Research On Flow Shop Batch Scheduling Problem Considering Energy Consumption

The flow shop batch scheduling problem widely exists in the production and manufacturing industry,ranging from the aerospace industry,ship manufacturing,and steel companies;as small as the production of paper and beverage bottle packaging boxes,most of them can be simplified into the flow shop batch scheduling model.Reasonable optimization of batch scheduling tasks can not only improve the production efficiency of the enterprise,but also reduce the operating cost of the enterprise.Most of the existing researches focus on the multi-objective problems related to the manufacturing cycle.As environmental problems become more and more serious,the multi-objective batch scheduling problem of energy consumption and energy consumption cost is more realistic.Aiming at this NP-hard problem,this article mainly studies the following aspects:(1)First of all,we focus on minimizing the maximum completion time for the two-stage permutation flow shop scheduling problem with batch processing machines and nonidentical job sizes by considering blocking,arbitrary release times,and fixed setup and cleaning times.Two hybrid ant colony optimization algorithms,one based on job sequencing(JHACO)and the other based on batch sequencing(BHACO),are proposed to solve this problem.First,max-min pheromone restriction rules and a local optimization rule are embedded into JHACO and BHACO,respectively,to avoid trapping in local optima.Then,an effective lower bound is estimated to evaluate the performances of the different algorithms.Finally,the Taguchi method is adopted to investigate and optimize the parameters for JHACO and BHACO.The performances of the proposed algorithms are compared with that of CPLEX on small-scale instances and those of a hybrid genetic algorithm(HGA)and a hybrid discrete differential evolution(HDDE)algorithm on full-scale instances.The computational results demonstrate that BHACO outperforms JHACO,HDDE,and HGA in terms of solution quality.Besides,JHACO strikes a balance between solution quality and run time.(2)Secondly,reducing energy costs has become an important concern for sustainable manufacturing systems,owing to concern for the environment.We present a multi-objective hybrid ant colony optimization(MHACO)algorithm for a real-world two-stage blocking permutation flow shop scheduling problem to address the trade-off between total energy costs(TEC)and makespan(Cmax)as measures of the service level with the time-of-use(TOU)electricity price.We explore the energy-saving potential of the manufacturing industry in consideration of the differential energy costs generated by variable-speed machines.A mixed integer programming model is developed to formulate this problem.In the MHACO algorithms,the max-min pheromone restriction rules and the local search rules avoid the localization trap and enhance neighbourhood search capabilities,respectively.The Taguchi method and small-scale pilot experiments are employed to determine the appropriate experimental parameters.Based on three well-known multi-objective optimization algorithms,viz.,NSGAII,SPEA2,and MODEA,six algorithms with different batch-sorting methods are adopted as a comparison in small-,moderate-,and large-scale instances.A four-dimensional performance evaluation system is established to evaluate the obtained Pareto frontier approximations.The computational results show that the proposed MHACO-Johnson algorithm outperforms other algorithms in terms of solution quality,quantity,and distribution,although it is time-consuming when dealing with moderate-to large-scale instances.(3)Finally,a special multi-objective two-stage replacement flow shop batch scheduling problem is studied.In this problem,the two-stage batch processing machine is different.In the first stage,all jobs can be processed at the same time,while in the second stage machine The jobs in the batch can only be processed sequentially,which causes a huge difference in the processing time spent in the two stages.Similarly,in order to make the research question more general,we examined its specific energy consumption through a variable speed machine.The goal of the problem is to minimize the manufacturing cycle while minimizing energy consumption.Then we give the mathematical programming model of the problem.Because it is NP-hard,GUROBI only finds the optimal solution on the smallest set of artifacts.Therefore,we developed a hybrid discrete artificial bee colony algorithm to try to solve this problem and proposed an optimization solution process for four kinds of neighborhood search operators based on the problem.Based on different batch scheduling rules,four different hybrid discrete artificial bee colony algorithms are generated.Similarly,the Taguchi method is used to find the optimal parameter combination for it.Finally,by comparing with the well-known multi-objective algorithm,it is proved that our proposed MDABC-SPT algorithm can obtain the best approximate Pareto solution on medium and large-scale job instances.