A modified branch and bound algorithm for a vague flow-shop scheduling problem (original) (raw)
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Fuzzy branch-and-bound algorithm for flow shop scheduling
Journal of Intelligent Manufacturing, 2000
Scheduling is the allocation of resources over time to perform a collection of task. It is an important subject of production and operations management area. For most of scheduling problems made so far, the processing times of each job on each machine and due dates have been assigned as a real number. However in the real world, information is often ambiguous or imprecise. In this paper fuzzy concept are applied to the¯ow shop scheduling problems. The branch-and-bound algorithm of Ignall and Schrage was modi®ed and rewritten for three-machine¯ow shop problems with fuzzy processing time. Fuzzy arithmetic on fuzzy numbers is used to determine the minimum completion time C max . Proposed algorithm gets a scheduling result with a membership function for the ®nal completion time. With this membership function determined, a wider point of view is provided for the manager about the optimal schedule.
Advances in Fuzzy Systems, 2021
is paper deals with constrained multistage machines flow-shop (FS) scheduling model in which processing times, job weights, and breakdown machine time are characterized by fuzzy numbers that are piecewise as well as quadratic in nature. Avoiding to convert the model into its crisp, the closed interval approximation for the piecewise quadratic fuzzy numbers is incorporated. e suggested method leads a noncrossing optimal sequence to the considered problem and minimizes the total elapsed time under fuzziness. e proposed approach helps the decision maker to search for applicable solution related to real-world problems and minimizes the total fuzzy elapsed time. A numerical example is provided for the illustration of the suggested methodology.
A Mathematical Model for a Flow Shop Scheduling Problem with Fuzzy Processing Times
2009
This paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. In the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). However,, two significant criteria for each schedule in stochastic models are: expectable makespan and the probability of minimizing the makespan. These criteria can be considered for fuzzy problems as well. In this paper, we propose a solution for the fuzzy model by the use of fuzzy logic based on developing the model presented by MacCahon [18].
Uncertainty Management by Relaxation of Conflicting Constraints in Production Process Scheduling
Mathematical-analytical methods as used in Operations Research approaches are often insufficient for scheduling problems. This is due to three reasons: The combinatorial complexity of the search space, conflicting objectives for production optimization, and the uncertainty in the production process. Knowledgebased techniques, especially approximate reasoning and constraint relaxation, are promising ways to overcome these problems. A case study from an industrial CIM environment, namely high-grade steel production, is presented to demonstrate how knowledge-based scheduling with the desired capabilities could work. By using fuzzy set theory, the applied knowledge representation technique covers the uncertainty inherent in the problem domain. Based on this knowledge representation, a classification of jobs according to their importance is defined which is then used for the straightforward generation of a schedule. A control strategy which comprises organizational, spatial, temporal, and chemical constraints is introduced. The strategy supports the dynamic relaxation of conflicting constraints in order to improve tentative schedules.
Scheduling optimization under uncertainty—an alternative approach
Computers & Chemical Engineering, 2003
The prevalent approach to the treatment of processing time uncertainties in production scheduling problems is through the use of probabilistic models. Apart from requiring detailed information about probability distribution functions, this approach also has the drawback that the computational expense of solving these models is very high. In this work, we present a non-probabilistic treatment of scheduling optimization under uncertainty, based on concepts from fuzzy set theory and interval arithmetic, to describe the imprecision and uncertainty in the task durations. We first provide a brief review on the fuzzy set approach, comparing it with the probabilistic approach. We then present MILP models derived from applying this approach to two different problems-flowshop scheduling and new product development process scheduling. Results indicate that these MILP models are computationally tractable for reasonably sized problems. We also describe tabu search implementations in order to handle larger problems.
Multi-Objective Routing and Scheduling in Flexible Manufacturing Systems Under Uncertainty
Iranian Journal of Fuzzy Systems, 2017
The efficiency of transportation system management plays an important role in the planning and operation efficiency of flexible manufacturing systems. Automated Guided Vehicles (AGV) are part of diversified and advanced techniques in the field of material transportation which have many applications today and act as an intermediary between operating and storage equipment and are routed and controlled by an intelligent computer system. In this study, a two-objective mathematical programming model is presented to integrate flow shop scheduling and routing AVGs in a flexible manufacturing system. In real-life problems parameters like demand, due dates and processing times are always uncertain. Therefore, in order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed model. Subsequently, to solve fuzzy mathematical programming model, one of the most effective technique in the literature is used. To solve the problem studied, two meta-heuristic algorit...
IEEE Access
The management of the uncertainty existing in any production system is fundamental to define machine scheduling models that allow programming production instances attached to the real world. In this research, a generalized decision-making system is developed for the management of uncertainty existing in flow shop machine scheduling models. The system assessment the uncertainty existing in internal and external factors that influence the decision-making process of production programming experts, and that is decisive in a final machine scheduling. The system is based on the combination of the Fuzzy Hierarchical Analysis Process, a membership analysis, and an Artificial Neural Network (ANN). The system allows to concentrate the experience of experts in machine scheduling and generalize their knowledge. The efficiency of the system is verified with a Fuzzy Hierarchical Analysis Process Model, the ''ANN toolbox'' preloaded in MATLAB and variety of structures of an Artificial Neural Network. The results are validated in an industrial application and the system is contrasted against an expert. The results show the efficiency of the system as it defines and predicts the final machine scheduling of production instances; the joint assessment of variables that add uncertainty to the production system allowed to reduce delays in product deliveries. INDEX TERMS Artificial neural network, decision-making system, flow shop, fuzzy hierarchical analysis process, machine scheduling, uncertainty.
A new approach to two-machine flow shop problem with uncertain processing times
Optimization and Engineering, 2006
This paper deals with the problem of optimization of job sequence in a two-machine flow shop problem in the presence of uncertainty. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. A new optimization algorithm based on Johnson's algorithm for deterministic processing times and on an improvement of McCahon & Lee's algorithm is developed and presented. In order to compare fuzzy processing times, McCahon and Lee use mean values of their corresponding fuzzy sets. It is shown that this approach cannot fully explore possible relationships between fuzzy sets. In order to overcome this drawback we consider different fuzzy sets determined by -cuts of the fuzzy processing times. Extensive experiments show that the new algorithm gives better solutions with respect to makespan than existing McCahon and Lee's algorithm.
An effective approach for job-shop scheduling with uncertain processing requirements
IEEE Transactions on Robotics and Automation, 1999
Production systems often involve various uncertainties such as unpredictable customer orders or inaccurate estimate of processing times. Managing such uncertainties is becoming critical in the era of "time-based competition." For example, if a schedule is generated without considering possible orders in the future, new orders of significant urgency may interrupt those already scheduled, causing serious violation of their promised delivery dates. The consideration of uncertainties, however, has been proven to be very difficult because of the combinatorial nature of discrete optimization compounded further by the presence of uncertain factors. This paper presents an effective approach for job-shop scheduling considering uncertain arrival times, processing times, due dates, and part priorities. A separable problem formulation that balances modeling accuracy and solution method complexity is presented with the goal to minimize expected part tardiness and earliness cost. This optimization is subject to arrival time and operation precedence constraints (to be satisfied for each possible realization), and machine capacity constraints (to be satisfied in the expected value sense). A solution methodology based on a combined Lagrangian relaxation and stochastic dynamic programming is developed to obtain dual solutions. A good dual solution is then selected by using "ordinal optimization," and the actual schedule is dynamically constructed based on the dual solution and the realization of random events. The computational complexity of the overall algorithm is only slightly higher than the one without considering uncertainties. To evaluate the quality of the schedule, a dual cost is proved to be a lower bound to the optimal expected cost for the stochastic formulation considered here. Numerical testing supported by simulation demonstrates that near optimal solutions are obtained, and uncertainties are effectively handled for problems of practical sizes.
Robust Scheduling for Flexible Job-Shop Problems with Uncertain Processing Times
IEEJ Transactions on Electronics, Information and Systems, 2015
In reality, several types of uncertainties should be considered for production scheduling, and robust scheduling is a method that enable uncertainty to be taken into account. In this paper, an enhanced technique of robust scheduling in manufacturing system is proposed to handle uncertain processing times factor. Effectiveness of the proposed technique is evaluated through a case study of Flexible Job-Shop scheduling problem (FJSP) with uncertain job processing time. This paper proposes a robust scheduling method of FJSP which consists of hybridized Genetic Algorithm (GA) and Binary Particle Swarm Optimization (BPSO) named HGABPSO. It utilizes scenarios of routing and sequences to find schedules that are confident and less sensitive against processing time uncertainties. A bi-objective evaluation measure of robust schedule is defined as minimizing the expected makespan under possible scenarios and also minimizing variability of it. Computational results indicated that the proposed method produces better solutions in comparison with a conventional method regarding the measure of robustness under different problem sizes and different levels of uncertainty for job processing time.