Study On Two-stage Parallel Speed-scaling Machines Scheduling Problem Under Time-of-use Tariffs

In the process of the rapid development of global economy,energy and environmental issues are constantly emerging,and reducing energy costs has become an increasingly important consideration in the development of enterprises.As a pillar industry of China's economic development,the manufacturing industry not only brings economic benefits,but also consumes a large amount of energy,which has a great impact on the environment and sustainable development.Electric energy is the main energy consumed by the manufacturing industry.In order to balance the supply and demand of electricity,China implements time-of-use electricity price policy to encourage enterprises to shift their electricity load from high-load period to low-load period.This not only reduces the cost of electricity for the enterprise,but also relieves the load pressure on the grid and achieves a balance between power supply and demand.The parallel machine scheduling problem is a generalization of the single machine scheduling problem,and it is a special case of hybrid flow shop,which has received more and more attention in recent years.It has received more and more attention in recent years,and the two-stage parallel machine scheduling problem has more important research value.The change of speed makes the processing time and power consumption rate of the job change accordingly,and then affects the processing of the job.The combination of time-of-use tariffs and speed-scaling mechanism makes it more possible to reduce the total electricity costs of processing.This paper studies the two-stage parallel speed-scaling machines scheduling problem under time-of-use electricity tariffs.The first stage is a set of identical parallel speed-scaling machines,and the second stage is a set of unrelated parallel machines with fixed processing speed.The key to this problem is how to select the appropriate processing machine for each job at each stage and select the appropriate processing speed for jobs at first stage.At the same time,each job is allocated reasonably on the selected machine to minimize the total electricity costs.To solve this problem,this paper constructs a continuous time mixed integer linear programming model(MILP)to obtain the minimum total electricity cost.Based on the problem analysis and model construction,an effective tabu search-greedy insertion heuristic hybrid algorithm(TS-GIH)is designed to solve this problem.In this algorithm,the greedy insertion heuristic algorithm including list scheduling and speed selecting and adjusting heuristics is used to calculate the optimal value of each generation,and the tabu search algorithm is used for iterative optimization,so as to obtain the optimal solution of the problem.In order to test the performance of the model and the algorithm,this paper applies an example of a motor factory and a set of random examples to test and evaluate the algorithm and model.The experimental results demonstrate the effectiveness of the proposed MILP model and the algorithm,and the algorithm designed in this paper is more suitable for production decision.