scholarly journals Managing cost uncertainties in transportation and assignment problems

1998 ◽  
Vol 2 (1) ◽  
pp. 65-104 ◽  
Author(s):  
V. Adlakha ◽  
H. Arsham
Keyword(s):  
Time Lag ◽  
Real Life ◽  
Optimal Solution ◽  
Global Market ◽  
Solution Algorithm ◽  
Assignment Problems ◽  
The Stability ◽  
Order Assignment ◽  
Cost Parameters ◽  
The Cost

In a fast changing global market, a manager is concerned with cost uncertainties of the cost matrix in transportation problems (TP) and assignment problems (AP).A time lag between the development and application of the model could cause cost parameters to assume different values when an optimal assignment is implemented. The manager might wish to determine the responsiveness of the current optimal solution to such uncertainties. A desirable tool is to construct a perturbation set (PS) of cost coeffcients which ensures the stability of an optimal solution under such uncertainties.The widely-used methods of solving the TP and AP are the stepping-stone (SS) method and the Hungarian method, respectively. Both methods fail to provide direct information to construct the needed PS. An added difficulty is that these problems might be highly pivotal degenerate. Therefore, the sensitivity results obtained via the available linear programming (LP) software might be misleading.We propose a unified pivotal solution algorithm for both TP and AP. The algorithm is free of pivotal degeneracy, which may cause cycling, and does not require any extra variables such as slack, surplus, or artificial variables used in dual and primal simplex. The algorithm permits higher-order assignment problems and side-constraints. Computational results comparing the proposed algorithm to the closely-related pivotal solution algorithm, the simplex, via the widely-used pack-age Lindo, are provided. The proposed algorithm has the advantage of being computationally practical, being easy to understand, and providing useful information for managers. The results empower the manager to assess and monitor various types of cost uncertainties encountered in real-life situations. Some illustrative numerical examples are also presented.

scholarly journals Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint

2020 ◽  
Vol 30 (1) ◽  
Author(s):  
Hamiden Abd El-Wahed Khalifa
Keyword(s):  
Goal Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solution Approach ◽  
Fuzzy Transportation Problem ◽  
The Stability ◽  
The Cost

Transportation problem (TP) is a special type of linear programming problem (LPP) where the objective is to minimize the cost of distributing a product from several sources (or origins) to some destinations. This paper addresses a transportation problem in which the costs, supplies, and demands are represented as heptagonal fuzzy numbers. After converting the problem into the corresponding crisp TP using the ranking method, a goal programming (GP) approach is applied for obtaining the optimal solution. The advantage of GP for the decision-maker is easy to explain and implement in real life transportation. The stability set of the first kind corresponding to the optimal solution is determined. A numerical example is given to highlight the solution approach.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

2022 ◽  
Vol 11 (1) ◽  
pp. 0-0
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Concept ◽  
Proper Understanding ◽  
Fuzzy Environment ◽  
The Stability ◽  
The Right ◽  
The Cost ◽  
Stability Sets ◽  
Fuzzy Parameters

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

scholarly journals Stability of Solutions for Parametric Inverse Nonlinear Cost Transportation Problem

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2027
Author(s):  
Abd Allah A. Mousa ◽  
Yousria Abo-Elnaga
Keyword(s):  
Nonlinear Programming ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Solution Stability ◽  
Tuning Parameters ◽  
Input Parameters ◽  
Feasible Alternative ◽  
The Stability ◽  
The Cost

This paper investigates the solution for an inverse of a parametric nonlinear transportation problem, in which, for a certain values of the parameters, the cost of the unit transportation in the basic problem are adapted as little as possible so that the specific feasible alternative become an optimal solution. In addition, a solution stability set of these parameters was investigated to keep the new optimal solution (feasible one) is unchanged. The idea of this study based on using a tuning parameters λ∈Rm in the function of the objective and input parameters υ∈Rl in the set of constraint. The inverse parametric nonlinear cost transportation problem P(λ,υ), where the tuning parameters λ∈Rm in the objective function are tuned (adapted) as less as possible so that the specific feasible solution x∘ has been became the optimal ones for a certain values of υ∈Rl, then, a solution stability set of the parameters was investigated to keep the new optimal solution x∘ unchanged. The proposed method consists of three phases. Firstly, based on the optimality conditions, the parameter λ∈Rm are tuned as less as possible so that the initial feasible solution x∘ has been became new optimal solution. Secondly, using input parameters υ∈Rl resulting problem is reformulated in parametric form P(υ). Finally, based on the stability notions, the availability domain of the input parameters was detected to keep its optimal solution unchanged. Finally, to clarify the effectiveness of the proposed algorithm not only for the inverse transportation problems but also, for the nonlinear programming problems; numerical examples treating the inverse nonlinear programming problem and the inverse transportation problem of minimizing the nonlinear cost functions are presented.

scholarly journals Analysis of the ReSuMe Learning Process For Spiking Neural Networks

2008 ◽  
Vol 18 (2) ◽  
pp. 117-127 ◽  
Author(s):  
Filip Ponulak
Keyword(s):  
Neural Networks ◽  
Learning Process ◽  
Learning Algorithm ◽  
Real Life ◽  
Optimal Solution ◽  
Spiking Neural Networks ◽  
Fast Learning ◽  
Life Tasks ◽  
The Neural Networks ◽  
The Stability

Analysis of the ReSuMe Learning Process For Spiking Neural NetworksIn this paper we perform an analysis of the learning process with the ReSuMe method and spiking neural networks (Ponulak, 2005; Ponulak, 2006b). We investigate how the particular parameters of the learning algorithm affect the process of learning. We consider the issue of speeding up the adaptation process, while maintaining the stability of the optimal solution. This is an important issue in many real-life tasks where the neural networks are applied and where the fast learning convergence is highly desirable.

scholarly journals Fuzzy Hungarian Approach for Transportation Model

2013 ◽  
pp. 189-192
Author(s):  
Arun Patil ◽  
S. B. Chandgude
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Transportation Model ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Transportation Models ◽  
Fuzzy Transportation Problem ◽  
The Cost

In this paper, a method is proposed to find the fuzzy optimal solution of fuzzy transportation model by representing all the parameters as trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem is solved by using the proposed method and the results are obtained. The proposed method is easy to understand, and to apply for finding the fuzzy optimal solution of fuzzy transportation models in real life situations. However, we propose the method of fuzzy modified distribution for finding out the optimal solution for minimizing the cost of total fuzzy transportation. The advantages of the proposed method are also discussed.

scholarly journals Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment

2020 ◽  
Vol 9 (1) ◽  
pp. 1-34 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Reduction Method ◽  
Real Life ◽  
Optimal Solution ◽  
Assignment Problems ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Computing Procedure ◽  
Fuzzy Representation ◽  
Objective Value

When people solve real-life SAP they tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the SAP under uncertain environment. He formulates the IFSAP and utilizes the TIFN to deal with uncertainty and hesitation. The SAP has uncertainty and hesitation in cost/time/profit/production is known as FIFSAP. The PSK (P. Senthil Kumar) method for finding an optimal solution for FIFAP is extended to solve the FIFSAP and the optimal objective value of FIFSAP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution/assignment of FIFSAP is obtained without using the Hungarian method and intuitionistic fuzzy reduction method. Moreover, the proposed method is computationally very simple and easy to understand. The numerical example is presented to demonstrate computing procedure. The results affirm efficiency of the proposed method.

The economic average cost Brownian control problem

2019 ◽  
Vol 51 (01) ◽  
pp. 300-337
Author(s):  
Melda Ormeci Matoglu ◽  
John H. Vande Vate ◽  
Haiyue Yu
Keyword(s):  
Control Problem ◽  
Average Cost ◽  
Drift Rate ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Fixed Costs ◽  
Long Run ◽  
Brownian Control Problem ◽  
Cost Parameters ◽  
The Cost

AbstractIn this paper we introduce and solve a generalization of the classic average cost Brownian control problem in which a system manager dynamically controls the drift rate of a diffusion process X. At each instant, the system manager chooses the drift rate from a pair {u, v} of available rates and can invoke instantaneous controls either to keep X from falling or to keep it from rising. The objective is to minimize the long-run average cost consisting of holding or delay costs, processing costs, costs for invoking instantaneous controls, and fixed costs for changing the drift rate. We provide necessary and sufficient conditions on the cost parameters to ensure the problem admits a finite optimal solution. When it does, a simple control band policy specifying economic buffer sizes (α, Ω) and up to two switching points is optimal. The controller should invoke instantaneous controls to keep X in the interval (α, Ω). A policy with no switching points relies on a single drift rate exclusively. When there is no cost to change the drift rate, a policy with a single switching point s indicates that the controller should change to the slower drift rate when X exceeds s and use the faster drift rate otherwise. When there is a cost to change the drift rate, a policy with two switching points s < S indicates that the controller should maintain the faster drift rate until X exceeds S and maintain the slower drift rate until X falls below s.

scholarly journals Partition of Water Distribution Networks into District Metered Areas Using a Graph Theoretical Approach

10.29007/l442 ◽  
2018 ◽  
Author(s):  
Jure Zevnik ◽  
Daniel Kozelj
Keyword(s):  
Water Distribution ◽  
Real Life ◽  
Optimal Solution ◽  
Distribution Networks ◽  
Water Distribution Networks ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretical Approach ◽  
Connected Subgraphs ◽  
The Cost

We present a method for partitioning Water Distribution Networks (WDNs) into District Metered Areas (DMAs) by using a spectral graph partitioning algorithm. The effectiveness of DMA design was tested for selected edge weights and multiple numbers of established DMAs. The presented method includes a novel graph theoretic approach to determine and evaluate only relevant combinations of DMA connection. It was tested on a real-life case study for which several different solutions were generated and evaluated against their hydraulic performance. The optimal solution, i.e. design of DMAs, was selected regarding the quality of partition and the cost of WDN segmentation, since hydraulic adequacy was met for all cases where partitioning resulted in connected subgraphs.

scholarly journals MIN-MAX SOLUTIONS FOR PARAMETRIC CONTINUOUS STATIC GAME UNDER ROUGHNESS (PARAMETERS IN THE COST FUNCTION AND FEASIBLE REGION IS A ROUGH SET)

2020 ◽  
Vol 6 (2) ◽  
pp. 3
Author(s):  
Yousria A. Aboelnaga ◽  
Mai Zidan
Keyword(s):  
Cost Function ◽  
Parametric Study ◽  
Optimal Solution ◽  
Feasible Region ◽  
Roughness Parameters ◽  
Static Game ◽  
Solution Approach ◽  
Solution Point ◽  
The Stability ◽  
The Cost

Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the \(1^{st}\) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.

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