Arezoo Osati; Esmaeil Mehdizadeh; Sadoullah Ebrahimnejad
Abstract
The purpose of this paper is to optimize the integrated problem of lot-sizing and scheduling in a flexible job-shop environment considering energy efficiency. The main contribution of the paper is simultaneously considering lot-sizing and scheduling decisions, while accounting for energy efficiency. ...
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The purpose of this paper is to optimize the integrated problem of lot-sizing and scheduling in a flexible job-shop environment considering energy efficiency. The main contribution of the paper is simultaneously considering lot-sizing and scheduling decisions, while accounting for energy efficiency. In order to achieve this objective, a mathematical model has been developed for integrated optimization of scheduling and lot-sizing problems. The developed model uses a big bucket approach and is presented as a mixed integer nonlinear problem (MINLP). The BARON solver in GAMS software has been used to solve the proposed MINLP model. By defining the relative optimality limit (OPTCR) of 0.05 for the termination criterion in BARON solver, GAMS has not been able to solve large problems at a specified time to achieve relative optimality. Therefore, due to the NP-hard nature of the problem, a new genetic-based evolutionary algorithm has been developed to solve the problem of large scale. In the developed algorithm, a different approach (instead of cross-over and mutation operators) is used to generate a new solution. By presenting and solving various problems, the efficiency of this algorithm for solving big problems is shown. Comparing the values of the objective function obtained from the genetic algorithm and the exact method shows that, especially in large problems, the genetic algorithm has been able to achieve a better solution than GAMS software in a limited time. It has also been shown that energy efficiency has a significant effect on the solution of the problem.
Behnam Ayyoubzadeh; Sadoullah Ebrahimnejad; Mahdi Bashiri; Vahid Bardaran; Seyed Mohammad Hasan Hosseini
Abstract
This paper aims to confront the uncertainties in the flexible job shop scheduling (FJSS) problem by considering the tax regulations of energy consumption and timely delivery. Uncertainties include all unexpected disruptions such as machine breakdowns, modifications or cancellation of the orders, and ...
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This paper aims to confront the uncertainties in the flexible job shop scheduling (FJSS) problem by considering the tax regulations of energy consumption and timely delivery. Uncertainties include all unexpected disruptions such as machine breakdowns, modifications or cancellation of the orders, and receiving new orders that lead to failure in initial scheduling. Two strategies with the energy-saving approach have been proposed based on scheduling repair. Two considered objective functions are to minimize the tax cost on surplus energy consumption and to minimize total cost of jobs tardiness. The problem is described with the parameters and decision variables clearly in the form of MIP model. Moreover, the proposed model is investigated using data of a real case study in a company based on casting processes. Since the problem is well known strongly NP-hard, a new approach is introduced based on the Non-dominated Sorting Genetic Algorithm (NSGA-II) to find proper solutions for decision-makers. The computational results show that the proposed model and solution approach repairs properly the original scheduling and could improve the Pareto front comparing with the original scheduling. Due to the result, two proposed strategies could reduce total cost of jobs tardiness more than 47.56% compared with the original scheduling in eight different cases. It could also improve the second objective more than 56.91%. This approach will help the manufacturing industry managers, especially in make-to-order (MTO) systems with high-powered machines to respond rapidly to unexpected disruptions with the lowest energy consumption and tardiness penalty.