Multi-objective Transportation Research Articles

Fuzzy multi objective transportation problem – evolutionary algorithm approach

This paper deals with fuzzy multi objective transportation problem. An fuzzy optimal compromise solution is obtained by using Fuzzy Genetic Algorithm. A numerical example is provided to illustrate the methodology.

A Novel Approach for the Solution of Multi Objective Interval Transportation Problem

In this paper, we propose a Multi-objective transportation problem where the source and destination parameters are chosen as interval numbers. The main objective of the problem is to minimize the total transportation cost and total delivery time. A new algorithm is proposed to determine initial allocation to the basic cells and the corresponding Multi-objective interval transportation cost without converting the problem to its classical version. The initial interval transportation cost may vary during optimality test when allocations are changed. Numerical examples are presented to illustrate the proposed method.

Bi-criteria transportation problem with multiple parameters

This paper introduces a bi-criteria transportation problem with multiple parameters which brings together the concept of price discrimination from the area of marketing management to the world of multi objective transportation problems. The problem deals with two objectives, the overall shipment cost and the bottleneck time of shipment. Both the objectives are of minimization type and have multi-choice coefficients pertaining to differential marketing strategies or different modes of transportation available. First, the problem with minimum availability and demand of goods is solved and then the problem is extended to the case of interval demand and supply. By iteratively solving multi-choice variants of a cost minimizing transportation problem/minimum cost flow problem, all Pareto optimal time–cost pairs are obtained. The proposed algorithm for both the variants is successfully implemented and solved using the CPLEX optimization package.

A multi-objective transportation model under neutrosophic environment

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 multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

New approach for solving intuitionistic fuzzy multi-objective transportation problem

Multi-objective transportation problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IF numbers. Considering the specific cut interval, the IF transportation cost matrix is converted to interval cost matrix in our proposed problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, which includes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed problem. Finally, we present the conclusions with the future scopes of our study.

Paradox in a Linear Multi Objective Transportation Problem

Paradox in a Linear Multi Objective Transportation Problem

Multi Dimensional Honey Bee Foraging Algorithm Based on Optimal Energy Consumption

In this paper a new nature inspired algorithm is proposed based on natural foraging behavior of multi-dimensional honey bee colonies. This method handles issues that arise when food is shared from multiple sources by multiple swarms at multiple destinations. The self organizing nature of natural honey bee swarms in multiple colonies is based on the principle of energy consumption. Swarms of multiple colonies select a food source to optimally fulfill the requirements of its colonies. This is based on the energy requirement for transporting food between a source and destination. Minimum use of energy leads to maximizing profit in each colony. The mathematical model proposed here is based on this principle. This has been successfully evaluated by applying it on multi-objective transportation problem for optimizing cost and time. The algorithm optimizes the needs at each destination in linear time.

Integrating uncertainty considerations into multi-objective transportation network design projects accounting for environment disruption

Few previous works integrated both uncertainty and environment disruption into traffic network design problems (NDPs). This study aims to address this gap. First, the mathematical framework of the strategic user equilibrium (StrUE) traffic assignment under volatility of both total travel demand and link capacity is analyzed. Second, we incorporate the StrUE traffic assignment into a network design project and propose a multi-objective bi-level NDP program. Two objective functions are formulated, which are respectively to minimize the expected total system travel time and minimize the expected total system off-gas emissions under StrUE. Third, we develop two tailored solution methods – an enumerative algorithm and a metaheuristic method based on a genetic algorithm. Finally, systematic evaluation of the performance of the proposed approach is conducted. The results highlight that ignoring uncertainty considerations can result in sub-optimal design solutions in terms of expected network performance. Also, the two objectives, to minimize system-level travel time and vehicle emission, are conflicting for certain design scenarios.

A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment

In this paper, we employ all the parameters as trapezoidal interval type-2 fuzzy numbers to cope with ambiguity and vagueness problem. There are two issues being addressed in this paper. The first is the selection of the most convenient transportation mode. We present a method for solving multi-criteria decision-making problem to deal with evaluating and ranking alternatives from the best to the worst with respect to decision maker(s) preferences. This is applied to find the most preferred transportation mode among available modes concerning some evaluation criteria for a transportation problem. A possibility degree is used for comparisons between the overall values of alternatives to raise a possibility degree matrix. Based on that matrix, the alternatives are ranked according to the ranking vector derived from the matrix, and the best one is selected. The second is to construct a multi-item transportation problem using that preferred mode of transportation. To get the crisp model, a defuzzification approach is adopted. To convert multi-objective transportation problem into a single-objective problem, two different techniques (i) fuzzy goal programming method and (ii) convex combination method are used. Then the reduced single-objective problem is solved by generalized reduced gradient method (LINGO-14.0) and a set of optimal solutions are obtained and presented graphically.

On Solving Multiobjective Transportation Problems with Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

Multiobjective Transportation Problem Using Fuzzy Decision Variable Through Multi-Choice Programming

This paper analyzes the study of Multiobjective Transportation Problem (MOTP) under the consideration of fuzzy decision variable. Usually, the decision variable in a Transportation Problem is taken as real variable. But, in this paper, the decision variable in each node is selected from a set of multi-choice fuzzy numbers. Inclusion of multiple objectives into transportation problem with fuzzy decision variable makes it a Multiobjective Fuzzy Transportation Problem (MOFTP). In this paper, a new formulation of mathematical model of MOFTP with fuzzy goal of each objective function is enlisted. Thereafter the solution technique of the formulated model is described through multi-choice goal programming approach. Finally, a numerical example is presented to show the feasibility and usefulness of this article.

Comparative study on credibility measures of type-2 and type-1 fuzzy variables and their application to a multi-objective profit transportation problem via goal programming

Abstract In real world applications supply, demand and transportation costs per unit of the quantities in multi-objective transportation problems may be hardly specified accurately because of the changing economic and environmental conditions. It is also significant that the time required for transportation should be minimized. In this paper, we have presented three reduction methods for a type-2 triangular fuzzy variable (T2TrFV) by adopting the critical value (CV). Three generalized expected values (optimistic, CV and pessimistic) are derived for T2TrFVs with some special cases. Then a multi-objective profit transportation problem (MOPTP) with fixed charge (FC) cost has been formulated and solved in type-2 fuzzy environment. Unit transportation costs, FC, selling prices, unit transport times, loading and unloading times, total supply capacities and demands are all considered as triangular Type-2 fuzzy numbers. The MOPTP has been converted into a single objective by using the goal programming technique and the weighted sum method. The deterministic model is then solved using the Generalized Reduced Gradient method Lingo 14.0. Numerical experiments with some sensitivity analysis are illustrated the application and effectiveness of the proposed approaches.

Expectations of the reductions for type-2 trapezoidal fuzzy variables and its application to a multi-objective solid transportation problem via goal programming technique

In this paper, based on the concepts of credibility measure and expectation theory, we derive the expectation formulae for the three reductions of a type-2 trapezoidal fuzzy variable (T2TrFV), which are attained by adopting the critical value (CV) reduction methods. We minimize the total transportation cost and the total transportation time over a single layered distribution system consisting of vendors and customers represented as a multi-objective solid transportationproblem. To portray the uncertainty in a real life choice environment, we consider the unit cost of transportation, demands, availabilities, conveyance capacities, unit transportation time and unit loading and unloading time as T2TrFVs. The corresponding deterministic model, which is obtained by the application of expectation formulas deduced earlier, is converted to a single objective optimization problem using goal programming technique and weighted sum method via the soft computing technique—generalized reduced gradient (LINGO-14.0). A numerical experiment is finally illustrated and corresponding graphical representations are provided.

Interactive fuzzy stochastic multiobjective purchase and transportation planning for food retailing

Interactive fuzzy stochastic multiobjective purchase and transportation planning for food retailing

Interactive fuzzy stochastic multiobjective purchase and transportation planning for food retailing

This paper considers purchase and transportation planning for food retailing in Japan where the food retailer deals with vegetables and fruits which are purchased at the central wholesale markets in several cities, and transports them by truck from each of the central wholesaler markets to the food retailer's storehouse. From a stochastic perspective, by carefully reviewing parameters in our original problem formulation, through the introduction of stochastic parameters, multiobjective linear stochastic programming problems are introduced. By using the typical stochastic models including the expectation model, the fractile model, the probability model together with chance constrained programming, the formulated multiobjective linear stochastic programming problems are transformed into deterministic ones. Assuming the decision maker has the fuzzy goal for each of the objective functions, several interactive fuzzy satisficing methods are presented for deriving a satisficing solution for the decision maker by updating the reference membership levels.

English

English

Multi-objective two-stage grey transportation problem using utility function with goals

Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.

A Fuzzy Technique for Solving Rough Interval Multiobjective Transportation Problem

In this paper the rough interval multiobjective transportation problem (RIMOTP) is presented and its solution procedure is introduced. The concept of solving the interval multiobjective transportation problem is applied for solving RIMOTP. So, The rough interval in the objective function and the constrains, is represented by three different models and such models are solved by using fuzzy programming technique based on the right limit, the center and the half-width of each rough interval using possibly region. Numerical examples are provided to illustrate the solution procedure of three possible types of the original problem. General Terms Fuzzy Programming Technique, Transportation Problem, rough interval multiobjective transportation

Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.