The Fuzzy Optimization Algorithms And Theory Of Transportation Problem

Transportation Problem(denoted by TP)means the distribution of a certain productfrom sources to localities at minimum cost,and a typical problem of LinearProgramming．The model of TP has a wide applications in the real world．andrepresents a lot of practical problems such as 10cation problem,assignment problem,production planning and stock management and so on． A traditional TP is to minimizethe total transportation cost of a homogeneous product from several sources to numerousdestinations．On the other hand,a multiobjective TP involves the optimization of multipleobj ectives such as less the cost of transportation,more the quantity of goods deliveredand shorter the date of delivery etc．．The research for the algorithm of TP is a focal point problem paid close attention byscholars and the application departments．The systematic theory of TP is rather rare． This paper is devoted to study systematically TP from theory to algorithms,andfruitful for TP.Firstly,the algorithms of TP fuzzy programming on basisof existing results are developed．For the classical multiobjective TP．we presentalgorithms by using maximum multiplication operator,the combining max．min operatorwith average operator and perator,respectively．The TP with fuzzy numbers andinterval numbers are considered．algorithms for the interval numbers and fuzzy numbersprogrammings of a single objective and multi-objective TP are proposed,respectively．Secondly,scheduling problems in emergency systems for traffic accidents are discussed．In this paper,a bi—level optimization mathematical model based on"the earliestemergency—start—time"and"the fewer number of retrieval deports"is established．analgorithm is proposed．Since the time from retrievel depots to emergency depot inmulti。resource emergency systems scheduling problem is uncertain,theabove-mentioned problem is described and solved by using the connection numbers ofthe Set Fair Analysis theory for the first time．Finally,in order to tum TP into anunrestrained optimal problem,resultant matrices are discussed．The generalized inverseof constrained matrix for TP can be transformed into the one of resultant matrix．Therefore,fast algorithms and Euclid algorithms for the inverses and generalizedinverses of resultant matrices over any field are proposed．Algorithms are presentedfor finding the inverse of partitioned matrix with resultant matrix blocks．Furthermore,the GrSbner application in resultant matrices is discussed．The main results are listedin thefollowing:The background,status and three models of TP are introduced briefly．·A fuzzy maximum multiplication operator algorithm for multi．objective TP withexponential membership functions is presented by using the multiplication operator,which synthesizes difierent objective membership level to obtain the optimal compromise solution．·Due to non—compensatory of minimum operator．two．phase fuzzy algorithms are presented to solve the multi—obj ective TP with linear membership functions and non-linear membership functions according to a new upper bound for each obj ectivefunction and different average operators,respectively．An optimal compromise solutionis obtained．Numerical examples illustrate that the above approaches are feasible andefficient．·A fuzzy relaxed approach for multi-objective TP is presented by using y-operator,which allows some degree of compensation between aggregated membership functions．By inequalities,we turn the original problem into a single obj ective linear programming,an optimal compromise solution is obtained and the computation of parameter y isavoided simultaneously．Numerical examples are given to demonstrate the efficiencyand practicality of the proposed approach．·A new algorithm for fuzzy linear programming with constraint coefficients oftriangle fuzzy numbers is presented by using a new ranking criteria of fuzzy numbers．Compared with existing methods,firstly,the obtained solution is p...