A stability concept for matrix game optimal strategies and its application to linear programming sensitivity analysis

1986 ◽  
Vol 36 (3) ◽  
pp. 353-361 ◽  
Author(s):  
Marvin D. Troutt
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Optimal Strategies ◽  
Matrix Game ◽  
Stability Concept

Algorithm for optimal allocation of limited resources based on the game iteration method

2019 ◽  
pp. 89-99
Author(s):  
V. Ya. Vilisov
Keyword(s):  
Optimal Control ◽  
Linear Programming ◽  
Embedded Systems ◽  
Iterative Method ◽  
High Speed ◽  
Optimal Allocation ◽  
Software Implementation ◽  
Limited Resources ◽  
Matrix Game ◽  
Acceptable Accuracy

The article proposes an algorithm for solving a linear programming problem (LPP) based on the use of its representation in the form of an antagonistic matrix game and the subsequent solution of the game by an iterative method. The algorithm is implemented as a computer program. The rate of convergence of the estimates of the solution to the actual value with the required accuracy has been studied. The software implementation shows a high speed of obtaining the LPP solution with acceptable accuracy in fractions or units of seconds. This allows the use algorithm in embedded systems for optimal control.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

scholarly journals Max-min solution approach for multi-objective matrix game with fuzzy goals

2016 ◽  
Vol 26 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Sandeep Kumar
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Optimization Problem ◽  
Matrix Game ◽  
Game Model ◽  
Solution Approach ◽  
Multi Objective ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Zero Sum

In this paper, we consider a multi-objective two person zero-sum matrix game with fuzzy goals, assuming that each player has a fuzzy goal for each of the payoffs. The max-min solution is formulated for this multi-objective game model, in which the optimization problem for each player is a linear programming problem. Every developed model for each player is demonstrated through a numerical example.

The tolerance approach to sensitivity analysis in network linear programming

Networks ◽  
1988 ◽  
Vol 18 (3) ◽  
pp. 159-171 ◽  
Author(s):  
N. Ravi ◽  
Richard E. Wendell
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Tolerance Approach

Local Perturbation Analysis of Linear Programming with Functional Relation Among Parameters

2013 ◽  
pp. 1-24
Author(s):  
Payam Hanafizadeh ◽  
Abolfazl Ghaemi ◽  
Madjid Tavana
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Objective Function ◽  
Perturbation Analysis ◽  
Functional Relation ◽  
Local Perturbation ◽  
Nonlinear Functional ◽  
Functional Relations ◽  
Software Packages ◽  
The Right

In this paper, the authors study the sensitivity analysis for a class of linear programming (LP) problems with a functional relation among the objective function parameters or those of the right-hand side (RHS). The classical methods and standard sensitivity analysis software packages fail to function when a functional relation among the LP parameters prevail. In order to overcome this deficiency, the authors derive a series of sensitivity analysis formulae and devise corresponding algorithms for different groups of homogenous LP parameters. The validity of the derived formulae and devised algorithms is corroborated by open literature examples having linear as well as nonlinear functional relations between their vector b or vector c components.

Optimal Strategies for Deteriorating Inventory Systems Under Trapezoidal Type Demand

2018 ◽  
pp. 1-31
Author(s):  
Kunal Tarunkumar Shukla ◽  
Mihir S. Suthar
Keyword(s):  
Sensitivity Analysis ◽  
Continuous Function ◽  
Optimal Strategy ◽  
Piecewise Linear ◽  
Optimal Strategies ◽  
Literature Survey ◽  
Inventory Systems ◽  
Future Research ◽  
Partial Backlogging ◽  
Demand Rate

In this chapter, we study different inventory systems with trapezoidal demand rate, i.e., demand rate is a piecewise linear and continuous function. This chapter presents mathematical formulations of optimal replenishment policies for items with trapezoidal demand rate. Section 1 presents detailed literature survey for inventory systems with ramp type and trapezoidal type demand. In Section 2, Formulation technique for inventory system of items, which follows trapezoidal type demand rate. Section 3 presents effect of deterioration in model discussed in Section 2. Optimal strategy for deteriorating items with expiration dates under trapezoidal type demand and partial backlogging is discussed in Section 4. In Section 5, sensitivity analysis is carried out and chapter is concluded along with future research scope in Section 6.

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