Cyclic Job Shop Problem Research Articles

The robust cyclic job shop problem

This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, row and row-and-column generation algorithms are the most common. In this paper, we propose a branch-and-bound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard’s algorithm to derive a lower bound on the optimal cycle time. Moreover, we design a row generation algorithm and a column-and-row generation algorithm and compare it to the branch-and-bound method. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.

A mixed integer linear programming modelling for the flexible cyclic jobshop problem

This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.

TOWARDS THE LEVELING OF MULTI-PRODUCT BATCH PRODUCTION FLOWS. A MULTIMODAL NETWORKS PERSPECTIVE.

The problem studied in this paper is a cyclic job-shop problem with multiple Automated Guided Vehicles (AGVs). Job batches, which follow specific production routes, are processed, in the order of their operations, on multiple machines with standard processing times, and the fleet of AGVs perform the transportation operations of moving these job batches between the workstations. In this system, part sets of items are produced at fixed time intervals (takts). In the adopted model of the system, one can distinguish a layer of station-to-station transport, which is a network of local loops connecting subsets of workstations serviced cyclically by dedicated AGVs, and a layer of repetitive production flows which comprise job batches following a given set of production routes. The relationship between the elements of the structure of the system being modelled and its potential behavior is described by a system of integer equations. The resulting solutions enable the fast evaluation of production flow parameters including part sets, takt time, as well as repetitive-flow balancing aimed at maximization of the rate of system resource utilization. The high efficiency of the proposed approach, enabling the online prototyping of the production flow, is a consequence of omitting the time-consuming calculation of the sequencings of jobs within a cycle.

Parallel tabu search for the cyclic job shop scheduling problem

Abstract In this paper, we consider a cyclic job shop problem, consisting of production of a certain set of elements at fixed intervals. Optimization of the process is reduced to a minimization of a cycle time, i.e. the time, after which the next batch of the same elements may be produced. We introduce a new parallel method for the cost function calculation. The parallelization is not trivial and cannot be done automatically by the existing compilers due to the recurrent character of formulas. Since the problem is strongly NP-hard, a heuristic algorithm was designed to solve it. Computational experiments were done in a multiprocessor environment, namely – in Intel Xeon Phi.

Cyclic Job Shop Problem with varying processing times

In this paper, we consider a cyclic job shop problem where a subset of tasks have varying processing times. The minimum processing times and maximum processing times of these tasks are known. We propose a branch and bound method that finds the schedule which minimizes the mean cycle time with respect to variations. We show that the evaluation of a schedule can be considered as a volume calculus of some polytopes. Indeed, for each schedule we can associate a set of polytopes whose volumes provide information on the variation effect on the considered schedule.

Recurrent neural network approach for cyclic job shop scheduling problem

While cyclic scheduling is involved in numerous real-world applications, solving the derived problem is still of exponential complexity. This paper focuses specifically on modelling the manufacturing application as a cyclic job shop problem and we have developed an efficient neural network approach to minimise the cycle time of a schedule. Our approach introduces an interesting model for a manufacturing production, and it is also very efficient, adaptive and flexible enough to work with other techniques. Experimental results validated the approach and confirmed our hypotheses about the system model and the efficiency of neural networks for such a class of problems.

A mixed integer programming model for the cyclic job-shop problem with transportation

This paper focuses on the study of cyclic job-shop problems with transportation and blocking. Within this domain, there are many real world problems like large scale productions, robotic cells, software pipelining or hoist scheduling. The aim in general is to find, for each machine, a feasible order of all the operations processed on this machine, so that an objective function is optimised. In this paper, we consider the problem of minimising the cycle time (maximising the throughput) in a job-shop environment, where the jobs are transported by a single robot between the machines. Additionally to the problem description, we will give some explanations and interpretation possibilities of the problem height, which is often omitted in the literature. As the main contribution, we will present a new integer programming formulation and show that it outperforms an existing model from the literature.

A New Procedure for the Cyclic Job Shop Problem

The topic of this paper is the cyclic job shop problem which aims at minimizing the cycle time under precedence and resource constraints. Based on graph theory, we propose a new branch and bound enumeration procedure to solve this problem. We compare the new procedure with other exact methods and present numerical test results.

A branch and bound algorithm for the cyclic job-shop problem with transportation

The cyclic job-shop problem with transportation can be used to describe optimization problems in fully automated manufacturing systems or assembly lines. We study the problem where the machines have no buffers, which rapidly decreases the number of feasible solutions and, therefore, makes it a lot harder to find those feasible solutions. After formulating the problem, we will characterize feasible solutions based on the route of the robot and their properties. With the aim of minimizing the cycle time, we have developed a tree search method to construct feasible solutions and combined it with a bounding procedure. Computational results are reported and compared to those gained by solving the problem with an LP solver.

Cyclic jobshop problem and (max, plus) algebra

AbstractIn this paper, we focus on the cyclic job-shop problem. This problem consists in determining the order of a set of generic tasks on machines in order to minimize the cycle time of the sequence. We propose an exact method to solve this problem. For each solution, a linear max-plus model (possibly non causal) is obtained. To evaluate the performance of a considered schedule, we build the causal max-plus representation and compute the eigenvalue of the evolution matrix. A branch and bound procedure is presented.

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.