single and identical parallel machines at each workstation with the makespan criterion. We adapted a constraint programming formulation previously presented for the classical resource‐constrained project scheduling problem. The effectiveness of our approach is evident in the fact that it achieved optimality in 107 out of 130 classical group shop scheduling problem instances and in 320 classical mixed shop scheduling problem instances. In the last set, we obtained 13 new optimal solutions.

A competitive constraint programming approach for the group shop scheduling problem

In this paper, we propose a competitive Constraint Programming (CP) approach to solve the Group Shop Scheduling Problem (GSSP) under the makespan minimization criteria. Our contribution is two-fold: we provide a flexible mathematical formulation to solve the GSSP that can be used without change to solve other closed-related scheduling problems such as the Open Shop Scheduling Problem (OSSP), Job Shop Scheduling Problem (JSSP), and Mixed Shop Scheduling Problem (MSSP); and we improve several lower bounds and upper bounds from 130 classical GSSP instances from the literature. We evaluate our approach by comparing the performance with competitive methods mainly based on metaheuristics, where we were able to prove optimality in more than 85% of the instances in competitive running time, with a relative percentage deviation lower than 3% on average. In contrast to metaheuristics approaches, our CP method does not require calibrations of multiple parameters, several replicates for each instance, and complex computational coding to be competitive in both, solution quality and computational running times.

Improved Scheduling for the Three-Machine Proportionate Open Shop and Mixed Shop Minimum Makespan Problems

Open shop scheduling problems have many practical applications, in which the jobs can be in any order with the only restriction that their durations do not overlap with each other. In some cases, the order of a subset of jobs dictates the flow shop model while the remaining jobs can be processed in any order according to the open shop model, and the corresponding problem is called mixed shop scheduling. For every job, if its processing times on all machines are the same, then the shop is called proportionate shop. In this article we investigate the three-machine proportionate open shop and mixed shop minimum makespan problems proposed by Koulamas and Kyparisis. Our result improves the previous work in three ways. First, for both the open shop and the mixed shop scheduling problems, we derive additional sufficient conditions under which the corresponding problems are solvable in polynomial time. Second, for the non-solvable cases of the open shop scheduling problem we present an improved 13/12-approximation algorithm. Third, for the non-solvable cases of the mixed shop scheduling problem we present an improved approximation algorithm with the worst-case ratio bound of (7/6 + ϵ). All the algorithms proposed in this article run in polynomial time.

Improved hybrid immune clonal selection genetic algorithm and its application in hybrid shop scheduling

This paper is based on the multi-objective optimization problem of mixed shop scheduling problem, the strong coupling of the maximum flow and the minimum time, and the deficiencies of the immune genetic algorithm including high computational complexity and high spatial dimension. This paper establishes a mixed shop scheduling mathematical model with the minimization of the maximum total completion time as the target, and puts forward to use the immune clonal selection algorithm to solve the problem. In the algorithm population construction, it uses the grouping strategy, introduces the cross and delete operator, retains the excellent individuals through memory space, deletes the relatively bad individual, and improves the algorithm’s global optimization ability. In order to verify the effectiveness of the proposed algorithm, under the two experimental environments of workpiece machining and automobile shock absorber processing workshop scheduling, simulation experiments are conducted. The experimental results show that the proposed algorithm has better performance, and can achieve smaller maximum total completion time with less iteration. The algorithm can find the global optimal solution of the multi-objective problem, which has a strong practical significance.

An effective heuristic algorithm for the partial shop scheduling problem

In a partial shop scheduling problem the operations of each job have to respect a partial order, which can be different for each job. We study the problem of finding a solution of minimal makespan in partial shops. This problem generalizes many problems which have been studied independently in the literature, such as the group shop scheduling problem, the mixed shop scheduling problem, and the open shop scheduling problem. In this paper we propose an algorithm which is able to find solutions for the partial shop scheduling problem. In computational experiments we find that the proposed single heuristic can compete with the state-of-the-art heuristics for the partial shop, group shop, mixed shop, and open shop, and in many cases, improves the state of the art. The main contribution of this paper is the demonstration that a single algorithm can solve effectively many special cases of the partial shop without taking into consideration their particular structure. We highlight the contribution of the main novel components of the algorithm, namely the initial solution generator, neighbourhood structure, and the lower bound for new solutions generated by such neighbourhood.

An Efficient Solution to the Mixed Shop Scheduling Problem Using a Modified Genetic Algorithm

The mixed job shop scheduling problem is one in which some jobs have fixed machine orders and other jobs may be processed in arbitrary orders. In past literature, optimal solutions have been proposed based on adaptations of classical solutions such as by Johnson, Thompson and Giffler among many others, by pseudopolynomial algorithms, by simulation, and by Genetic Algorithms (GA). GA based solutions have been proposed for flexible Job shops. This paper proposes a GA algorithm for the mixed job shop scheduling problem. The paper starts with an analysis of the characteristics of the so-called mixed shop problem. Based on those properties, a modified GA is proposed to minimize the makespan of the mixed shop schedule. In this approach, sample instances used as test data are generated under the constraints of shop scheduling problems. A comparison of our results based on benchmark data indicate that our modified GA provides an efficient solution for the mixed shop scheduling problem.

A Novel Metaheuristics To Solve Mixed Shop Scheduling Problems

A Novel Metaheuristics To Solve Mixed Shop Scheduling Problems

Lot streaming in a two-machine mixed shop

Most classical scheduling models overlook the fact that products are often produced in job lots and assume that job lots are indivisible single entities, although an entire job lot consists of many identical items. However, splitting an entire lot (process batch) into sublots (transfer batches) to be moved to downstream machines allows the overlapping of different operations on the same product while work needs to be completed on the upstream machine. This approach is known as lot streaming in scheduling theory. In this study, the lot streaming problem of multiple jobs in a two-machine mixed shop where there are two different job types as flow shop and open shop is addressed so as to minimize the makespan. The optimal solution method is developed for the mixed shop scheduling problem in which lot streaming can improve the makespan.

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).

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.

METAHEURISTICS FOR THE MIXED SHOP SCHEDULING PROBLEM

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.

Complexity of mixed shop scheduling problems: A survey

We survey recent results on the computational complexity of mixed shop scheduling problems. In a mixed shop, some jobs have fixed machine orders (as in the job shop), while the operations of the other jobs may be processed in arbitrary order (as in the open shop). The main attention is devoted to establishing the boundary between polynomially solvable and NP -hard problems. When the number of operations per job is unlimited, we focus on problems with a fixed number of jobs.

Two-Machine Super-Shop Scheduling Problem

The paper introduces the two-machine super-shop scheduling problem to minimize makespan. The well-known flow-shop, open-shop, job-shop and mixed-shop scheduling problems are special cases of our model. A polynomial-time algorithm to find both pre-emptive and non-pre-emptive optimal schedules is described.

Two machine mixed shop scheduling problem with controllable machine speeds

This paper considers a scheduling problem in which the objective is to determine an optimal machine speed pair and an optimal schedule. There are two machines A, B and n jobs each of which consists of two operations. One operation is to be processed on machine A and the other on machine B. The job set consisits of two disjoint subsets F and O. F is a set of flow shop type jobs, while O is a set of open shop type jobs. That is, for each job i in F, processing on A must be completed before processing on B. On the other hand, processing order of each job i in O is not specified and so processing of each job can be started on either machine. Each machine processes at most one job and each job is processed on at most one machine, simultaneously. Further it is assumed that the speed of each machine is controllable. In the situation, the total sum of costs associated with the maximum completion time and machine speeds is to be minimized. The problem is a generalization of two machine mixed shop scheduling problem [6] in a sense that machine speeds are not fixed but variables. For the problem, this paper provides a polynomial time order solution procedure.

The mixed shop scheduling problem

In this paper, we consider a two-machine shop scheduling problem consisting of two disjoint job subsets F and O . F is a set of the flow shop type jobs, while O is a set of the open shop type jobs. Our objective is to find the schedule minimizing the maximum completion time. For the case that O is empty, this problem reduces to a two-machine flow shop scheduling problem for which Johnson developed an optimal algorithm. Also for the case that F is empty, the problem reduces to a two-machine open shop scheduling problem for which there is an optimal algorithm developed by Gonzalez and Sahni. While for the case that both F and O are not empty, the situation is complicated in the sense that the preceding two cases are not extensible to our case. We give the optimal algorithm for our nontrivial case.