Research On Models And Algorithms Of One Kind Of Network Optimization Problems Under Fuzzy Environment

The development of science and technology promotes the development of operations research.Many branches of operations research are more and more mature,among which transportation models are widely used in industry.The traditional transportation problems lie in determining the optimal transportation modes,which minimize the total cost.However,the supply and demand in the transportation problems are very difficult to give exact figures.Most of the time,the supply is more than the demand.Therefore,we need to coordinate the modes of transportation to satisfy both the supply places and the demand places.However,there is more than one route that can be chosen for transportation.And there is a difference between the advantages and disadvantages of each route.Decision makers tend to choose a better route and need to control the transportation time at the same time.The flexibility of these factors makes it impossible for precise mathematics to study such problems strictly.Therefore,random factors and fuzzy factors need to be added to such problems.Random factors refer to the uncertainty of whether something happens or not,and fuzzy refers to the uncertainty of itself.The purpose of the transportation problems is to reduce the cost as much as possible while solving the problems.In order to effectively plan the system and improve the efficiency,this paper blurs the total transportation cost and replaces the total transportation cost with the satisfaction of decision makers.Under the fuzzy environment,three transportation problems with different influencing factors are discussed.The first is the problem with supply and demand factors and decision satisfaction factors,the second is the problem with route factors and decision satisfaction factors,and the third is the problem with supply and demand factors,route factors and decision satisfaction factors.In order to solve the above problems,based on fuzzy mathematics,stochastic equations and other mathematical theories,this paper establishes three transportation models,discusses the solving algorithms of the models by using the binary search method,and gives the feasibility and complexity of the first two.Finally,it deduces the validity of the models by using concrete examples.