Integrated Optimization of Makespan,Robustness and Energy Cost for the Flow Shop in Manufacturing Plant
Managers within manufacturing plants confront increasingly intricate scenarios,necessitating efforts to minimize manufacturing lead times amidst the destabilizing impact of random failures.Concurrently,they must also endeavor to curtail energy costs within time-of-use tariffs,thereby bolstering the price competitiveness of products.Focusing on the discrete flow shop,this study incorporates considerations of energy consumption costs within the framework of TOU tariff policies and the stochastic nature of equipment failures.Through the integra-tion of production scheduling and equipment maintenance,this study aims to devise a cohesive modeling approach that enables comprehensive planning for both activities.The devised integrated optimization scheme outlined in this paper is poised to significantly aid enterprises in achieving peak shaving and valley filling,along-side cost reduction and efficiency enhancements under time-sharing tariff policies.Furthermore,it offers valuable insights for workshop managers seeking to formulate judicious and effective production plans within complex and uncertain production environments.This study focuses on multiple interrelated dimensions within the manufacturing shop,establishing a mathe-matical model that encompasses three decision dimensions:production scheduling,equipment maintenance,and energy allocation.A two-layer algorithm is devised to tackle this model effectively.Firstly,a method based on surrogate measures is designed to evaluate the performance of solutions.Then,a metaheuristic algorithm is designed combining the NSGA-Ⅱ framework and the constructive-heuristic rules to search the Pareto curve of this multi-objective problem.Data are acquired through Monte Carlo simulation.Under the assumption that random faults follow an exponential distribution,random numbers are generated by sampling iteratively to simulate the system,followed by conducting several tests.In the algorithm's validation phase,Monte Carlo sampling simulation is employed to compute the expected value of the objective function within the inner algorithm.Subsequently,an appropriate proxy index function is devised to effectively approximate the expected target value,significantly reducing operational time while maintai-ning a certain level of precision.Comparative analysis of VEGA reveals substantial enhancements in the robust-ness index of the NSGA-Ⅱ algorithm,formulated within the outer algorithm,along with improvements in product delivery time and electricity cost.The intricate strategy proposed herein for model validation effectively mitigates electricity costs.In essence,the incorporation of buffer time insertion and the algorithm outlined in this study enhances system performance concerning stability and electricity cost indices when encountering random faults.Our findings demonstrate the efficacy of buffer time insertion:it mitigates fault impacts on subsequent processes,ensuring current process stability,and diminishes the proportion of processing time subject to peak electricity prices,thus economizing on electricity costs.Additionally,our investigation indicates that an increase in buffering time leads to a gradual reduction in peak power,further curtailing total electricity costs.However,practical imple-mentation may be constrained by extended delivery times,rendering this approach less advisable in practice.In future research,the problem can be extended by addressing the following two aspects:(1)Assessing the influence of renewable energy power supply modes on all facets of the system.(2)Investigating pertinent issues within alternative production layouts,such as flexible assembly line shops,open shops,and others.
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