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.

Entropy-based multi-item solid transportation problems with uncertain variables

This paper focuses on modeling and optimization of entropy-based uncertain multi-item solid transportation problems (MISTPs), in which direct costs, supplies, demands, conveyance capacities are uncertain nature. The purpose is to minimize the total uncertain cost via maximum entropy which ensures uniform delivery of products from sources to destinations through conveyances. The expected value programming and expected constrained programming models for optimizing the entropy-based uncertain MISTPs are constructed. These models are based on uncertainty theory. Subsequently, the constructed models are converted into their deterministic equivalences which are solved using two known mathematical programming methods. Finally, a numerical example is given to illustrate the models.

Uncertain random programming models for fixed charge multi-item solid transportation problem

Uncertain random programming models for fixed charge multi-item solid transportation problem

Simulation approach to solve fuzzy fixed charge multi-item solid transportation problems under budget constraint

Simulation approach to solve fuzzy fixed charge multi-item solid transportation problems under budget constraint

Simulation approach to solve fuzzy fixed charge multi-item solid transportation problems under budget constraint

In this paper, we have developed a dominate-based genetic algorithm to solve fuzzy fixed charge multi-item solid transportation problems (FFCMISTPs) under budget constraint in fuzzy environment, in which sources, demands, capacities of conveyances, unit selling prices, unit purchasing costs, fixed charges, unit transportation costs and transportation times are fuzzy in nature. Here, transportation problems are formulated in the form of profit maximisation problems and solved. For maximisation, a dominate-based genetic algorithm (DBGA) with varying population size, cyclic crossover, two-point mutation is developed which can deal with single-objective transportation problems. The developed algorithm is tested against some test functions and its efficiency is established in terms of iteration numbers for single objective. The fuzzy objective function and constraints are reduced to corresponding deterministic ones using graded mean integrating value, possibility/necessity measures and chance constrained programming method. The reduced crisp problems are solved using developed genetic algorithm. The models are illustrated with numerical examples. The real life practical implication of the model is also presented.

Some special fixed charge solid transportation problems of substitute and breakable items in crisp and fuzzy environments

In this paper, some special fixed charge multi-item solid transportation problems which include damageability (breakability), substitutability and paths into consideration are developed and investigated in crisp and fuzzy environments. The breakability of substitute items varies due to the transported amount, conveyance type and traversed distance (path). The substitutability of the items depends on both the supply side by the management’s discretion (ad hoc quantity), and the demand side by the item’s price (price dependent). The vagueness of the model parameters is introduced by fuzzy set theories and then defuzzied applying possibility measure. Models are formulated as profit maximization problems, solved using generalized reduced gradient method and illustrated through numerical experiments. Sensitivenesses of profits on the degrees of substituteness are also presented numerically. Conventional solid (3D) and general (2D) transportation problems are derived as particular cases. Some useful managerial decisions are derived.

Uncertain programming models for fixed charge multi-item solid transportation problem

This paper investigates the fixed charge multi-item solid transportation problem, in which the fixed charges, direct costs, transportation capacities, supply and demand are uncertain variables. Based on the uncertainty theory, expected value programming model and chance-constrained programming model for fixed charge multi-item solid transportation problem are constructed, respectively. We can obtain the optimal solution of two models via solving the relevant deterministic models. Finally, a numerical experiment is implemented to illustrate the application of the models.

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 note on “Fully fuzzy fixed charge multi-item solid transportation problem”

Giri et al. [P.K. Giri, M.K. Maiti, M. Maiti, Fully fuzzy fixed charge multi-item solid transportation problem, Applied Soft Computing, 27 (2015) 77–91] proposed an approach for solving mathematical programming of fully fuzzy fixed charge multi-item solid transportation problems (FFFCMISTP) and claimed that it is better to use their proposed approach as compared to the existing method [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathematical Modelling, 35 (2011) 817–823]. The aim of this note is to point out that Giri et al. have used some mathematical incorrect assumptions in their proposed approach and hence the claim of Giri et al. is not valid.

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.

Multi-item solid transportation problem with type-2 fuzzy parameters

In this paper, a multi-item solid transportation problem with parameters, e.g., transportation costs, supplies and demands as type-2 triangular fuzzy variables is formulated. In this problem there are restrictions on some items and conveyances so that some specific items cannot be transported through some particular conveyances. With the critical value (CV)-based reductions of type-2 fuzzy variables, a chance-constrained programming model is formulated for the problem and then this model is converted to an equivalent deterministic form. Here, we propose a method to find nearest interval approximations for continuous type-2 fuzzy variables. A deterministic form for the problem is also obtained by applying interval analysis using the interval approximations of continuous type-2 fuzzy variables. The reduced deterministic problems are solved using a gradient based optimization – Generalized Reduced Gradient (GRG) technique (using LINGO solver) and Genetic Algorithm. Numerical example is provided to illustrate the problem and methods.

English

English

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.

Interval Oriented Entropy Based Multi-item Solid Transportation Problem with Budget and Breakability

To maximization the total profit and minimization the total cost we investigate two transportation models with interval transportation parameters and we present a solution of our newly developed models using appropriate methods. The solid transportation problem has been formulated with and without interval entropy function defined by Shannon’s measure of entropy. Also an additional constraint on the total budget at each destination is imposed. When we transport the goods from plants to destination then few items should be damage due to bad condition of route and vehicles, for this reason we introduce the breakability in our respective models. We employ two different approaches (Hu and Wang’s Approach and Mahato and Bhunia’s Approach) based on interval ranking and made a comparison on it. To convert the multi-objective programming problem into single-objective problem we apply weighted sum method. The models are illustrated with numerical examples and solved using the LINGO.13 optimization software. The results of the models with and without entropy are also obtained and compared.