Multi-objective Multi-item Solid Transportation Problem Research Articles

New approach to solve fuzzy multi-objective multi-item solid transportation problem

This paper explores the study of Multi-Objective Multi-item Solid Transportation Problem (MMSTP) under the fuzzy environment. Realizing the impact of real-life situations, here we consider MMSTP with parameters, e.g., transportation cost, supply, and demand, treat as trapezoidal fuzzy numbers. Trapezoidal fuzzy numbers are then converted into nearly approximation interval numbers by using (P. Grzegorzewski, Fuzzy Sets Syst. 130 (2002) 321–330.) conversation rule, and we derive a new rule to convert trapezoidal fuzzy numbers into nearly approximation rough interval numbers. We derive different models of MMSTP using interval and a rough interval number. Fuzzy programming and interval programming are then applied to solve converted MMSTP. The expected value operator is used to solve MMSTP in the rough interval. Thereafter, two numerical experiments are incorporated to show the application of the proposed method. Finally, conclusions are provided with the lines of future study of this manuscript.

On Multi-Objective Multi-Item Solid Transportation Problem in Fuzzy Environment

This paper discusses the reliability of multi-objective multi-item solid transport (F-MOMIST) problem with the transportation of penalties represented by the trapezoidal fuzzy numbers. We extended the existing F-MOMIST by introducing the fuzzy efficient concept and fuzzy crisp. We propose a weighting Tchebycheff approach to efficiently solve F-MOMIST. In the proposed approach, we first describe the first type of stability set corresponding to the optimal $$\alpha $$ -Pareto solution and then use the proposed approach to evaluate the first type of stability set corresponding to the $$\alpha $$ -optimal compromise solutions. A numerical case study to check the validity of the proposed approach is presented. The results of comparative experiments show that the proposed method is sufficiently effective in solving F-MOMIST and has better performance than the existing methods.

An application of FISM and TOPSIS to a multi-objective multi-item solid transportation problem

This paper deals a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints in profit maximization and time minimization forms. Following fuzzy chance programming, more specificity possibility-necessity theory, an approach to conversion of the imprecise MMSTP to the equivalent deterministic form is formulated. Fuzzy interactive satisfied method is adopted to derive optimal compromise solutions of the MMSTP through generalized reduced gradient technique. In order to obtain best non-dominating solution, the technique for order preference by similarity to ideal solution is applied. Finally, a numerical example and a statistical test namely, analysis of variance illustrate and signify the feasibility and validity of the proposed model and techniques.

A multi-objective multi-item solid transportation problem with vehicle cost, volume and weight capacity under fuzzy environment

Generally, in transportation problem, full vehicles (e.g., light commercial vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and transportation cost of a vehicle has to be paid irrespective of the fulfilment of the capacity of the vehicle. Besides the transportation cost, total time that includes travel time of a vehicle, loading and unloading times of products is also an important issue. Also, instead of a single item, different types of items may need to be transported from some sources to destinations through different types of conveyances. The optimal transportation policy may be affected by many other issues like volume and weight of per unit of product, unavailability of sufficient number of certain types of vehicles, etc. In this paper, we formulate a multi-objective multi-item solid transportation problem by addressing all these issues. The problem is formulated with the transportation cost and time parameters as fuzzy variables. Using credibility theory of fuzzy variables, a chance-constraint programming model is formulated, and is then transformed into the corresponding deterministic form. Finally numerical example is provided to illustrate the problem.

Uncertain multi-objective multi-product solid transportation problems

The solid transportation problem is an important generalization of the classical transportation problem as it also considers the conveyance constraints along with the source and destination constraints. The problem can be made more effective by incorporating some other factors, which make it useful in real life situations. In this paper, we consider a fully fuzzy multi-objective multi-item solid transportation problem and present a method to find its fuzzy optimal-compromise solution using the fuzzy programming technique. To take into account the imprecision in finding the exact values of parameters, all the parameters are taken as trapezoidal fuzzy numbers. A numerical example is solved to illustrate the methodology.

Uncertain programming model for multi-item solid transportation problem

In this paper, an uncertain Multi-objective Multi-item Solid Transportation Problem (MMSTP) based on uncertainty theory is presented. In the model, transportation costs, supplies, demands and conveyances parameters are taken to be uncertain parameters. There are restrictions on some items and conveyances of the model. Therefore, some particular items cannot be transported by some exceptional conveyances. Using the advantage of uncertainty theory, the MMSTP is first converted into an equivalent deterministic MMSTP. By applying convex combination method and minimizing distance function method, the deterministic MMSTP is reduced into single objective programming problems. Thus, both single objective programming problems are solved using Maple 18.02 optimization toolbox. Finally, a numerical example is given to illustrate the performance of the models.

Expected value of intuitionistic fuzzy number and its application to solve multi-objective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment

Expected value of intuitionistic fuzzy number and its application to solve multi-objective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment

A Fuzzy Set-Based Approach to Multi-objective Multi-item Solid Transportation Problem Under Uncertainty

In this paper, a multi-objective multi-item solid transportation problem (MOMISTP) with parameters, e.g., transportation costs, supplies, and demands, as trapezoidal fuzzy variables is formulated. In this MOMISTP, there are limitations on some items and conveyances so that some special items cannot be carried by means of some special conveyances. With the use of the nearest interval approximation of trapezoidal fuzzy numbers, an interval programming model is constructed for the fuzzy MOMISTP and then this model is turned into its deterministic form. Then, a new interval fuzzy programming approach is developed to obtain the optimal solution of the problem. Finally, a numerical example is presented for illustration.

On Possibilistic Multi-Objective Multi-item Solid Transportation Problems

The solid transportation problem (STP) arises when bounds are given on three item properties. These properties are usually: sources destination and type of product or mode of transport. In this paper, a possibilistic multi-objective multi-item solid transportation problem (Poss MOMISTP) is studied. The problem is considered by incorporating possibilistic data into the objective functions coefficients. The efficient solutions and the stability of Poss MOMISTP problem are investigated. The concept of  -Possibly efficient is introduced in which the ordinary efficient solution is  -tended based on the  level of possibilistic variables. A necessary and sufficient condition for such solution is established. A relationship between solutions of possibilistic levels is constructed. The stability set of the first kind corresponding to one solution of the  level of possibilistic variables is determined. An illustrative numerical example is given in the sake of the paper to clarify the obtained results.

On Fuzzy Multiobjective Multi-Item Solid Transportation Problem

A transportation problem involving multiple objectives, multiple products, and three constraints, namely, source, destination, and conveyance, is called the multiobjective multi-item solid transportation problem (MOMISTP). Recently, Kundu et al. (2013) proposed a method to solve an unbalanced MOMISTP. In this paper, we suggest a method, which first converts an unbalanced problem to a balanced one. In one case of an example, while the method proposed by Kundu et al. concludes infeasibility, our method gives a feasible solution.

Multi-objective multi-item solid transportation problem with fuzzy inequality constraints

Abstract Zimmermann (Int. J. Gen. Syst. 2:209-215, 1976) first introduced the concept of fuzzy inequality in the field of linear programming problem (LPP). But this concept is hardly used in any real life applications of LPP. So, in this paper, a multi-objective multi-item solid transportation problem (MMSTP) with fuzzy inequality constraints is modeled. Representing different preferences of the decision maker for transportation, three different types of models are formulated and analyzed. Fuzzy inequality solid transportation problem is converted to parameter solid transportation problem by an appropriate choice of flexible index, and then the crisp solid transportation problem is solved by the algorithm (Cao in Optimal Models and Methods with Fuzzy Quantities, 2010) for decision values. Fuzzy interactive satisfied method (FISM), global criterion method (GCM) and convex combination method (CCM) are applied to derive optimal compromise solutions for MMSTP by using MatLab and Lingo-11.0. The models are illustrated with numerical examples and some sensitivity analysis is also presented.

Multi-objective multi-item solid transportation problem in fuzzy environment

A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of “minimum of fuzzy number” is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.