A new method for solving linear multi-objective transportation problems with fuzzy parameters

AbstractThere are several methods in the literature for solving transportation problems by representing the parameters as normal fuzzy numbers. Chiang [J. Chiang, The optimal solution of the transportation problem with fuzzy demand and fuzzy product, J. Inform. Sci. Eng. 21 (2005) 439–451] pointed out that it is better to represent the parameters as (λ,ρ) interval-valued fuzzy numbers instead of normal fuzzy numbers and proposed a method to find the optimal solution of single objective transportation problems by representing the availability and demand as (λ,ρ) interval-valued fuzzy numbers. In this paper, the shortcomings of the existing method are pointed out and to overcome these shortcomings, a new method is proposed to find solution of a linear multi-objective transportation problem by representing all the parameters as (λ,ρ) interval-valued fuzzy numbers. To illustrate the proposed method a numerical example is solved. The advantages of the proposed method over existing method are also discussed

On Solving Fixed Charge Transportation Problems Having Interval Valued Parameters

In this article, we propose a new method for solving the interval fixed charge transportation problem (IFCTP), wherein the parameters (associated cost, fixed cost, supply, and demand) are represented by interval numbers. First, an equivalent bi-objective fixed charge transportation problem (FCTP) is derived from the given IFCTP, and then the equivalent crisp problem is solved using a fuzzy programming technique. To demonstrate the solution procedure, two existing numerical examples (Safi and Razmjoo {\cite{bakp1}}) are coded and solved in LINGO 19.0. We establish the effectiveness of our proposed method through a comparison of the results achieved with those of two pre-existing methods

Nonessential Functionals in Multiobjective Optimal Control Problems

We address the problem of obtaining well-defined criteria for multiobjective optimal control systems. Necessary and sufficient conditions for an optimal control functional to be nonessential are proved. The results provide effective tools for determining nonessential objectives in vector-valued optimal control problems.Comment: Presented at the 5th Junior European Meeting on Control & Information Technology (JEM'06), September 20-22, 2006, Tallinn, Estoni

Bicriterion a priori route choice in stochastic time-dependent networks.

In recent years there has been a growing interest in using stochastic time-dependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a time-adaptive strategy. In some applications, however, it makes good sense to require that the routing policy corresponds to a loopless path in the network, that is, the time-adaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and min-max criteria are considered and a solution method based on the two-phase approach is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to previously reported results for the time-adaptive caseStochastic time-dependent networks; Bicriterion shortest path; A priori route choice; Two-phase method

Fixed-Charge Solid Transportation Problem with Budget Constraints Based on Carbon Emission in Neutrosophic Environment

This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The limits of air pollution and climate variation are solely dependent by exerting CO2 gas and rest greenhouse gases due to myriad transportation system. Henceforth, it is our apt mission to minimize carbon emission for pollution free environment. Again transportation system with single objective is hardly applicable to the situation with more than one criterion. Therefore multi- objective decision making is incorporated for designing reallife transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations or suspicions. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome the restriction on occurrence and non-occurrence of fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to accommodate such general structure of problems. Therefore neutrosophic environment with neutrosophic linear programming, fuzzy programming and global criterion method are profiled to search the compromise solution of the multi- objective transportation problem (MOTP). Thereafter, the performance of the considered model is useful by evaluating a numerical example; and then the derived results are compared. Finally sensitivity analysis and conclusions with upcoming works of this research are stated hereafter.PID2020-112754GB-I0 B-TIC-640-UGR2

Neutrosophic Sets and Systems, Vol. 10, 2015

This volume is a collection of thirteen papers, written by different authors and co-authors (listed in the order of the papers): J. J. Peng and J. Q. Wang, E. Marei, S. Kar, K. Basu, S. Mukherjee, I. M. Hezam, M. Abdel-Baset and F. Smarandache, K. Mondal, S. Pramanik, A. Ionescu, M. R. Parveen and P. Sekar, B. Teodorescu, D. Kour and K. Basu, P. P. Dey and B. C. Giri, A. A. A. Agboola. In first paper, the authors studied Multi-valued Neutrosophic Sets and its Application in Multi-criteria Decision-Making Problems. More on neutrosophic soft rough sets and its modification is discussed in the second paper. Solution of Multi-Criteria Assignment Problem using Neutrosophic Set Theory are studied in third paper. In fourth paper, Taylor Series Approximation to Solve Neutrosophic Multiobjective Programming Problem. Similarly in fifth paper, Decision Making Based on Some similarity Measures under Interval Rough Neutrosophic Environment is discussed. In paper six, Neutralité neutrosophique et expressivité dans le style journalistique is studied by the author. Neutrosophic Semilattices and Their Properties given in seventh paper. Liminality and Neutrosophy is proposed in the next paper. Application of Extended Fuzzy Program-ming Technique to a real life Transportation Problem in Neutrosophic environment in the next paper. Further, TOPSIS for Single Valued Neutrosophic Soft Expert Set Based Multi-attribute Decision Making Problems is discussed by the authors in the tenth paper. In eleventh paper, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers have been studied by the author. In the next paper, On Refined Neutrosophic Algebraic Structures. At the end, Neutrosophic Actions, Prevalence Order, Refinement of Neutrosophic Entities, and Neutrosophic Literal Logical Operators are introduced by the author

Optimization with interval data: new problems, algorithms, and applications.

The parameters of real-world optimization problems are often uncertain due to the failure of exact estimation of data entries. Throughout the years, several approaches have been developed to cope with uncertainty in the input parameters of optimization problems, such as robust optimization, stochastic optimization, fuzzy programming, parametric programming, and interval optimization. Each of these approaches tackles the uncertainty in the input data with different assumptions on the source of uncertainty and imposes different requirements on the returned solutions. In this dissertation, the approach we take is that of interval optimization, and more specifically, interval linear programming. The two main problems we consider in this context are, considering all realizations of the interval data, the problems of finding the range of the optimal values and determining the set of all possible optimal solutions. While the theoretical aspects of these problems are well-studied, the algorithmic aspects and the engineering implications have not been explored. In this dissertation, we partially fill these voids. In the first part of the dissertation, we present and test three heuristics to find bounds on the worst optimal value of the equality-constrained interval linear program, which is known to be an intractable problem. In the second part of the dissertation, motivated by a real-case problem in the healthcare context, we define and analyze a new problem, the outcome range problem, in interval linear programming. The solution to the problem would help decision-makers quantify unintended/further consequences of optimal decisions made under uncertainty. Basically, the problem finds the range of an extra function of interest (different from the objective function) over all possible optimal solutions of an interval linear program. We analyze the problem from the theoretical and algorithmic perspectives. We evaluate the performance of our algorithms on simulated problem instances and on a real-world healthcare application. In the third part of the dissertation, we extend our analysis of the outcome range problem, exploring different theoretical properties and designing several new solution algorithms. We also test our solution approaches on different datasets, highlighting the strengths and weaknesses of each approach. Finally, in the last part of the dissertation, we discuss an application of interval optimization in the sensor location problem in the traffic management context. Particularly, we propose an optimization approach to handle the measurement errors in the full link flow observability problem. We show the applicability of our approach on several real-world traffic networks

An ε-Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment

Effective decision-making requires well-founded optimization models and algorithms tolerant of real-world uncertainties. In the mid-1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and made it possible to represent hesitancy in a decision-making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function-based approaches stand out for their simplicity to transform these problems into conventional ones. However, these approaches do not always guarantee Pareto optimal solutions. In this study, the concepts of dominance and Pareto optimality are extended to the intuitionistic fuzzy case by using lexicographic criteria for ranking triangular intuitionistic fuzzy numbers (TIFNs). Furthermore, an intuitionistic fuzzy epsilon-constraint method is proposed to solve IFMOLP problems with TIFNs. The proposed method is illustrated by solving two intuitionistic fuzzy transportation problems addressed in two studies (S. Mahajan and S. K. Gupta's, "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Ann Oper Res, vol. 296, no. 1, pp. 211-241, 2021, and Ghosh et al.'s, "Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem," Complex Intell Syst, vol. 7, no. 2, pp. 1009-1023, 2021). Results show that, in contrast with Mahajan and Gupta's and Ghosh et al.'s methods, the proposed method guarantees Pareto optimality and also makes it possible to obtain multiple solutions to the problems.MCIN/AEI PID2020-112754GB-I00FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades/Proyecto B-TIC-640-UGR2