scholarly journals Multi-objective stochastic transportation problem involving three-parameter extreme value distribution

2019 ◽  
Vol 29 (3) ◽  
pp. 337-358 ◽  
Author(s):  
Mitali Acharya ◽  
Adane Gessesse ◽  
Rajashree Mishra ◽  
Srikumar Acharya
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Mathematical Programming Problem ◽  
Multi Objective ◽  
Stochastic Transportation Problem

In this paper, we considered a multi-objective stochastic transportation problem where the supply and demand parameters follow extreme value distribution having three-parameters. The proposed mathematical model for stochastic transportation problem cannot be solved directly by mathematical approaches. Therefore, we converted it to an equivalent deterministic multi-objective mathematical programming problem. For solving the deterministic multi-objective mathematical programming problem, we used an ?-constraint method. A case study is provided to illustrate the methodology.

Study of Typhoon Disaster Zoning and Prevention Criteria Along Coasts of China: A Type of Double Layer Nested Multi-Objective Probability Model and Its Application

2007 ◽  
Author(s):  
Defu Liu ◽  
Yuzhong Liu ◽  
Liang Pang ◽  
Botao Xie ◽  
Yuankang Wu
Keyword(s):  
Double Layer ◽  
Probability Model ◽  
Joint Probability ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Objective Probability ◽  
Multi Objective ◽  
Typhoon Disaster ◽  
China Coast

For prevention and mitigation of typhoon disaster in China, in this paper the double-layer nested multi-objective probability model of typhoon disaster zoning and prevention criteria is proposed. The Multivariate Compound Extreme Value Distribution (MCEVD) is used to predict the joint probability of seven typhoon characteristics and corresponding typhoon induced disaster. Predicted results can be used for both of typhoon disaster zoning and corresponding prevention criteria along China coast.

scholarly journals Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Min Jiang ◽  
Zhiqing Meng ◽  
Xinsheng Xu ◽  
Rui Shen ◽  
Gengui Zhou
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Programming Model ◽  
Weight Vector ◽  
Mathematical Programming Problem ◽  
Pricing Model ◽  
Multi Objective ◽  
Joint Solution ◽  
Joint Pricing ◽  
Better Than

This paper extends an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents). First, we define ans-optimal joint solution with weight vector to multi-objective interaction programming problem with interaction constraint for two players and get some properties of it. It is proved that thes-optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Then, we define anothers-optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties. It is proved that thes-optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain. Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.

scholarly journals MULTI-OBJECTIVE PROBABILISTIC FRACTIONAL PROGRAMMING PROBLEM INVOLVING TWO PARAMETERS CAUCHY DISTRIBUTION

2019 ◽  
Vol 24 (3) ◽  
pp. 385-403
Author(s):  
Srikumar Acharya ◽  
Berhanu Belay ◽  
Rajashree Mishra
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Cauchy Distribution ◽  
Solution Procedure ◽  
Mathematical Programming Problem ◽  
Multi Objective ◽  
Fractional Programming Problem ◽  
Two Parameters

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, ε -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

scholarly journals A Goal Programming Approach to Multichoice Multiobjective Stochastic Transportation Problems with Extreme Value Distribution

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Hadeel Al Qahtani ◽  
Ali El–Hefnawy ◽  
Maha M. El–Ashram ◽  
Aisha Fayomi
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Random Variables ◽  
Optimal Solution ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Mixed Integer ◽  
Programming Approach ◽  
Aspiration Levels

This paper presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multiple aspiration levels to achieve, and the parameters of supply and demand are random variables which are not predetermined. The random variables shall be assumed to follow extreme value distribution, and the demand and supply constraints will be converted from a probabilistic case to a deterministic one using a stochastic approach. A transformation method using binary variables reduces the MCMOTP into a multiobjective transportation problem (MOTP), selecting one aspiration level for each objective from multiple levels. The reduced problem can then be solved with goal programming. The novel adapted approach is significant because it enables the decision maker to handle the many objectives and complexities of real-world transportation problem in one model and find an optimal solution. Ultimately, a mixed-integer mathematical model has been formulated by utilizing GAMS software, and the optimal solution of the proposed model is obtained. A numerical example is presented to demonstrate the solution in detail.

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