On Solving Fuzzy Multi-Objective Multi-Choice Stochastic Transportation Problems

The real world conditions of transportation pose new challenges for development of intelligent assistive systems for effective decision making. The ignorance of relationships among various attributes and parameters is one of the major causes of uncertainty in existing models of transportation problems. Fuzzy sets have been explored by various investigators to address the uncertainty issues due to relationships among various attributes. However fuzzy sets are not fully capable of dealing all kinds of uncertainty to provide intelligent solutions of transportation problems. A soft set is explored in this paper to model the uncertainty arising from the relationships of attributes with the parameters in a multimodal and multi objective transportation problem. The three modes of transportation incorporated in this model are road, rail and air. The real data set is prepared using the tariff, distance and time duration of transport available on websites of transport service agencies. The objectives are to minimize the cost and time duration of transportation. The proposed model evaluates multiple criteria using various combinations of different modes of transport to optimize the objectives of the problem. The model has been illustrated using the real data set using existing methods of solution. The soft set approach is found to be quite effective in dealing with the relationships of attributes with the parameters arising due to multi criteria decision making and leads to intelligent optimal solutions. The proposed model can be used as intelligent assistive system for decision making of multi objective and multimodal transportation problems.

911 Emergency Medical Services and Re-Triage to Level I Trauma Centers

Transportation problem is an integral part of this competitive world. Minimizing transportation cost of a product from sources to destinations is the main objective of traditional transportation problems. In the present context single objective transportation problem fails to meet the managerial decision making requirements which demands the multi objective transportation problems. Many real life problems can be formulated as multi objective transportation problem, and their solution requires consideration of conflicting objectives. Naturally, these problems have a number of potentially Pareto-optimal solutions. Multi-objective transportation problem refers to a special class of vector minimum linear programming problem, which usually involves multiple, conflicting, and incommensurable objective functions. Solving these complexities, the decision maker has to develop a utility function. In this paper, we develop a utility function to attain the targeted goal for a multi objective transportation problem. This utility function is developed using fuzzy membership functions considering deviations of objective function from the goal value where deviation variable has chosen as fuzzy type. Moreover, fuzzy max-min operator has been included for taking limiting value of the objective functions. Performance of the utility function to achieve proper goal is evaluated and justified by solving numerical examples using fuzzy goal programming.

The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid transportation problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction.

In this paper, a new compromise algorithm for multi-objective transportation problem (MO-TP) is developed, which is inspired by Zimmermann's fuzzy programming and the neutrosophic set terminology. The proposed NCPA is characterized by assigning three membership functions for each objective namely, truth membership, indeterminacy membership and falsity membership. With the membership functions for all objectives, a neutrosophic compromise programming model is constructed with the aim to find best compromise solution (BCS). This model can cover a wide spectrum of BCSs by controlling the membership functions interactively. The performance of the NCPA is validated by measuring the ranking degree using TOPSIS approach. Illustrative examples are reported and compared with exists models in the literature. Based on the provided comparisons, NCPA is superior to fuzzy and different approaches.

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the environment of utility function approach. MCMTP is converted to multi-objective transportation problems (MOTP) by transforming the multi-choice parameters like cost, demand, and supply to real-valued parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTP are solved by goal programming (GP) approach. Using GP, the solution of MOTP may not be satisfied all the time by the decision maker (DM) when the proposed problem contains interval-valued aspiration level. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and utility function into the MOTP and then compared the solution between them. Finally, numerical examples are presented to show the feasibility and usefulness of our paper.

A fuzzy transportation problem (FTP) includes cost, supply and demand of transportation problems. Its numbers are fuzzy numbers. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Present research paper points out a technique with an alpha cut, optimal solution for solving transportation problem. We suggest a technique to find the fuzzy optimal solution on scales of transportation problem and propose a new hexagonal representation of fuzzy numbers. In general, the comparison of balanced fuzzy transportation problem (BFTP) and unbalanced fuzzy transportation problem (UFTP) shows that the optimal transportation cost of UFTP is less than BFTP.

Disasters are the unfortunate suddenly occurring events which collapse a living society within a moment. Facebook, the most trending social media have initiated an active role to response the crisis developing a safety check feature to know about the demand of victims in an area. Through this feature the Facebook authority can confirm the requirement of the affected people in a specific area. This research have introduced a mathematical model for multi-objective solid transportation problem to quick delivery of the relief products to the devastating society according to the most prior demand of an area acquiring the best information through safety check feature launched by Facebook with limited resources. The two main objectives of the model are to minimize the total cost and minimize the total time so that relief can be executed under a limited budget responding quickly to the affected area. In this paper, fuzzy goal programming is adopted to solve the multi-objective solid transportation problem. To contemplate the performance of the model, a numerical example is presented in this paper. The numerical example is solved with LINGO optimization solver.

The length of a rail line that will minimize total transportation (user and operator) costs, and the threshold demand necessary to ensure that the resulting length of the rail line is nonzero are investigated for an urban transportation corridor. A density of demand for travel to the central business district (CBD) represented by a general function P(x) passengers per unit length of the corridor where x is the distance from the CBD is considered. The line-cost as a function of x, the costs of the rail fleet, rail and bus operating costs and passenger time costs are also considered in the formulation. The fleet size is formulated considering the peaking of demand relative to time. When the line cost is nonuniform there could be several line lengths at which the total transportation cost is minimized or even maximized locally. When the line cost per unit length is uniform, a minimum transport cost rail line of nonzero length exists only if the net gain in travel time and operating cost of transporting the total ridership a unit distance by rail, when compared to bus, exceeds the marginal line and fleet costs per unit length. In either case, the minimum transport cost rail line length can be determined easily. The effects on the line length of shifts in demand are investigated. Closed-form solutions for the line length are obtained for the cases of sectorial and rectangular corridor-sheds with uniformly distributed demand per unit area.

With the continuous development of large-scale engineering projects such as construction projects, relief support, and large-scale relocation in various countries, engineering logistics has attracted much attention. This paper addresses a multimodal material route planning problem (MMRPP), which considers the transportation of engineering material from suppliers to the work zones using multiple transport modes. Due to the overall relevance and technical complexity of engineering logistics, we introduce the key processes at work zones to generate a transport solution, which is more realistic for various real-life applications. We propose a multi-objective multimodal transport route planning model that minimizes the total transport cost and the total transport time. The model by using the ε − constraint method that transforms the objective function of minimizing total transportation cost into a constraint, resulting in obtaining pareto optimal solutions. This method makes up for the lack of existing research on the combination of both engineering logistics and multimodal transportation, after which the feasibility of the model and algorithm is verified by examples. The results show that the model solution with the introduction of the key processes at work zones produces more time-efficient and less time-consuming route planning results, and that the results obtained using the ε − constraint method are more reliable than the traditional methods for solving multi-objective planning problems and are more in line with the decision maker’s needs.

We explore the effect of the non-economic factors in the safety of fishery products as well as economic and geological factors on fishery trade across countries, using the gravity model in this study. We focus on the effect of non-economic factors, especially, Seafood Traceability system, HACCP, and SPS agreements, which have not been considered in Korean studies using the gravity model. Our findings demonstrate the followings: First, for one trade pattern- fishery export-, Korean total fishery exports and each trading partner’s total fishery imports have a significant effect on Korean fishery exports to them. The proxy variable for distance across countries, transportation time, and companies with HACCP certification have a significant effect on Korea’s fishery exports to trading partners. Second, for the other trade pattern- fishery import-, trading partners’ total fishery exports and transportation time have positive effects on Korean fishery imports from them.

Ordered fuzzy random variables: Definition and the concept of normality

This paper presents a fuzzy goal programming approach for modelling and solving multi-objective decision making problem having fuzzy random variables and fuzzy numbers associated with the system constraints. In the model formulation process, the problem is converted into an equivalent fuzzy programming problem by using chance constrained programming technique. The problem is then decomposed into sub problems by considering the tolerance limits of fuzzy numbers relating to the system constraints. The individual optimal solution of each objective is found to construct the membership goals. A two-phase fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership goals of the objectives to the extent possible by minimising under deviational variables and thereby obtaining most satisfactory solution in the decision making environment. A numerical example is solved to illustrate the proposed approach and the achieved solutions are compared with other existing methodologies.

This article introduces a general fuzzy regression model, which separates the response function on a mode and spreads of an α-level set for an observed fuzzy number, to estimate a fuzzy relation between two fuzzy random variables. We construct the general fuzzy regression model using least squares estimation and best response functions on the mode and spread of an α-level set for the fuzzy number when the response variable is an LR-fuzzy number and independent variables are crisp numbers. Then we derive a crisp mean and variance of the predicted fuzzy number, and compare the accuracy of our proposed fuzzy regression model with other fuzzy regression models suggested by many authors.