Production scheduling for a job shop using a mathematical model (original) (raw)
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Mathematical Modeling of Production Scheduling Problem: A Case Study for Manufacturing Industry
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Mathematical formulations for production scheduling environment are very complex task. These complex real life problems cannot be solved by traditional exact solvers to get good quality solutions within feasible time. Inspired by a real-world case study in the manufacturing industry, this paper provides an efficient mathematical model for short-term production scheduling. This model can be easily modified for flexibility and dynamic nature of manufacturing industries. This mathematical model can be optimized by modern optimization methods.
A Mathematical Model for Production Planning and Scheduling in a Production System: A Case Study
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Integration in decision making at different organizational and time levels has important implications for increasing the profitability of organizations. Among the important issues of medium-term decision-making in factories, are production planning problems that seek to determine the quantities of products produced in the medium term and the allocation of corporate resources. Furthermore, at short-term, jobs scheduling and timely delivery of orders is one of the vital decision-making issues in each workshop. In this paper, the production planning and scheduling problem in a factory in the north of Iran is considered as a case study. The factory produces cans and bins in different types with ten production lines. Therefore, a mixed integer linear programming (MILP) model is presented for the integrated production planning and scheduling problem to maximize profit. The proposed model is implemented in the GAMS software with the collected data from the real environment, and the optimal...
An optimization approach and a model for Job Shop Scheduling Problem with Linear Programming
2019
Optimization approaches and models are developed for job shop scheduling problems over the last decades, particularly the most attempts have been done in industry and considerable progress has been made on an academic line. The Job-shop scheduling considered the most significant industrial activities, mostly in manufacturing. The JSSP (Job Shop Scheduling Problems) is typical NP-hard problem. To solve this problem, we have used the linear programming approach. Real data have been taken from the company of the metalworking industry. The model has been created, then it was analyzed using Spreadsheet-Excel Solver. The appropriate sequence has been obtained and the results shown that it is possible to achieve the minimum completion time compared to other sequence combination
A Mixed-Integer Programming Model for the Job Scheduling Problem in a Production Company
Verimlilik Dergisi, 2020
In this study, a mixed-integer programming model is developed to minimize the total lateness and total completion time of the jobs in an automotive company. In order to respond rapidly to the continuous customer demand through the production, the work schedule of engineers in the research and development department is considered flexibly. Methodology: In the study, the mixed-integer programming model is supported by the analytical hierarchy process model to determine the weighted values of total tardiness and total completion times. The developed model is applied to the automotive company using the real data and the problem is solved using the GAMS CPLEX 24.1.3 software. Findings: In this job scheduling problem, the total completion time is decreased to 622 hours from 10149 hours, maximum tardiness is decreased to 9 hours from 104 hours and total tardiness is decreased to 13 hours from 860 hours by using the proposed model. Originality: The proposed model is used for the job scheduling purpose in compliance with the structure of the automotive industry company using the machine scheduling modeling principles and Analytical Hierarchy Process together.
An optimization-based algorithm for job shop scheduling
Sadhana, 1997
Scheduling is a key factor for manufacturing productivity. Effective scheduling can improve on-time delivery, reduce inventory, cut lead times, and improve the utilization of bottleneck resources. Because of the combinatorial nature of scheduling problems, it is often difficult to find optimal schedules, especially within a limited amount of computation time. Production schedules therefore are usually generated by using heuristics in practice. However, it is very difficult to evaluate the quality of these schedules, and the consistency of performance may also be an issue.
Job Shop Scheduling Problem: an Overview
2001
The Job-shop scheduling is one of the most important industrial activities, especially in manufacturing planning. The problem complexity has increased along with the increase in the complexity of operations and product-mix. To solve this problem, numerous approaches have been developed incorporating discrete event simulation methodology. The scope and the purpose of this paper is to present a survey which covers most of the solving techniques of Job Shop Scheduling (JSS) problem. A classification of these techniques has been proposed: Traditional Techniques and Advanced Techniques. The traditional techniques to solve JSS could not fully satisfy the global competition and rapidly changing in customer requirements. Simulation and Artificial Intelligence (AI) have proven to be excellent strategic tool for scheduling problems in general and JSS in particular. The paper defined some AI techniques used by manufacturing systems. Finally, the future trends are proposed briefly.
Survey of Job Shop Scheduling Techniques
1998
Mathematical programming has been applied extensively to job shop scheduling problems. Problems have been formulated using integer programming , mixed-integer programming , and dynamic programming . Until recently, the use of these approaches has been limited because scheduling problems belong to the class of NP-complete problems. To overcome these deficiencies, a group of researchers began to decompose the scheduling problem into a number of subproblems, proposing a number of techniques to solve them. In addition, new solution techniques, more powerful heuristics, and the computational power of modern computers have enabled these approaches to be used on larger problems. Still, difficulties in the formulation of material flow constraints as mathematical inequalities and the development of generalized software solutions have limited the use of these approaches. proposed a methodology based on the decomposition of mathematical programming problems that used both Benders-type and Dantzig/Wolfe-type decompositions. The methodology was part of closed-loop, real-time, two-level hierarchical shop floor control system. The top-level scheduler (i.e., the supremal) specified the earliest start time and the latest finish time for each job. The lower level scheduling modules (i.e., the infimals) would refine these limit times for each job by detailed sequencing of all operations. A multicriteria objective function was specified that included tardiness, throughput, and process utilization costs. The decomposition was achieved by first reordering the constraints of the original problem to generate a block angular form, then transforming that block angular form into a hierarchical tree structure. In general, N subproblems would result plus a constraint set that contained partial members of each of the subproblems. The latter was termed the "coupling " constraints, and included precedence relations and material handling. The supremal unit explicitly considered the coupling constraints, while the infimal units considered their individual decoupled constraint sets. The authors pointed out that the inherent stochastic nature of job shops and the presence of multiple, but often conflicting, objectives made it difficult to express the coupling constraints using exact mathematical relationships. This made it almost impossible to develop a general solution methodology. To overcome this, a new real-time simulation methodology was proposed in to solve the supremal and infimal problems.
Applied Sciences
The overwhelming majority of methodologies for the flexible flow shop scheduling problem proposed so far have a common feature, which is the assumption of constant time and cost for the execution of individual technological operations (ignoring an optimal selecting combination of individual employees and tools). Even if the existence of the influence of the selection of production resources on the course of operations is signaled in the available works, the research so far has not focused on the measurable effect of such a solution that takes into account this phenomenon in scheduling. The proposed production scheduling methodology, including the influence of employees and tools, turned out to be more effective in terms of minimizing the maximum completion time and the cost of the production process compared to existing solutions. The efficiency of the new proposed scheduling methodology was assessed using examples of four technological processes. The research was carried out on the...
A linear programming-based method for job shop scheduling
Journal of Scheduling, 2013
We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach.
Solving a Real Job Shop Scheduling Problem
This work deals with a real job shop scheduling problem (jssp). The operations sequences, processing time, setup time, deadline time, due date time, priority, machine, fabric color and related technological decisions data are obtained from orders database along with a set of technological criteria about machines, which allows automatically analyzing and generating the initial scheduling sequences. These sequences are processed later by two procedures, one based on Ant Colony, and the other in Genetic Algorithms. Both procedures are integrated to a generative scheduling method and dispatching rules for big problems. In this approach is integrated technological information from: the process planning and scheduling process, in order to improve the processing time and the solution quality.