| With the rapid development of the global economy,the total amount of energy consumption and carbon emissions is increasing year by year,threatening the sustainable development of human society seriously.As a pillar of the national economy,manufacturing industry is not only the main consumer of resources,but also the source of environmental pollution.Therefore,in order to cope with the severe situation of energy saving and emission reduction,many leading countries have focused their attention on the manufacturing industry.As is known to all,electricity is the main energy used in the manufacturing industry.To tighten up the power demand side management(DSM),electricity providers have begun to vigorously promote the time-of-use(TOU)electricity tariffs,so as to reduce the on-peak load,increase the off-peak power efficiency,and maintain the stability of the power grid.Meanwhile,this move also provides electricity users with the opportunity to reduce electricity costs.Influenced by this background,the production scheduling problems with the main objective of reducing the total energy costs under the TOU electricity tariffs are gradually attracting widespread attention from the academia and industry.Among them,the single machine scheduling problem under the TOU electricity tariffs is not only the basis for studying scheduling problems in other manufacturing systems,but also has a wide range of applications.In this paper,the single machine scheduling problem with the target of minimizing total electricity cost under TOU electricity tariffs is studied.The main contents are as follows:(1)Single machine scheduling problem with the jobs processed at a uniform speed under the TOU electricity tariffs.At present,there are some algorithms based on discretetime or continuous-time models to solve this problem.However,these algorithms are always deficient in solution quality or time complexity,especially when dealing with large-size instances.To address large-scale problems more efficiently,a new greedy insertion heuristic algorithm with a multi-stage filtering mechanism including coarse granularity and fine granularity filtering is developed in this paper.Based on the concentration and diffusion strategy,the algorithm can quickly filter out many impossible positions in the coarse granularity filtering stage,and then,each job can find its optimal position in a relatively large space in the fine granularity filtering stage.To show the effectiveness and computational process of the proposed algorithm,a real case study is provided.Furthermore,two sets of contrast experiments are conducted,aiming to demonstrate the good application of the algorithm.The experiments indicate that the small-size instances can be solved within 0.02 s using our algorithm,and the accuracy is further improved.For the large-size instances,the computation speed of our algorithm is improved greatly compared with the classic greedy insertion heuristic algorithm.(2)Single machine scheduling problem with speed-discrete and speed-scaling mechanism under the TOU electricity tariffs.The problem studied in part 1 assumes that each job has only one fixed processing speed,hence the processing time and processing power of each job can be known before scheduling.However,some mechanical equipment can usually adjust the working speed according to the needs of the actual situation.Therefore,it is necessary to consider the speed-scaling mechanism in the scheduling.For this reason,a single machine scheduling problem with speed-discrete and speed-scaling mechanism under the TOU electricity tariffs is deeply studied in the second part,and a continuous-time MILP model aiming at minimizing electricity cost is established.In addition,based on the detailed analysis of the problem and the characteristics of the model,a hybrid genetic algorithm(HGA)is proposed.Through multiple experiments,the effectiveness of the algorithm is verified by comparison with CPLEX,and the factors influencing the performance of the models are discussed. |
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