Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance.A non-cooperative game model is established,considering the competition and self-interest behavior of jobs from different customers for machine resources.The job from different customers is mapped to the players in the game model,the corresponding optional processing machine and location are mapped to the strategy set,and the makespan of the job is mapped to the payoff.Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model.A Nash equilibrium solution algorithm based on the genetic algorithm(NEGA)is designed,and the effective solution of approximate Nash equilibrium for the game model is realized.The fitness function,single-point crossover operator,and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium.Rules are also designed to avoid the generation of invalid offspring chromosomes.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.Compared with other algorithms such as heuristic algorithms(FCFS,SPT,and LPT),the simulated annealing algorithm(SA),and the particle swarm optimization algorithm(PSO),experimental results show that the proposed NE-GA algorithm has obvious performance advantages.

Coordinated Scheduling of Two-Agent Production and Transportation Based on Non-Cooperative Game

A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average.

Cooperative Game Theory Based Coordinated Scheduling of Two-Machine Flow-Shop and Transportation

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop(TFS-PTCS problems)with an interstage transporter.The authors assume that there is an initial scheduling order for processing jobs on the machines.The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value.The properties of cooperative games under two different types of admissible rearrangements are analysed.For TFS-PTCS problems with identical processing time,it is proved that,the corresponding games areσ_(0)-component additive and convex under one admissible rearrangement.The Shapley value gives a core allocation,and is provided in a computable form.Under the other admissible rearrangement,the games neither need to beσ_(0)-component additive nor convex,and an allocation rule of modified Shapley value is designed.The properties of the cooperative games are analysed by a counterexample for general problems.

Storing Freshwater Versus Storing Electricity in Power Systems with High Freshwater Electric Demand

We consider a power system whose electric demand pertaining to freshwater production is high(high freshwater electric demand),as in the Middle East,and investigate the tradeoff of storing freshwater in tanks versus storing electricity in batteries at the day-ahead operation stage.Both storing freshwater and storing electricity increase the actual electric demand at valley hours and decrease it at peak hours,which is generally beneficial in term of cost and reliability.But,to what extent?We analyze this question considering three power systems with different generation-mix configurations,i.e.,a thermal-dominated mix,a renewable-dominated one,and a fully renewable one.These generation-mix configurations are inspired by how power systems may evolve in different countries in the Middle East.Renewable production uncertainty is compactly modeled using chance constraints.We draw conclusions on how both storage facilities(freshwater and electricity)complement each other to render an optimal operation of the power system.