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 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.

scholarly journals Study on coloring method of airport flight-gate allocation problem

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hongyan Li ◽  
Xianfeng Ding ◽  
Jiang Lin ◽  
Jingyu Zhou
Keyword(s):  
Graph Coloring ◽  
Programming Model ◽  
Weight Vector ◽  
Multi Objective ◽  
Average Value ◽  
Two Factors ◽  
Minimum Number ◽  
First Come First Serve ◽  
Airport Terminals ◽  
Single Objective

Abstract With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ w = ( 0.112 , 0.097 , 0.496 , 0.395 ) of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ α = 0.32 and $\beta =0.40$ β = 0.40 , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.

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