scholarly journals An Investigation of the Optimistic Solution to the Linear Trilevel Programming Problem

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 179
Author(s):  
Maryam Esmaeili ◽  
Habibe Sadeghi
Keyword(s):  
Programming Problem ◽  
Mathematical Formulation ◽  
Optimal Solution ◽  
Feasible Region ◽  
Optimal Solutions ◽  
General Version ◽  
Numerical Example ◽  
Optimistic Solution ◽  
Different Types ◽  
The Given

In this paper, we consider a general version of a linear trilevel programming problem. Three different types of optimistic optimal solutions for a special trilevel programming problem have formerly been suggested. This paper presents the mathematical formulation of all of the three types of optimistic optimal solutions for the given linear trilevel programming problem. Moreover, some properties of the inducible region (the feasible region for the trilevel programming problem) corresponding to each optimistic optimal solution are investigated. Finally, a numerical example is presented to compare the different types of optimistic optimal solutions.

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (04) ◽  
pp. 1165-1172
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

scholarly journals A Linearization to the Sum of Linear Ratios Programming Problem

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1004
Author(s):  
Mojtaba Borza ◽  
Azmin Sham Rambely
Keyword(s):  
Programming Problem ◽  
Computational Cost ◽  
Iterative Algorithms ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
Straightforward Method ◽  
Global Optimal ◽  
High Computational Cost ◽  
Real World Problems

Optimizing the sum of linear fractional functions over a set of linear inequalities (S-LFP) has been considered by many researchers due to the fact that there are a number of real-world problems which are modelled mathematically as S-LFP problems. Solving the S-LFP is not easy in practice since the problem may have several local optimal solutions which makes the structure complex. To our knowledge, existing methods dealing with S-LFP are iterative algorithms that are based on branch and bound algorithms. Using these methods requires high computational cost and time. In this paper, we present a non-iterative and straightforward method with less computational expenses to deal with S-LFP. In the method, a new S-LFP is constructed based on the membership functions of the objectives multiplied by suitable weights. This new problem is then changed into a linear programming problem (LPP) using variable transformations. It was proven that the optimal solution of the LPP becomes the global optimal solution for the S-LFP. Numerical examples are given to illustrate the method.

scholarly journals Effect of graphical method for solving mathematical programming problem

1970 ◽  
Vol 5 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Bimal Chandra Das
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Graphical Method ◽  
Optimal Solution ◽  
Mathematical Programming Problem ◽  
Feasible Region ◽  
Computer Implementation ◽  
International University ◽  
Short Time ◽  
Matlab Programming

In this paper, a computer implementation on the effect of graphical method for solving mathematical programming problem using MATLAB programming has been developed. To take any decision, for programming problems we use most modern scientific method based on computer implementation. Here it has been shown that by graphical method using MATLAB programming from all kinds of programming problem, we can determine a particular plan of action from amongst several alternatives in very short time. Keywords: Mathematical programming, objective function, feasible-region, constraints, optimal solution. DOI: 10.3329/diujst.v5i1.4379 Daffodil International University Journal of Science and Technology Vol.5(1) 2010 pp.29-36

scholarly journals Fundamentals of Transportation Problem

2021 ◽  
Vol 10 (5) ◽  
pp. 90-103
Author(s):  
Bhabani Mallia ◽  
Manjula Das ◽  
C. Das
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Basic Feasible Solution ◽  
Distribution Method

Transportation Problem is a linear programming problem. Like LPP, transportation problem has basic feasible solution (BFS) and then from it we obtain the optimal solution. Among these BFS the optimal solution is developed by constructing dual of the TP. By using complimentary slackness conditions the optimal solutions is obtained by the same iterative principle. The method is known as MODI (Modified Distribution) method. In this paper we have discussed all the aspect of transportation problem.

scholarly journals Total time minimizing transportation problem

2007 ◽  
Vol 17 (1) ◽  
pp. 125-133 ◽  
Author(s):  
Ilija Nikolic
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Lexicographic Order ◽  
Multiple Solution ◽  
Active Transportation ◽  
Optimal Solutions ◽  
Numerical Example ◽  
The Third ◽  
Time Problem ◽  
Transportation Routes

This paper shows the total transportation time problem regarding the time of the active transportation routes. If the multiple optimal solutions exist, it is possible to include other criteria as second level of criteria and find the corresponding solutions. Furthermore, if there is a multiple solution, again, the third objective can be optimized in lexicographic order. The methods of generation of the optimal solution in selected cases are developed. The numerical example is included. .

scholarly journals Strategic equilibrium versus global optimum for a pair of competing servers

2006 ◽  
Vol 43 (4) ◽  
pp. 1165-1172 ◽  
Author(s):  
Benjamin Avi-Itzhak ◽  
Boaz Golany ◽  
Uriel G. Rothblum
Keyword(s):  
Nash Equilibrium ◽  
Queueing System ◽  
Optimal Solution ◽  
Global Optimum ◽  
Optimal Solutions ◽  
Service Rates ◽  
Unique Nash Equilibrium ◽  
Person Game ◽  
The Given ◽  
Linear Penalties

Christ and Avi-Itzhak (2002) analyzed a queueing system with two competing servers who determine their service rates so as to optimize their individual utilities. The system is formulated as a two-person game; Christ and Avi-Itzhak proved the existence of a unique Nash equilibrium which is symmetric. In this paper, we explore globally optimal solutions. We prove that the unique Nash equilibrium is generally strictly inferior to a globally optimal solution and that optimal solutions are symmetric and require the servers to adopt service rates that are smaller than those occurring in equilibrium. Furthermore, given a symmetric globally optimal solution, we show how to impose linear penalties on the service rates so that the given optimal solution becomes a unique Nash equilibrium. When service rates are not observable, we show how the same effect is achieved by imposing linear penalties on a corresponding signal.

Fuzzy Dynamic Programming Problem for Single Additive Constraint with Additively Separable Return by Means of Trapezoidal Membership Functions

2017 ◽  
pp. 168-187
Author(s):  
Palanivel Kaliyaperumal
Keyword(s):  
Dynamic Programming ◽  
Programming Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Membership Functions ◽  
Optimal Arrangement ◽  
Fuzzy Membership Functions ◽  
Dynamic Programming Problem ◽  
Linear And Nonlinear

Dynamic Programming Problem (DPP) is a multivariable optimization problem is decomposed into a series of stages, optimization being done at each stage with respect to one variable only. DP stands a suitable quantitative study procedure that can be used to explain various optimization problems. It deals through reasonably large as well as complex problems; in addition, it involves creating a sequence of interconnected decisions. The technique offers an efficient procedure for defining optimal arrangement of decisions. Throughout this chapter, solving procedure completely deliberate about as Fuzzy Dynamic Programming Problem for single additive constraint with additively separable return with the support of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of Fuzzy Dynamic Programming Problem (FDPP). The fuzzified version of the problem has been stated with the support of a numerical example for both linear and nonlinear fuzzy optimal solutions and it is associated to showing that the proposed procedure offers an efficient tool for handling the dynamic programming problem instead of classical procedures. As a final point the optimal solution with in the form of fuzzy numbers and justified its solution with in the description of trapezoidal fuzzy membership functions.

scholarly journals A New Method for Optimal Solutions of Transportation Problems in LPP

2018 ◽  
Vol 10 (5) ◽  
pp. 60
Author(s):  
Muhammad Hanif ◽  
Farzana Sultana Rafi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
New Method ◽  
Optimal Solutions ◽  
Attractive Feature ◽  
Numerical Examples ◽  
Transportation Problems ◽  
Clear Idea

The several standard and the existing proposed methods for optimality of transportation problems in linear programming problem are available. In this paper, we considered all standard and existing proposed methods and then we proposed a new method for optimal solution of transportation problems. The most attractive feature of this method is that it requires very simple arithmetical and logical calculation, that’s why it is very easy even for layman to understand and use. Some limitations and recommendations of future works are also mentioned of the proposed method. Several numerical examples have been illustrated, those gives the clear idea about the method. A programming code for this method has been written in Appendix of the paper.

Aspects of the Cycling Phenomenon in the Linear Programming Problem (Lpp) Through the Example of Marshall and Suurballe

2018 ◽  
Vol 24 (3) ◽  
pp. 20-25
Author(s):  
Vasile Carutasu
Keyword(s):  
Complex System ◽  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Fundamental Question ◽  
Complete Analysis ◽  
System Of Inequalities ◽  
The Given

Abstract A complete analysis of the cycling phenomenon in the case of the linear programming problem (LPP) is far from being achieved. Even if [5] states that the answer to the fundamental question of this problem is found, the proposed solution is very difficult to apply, being necessary to find a solution of a complex system of inequalities. Additionally, it is difficult to recognize a problem that, by applying the primal simplex algorithm, leads us to the occurrence of this phenomenon. The example given by Marshall and Suurballe, but also the example given by Danzig, lead us to draw some useful conclusions about this phenomenon, whether the given problem admits the optimal solution or has an infinite optimal solution

Embodied displacements in young German children’s storytelling

2019 ◽  
Vol 3 (1-2) ◽  
pp. 168-195 ◽  
Author(s):  
Vivien Heller
Keyword(s):  
Picture Book ◽  
Book Reading ◽  
Lexical Resources ◽  
Narrative Space ◽  
Multimodal Analysis ◽  
Different Types ◽  
German Speaking ◽  
Picture Book Reading ◽  
The Given

This paper is concerned with embodied processes of joint imagination in young children’s narrative interactions. Based on Karl Bühler’s notion of ‘deixis in the imagination’, it examines in detail how a 19-month-old German-speaking child, engaged in picture book reading with his mother, brings about different subtypes of deixis in the imagination by either ‘displacing’ what is absent into the given order of perception (e.g. by using the hand as a token for an object) or displacing his origo to an imagined space (e.g. by kinaesthetically aligning his body with an imagined body and animating his movements). Drawing on multimodal analysis and the concept of layering in interaction, the study analyses the ways in which the picture book as well as deictic, depictive, vocal and lexical resources are coordinated to evoke a narrative space, co-enact the storybook character’s experiences and produce reciprocal affect displays. Findings demonstrate that different types of displacement are in play quite early in childhood; displacements in the dimension of space and person are produced through layerings of spaces, voices and bodies.

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