Strategic planning for addressing the multi-option parameters for sustainable decision-making in multi-objective solid transportation problem

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.

Solution of Multi-Objective Interval Solid Transportation Problems Using Expected Value     International Journal of Computer & Organization Trends  (IJCOT)             © 2014 by IJCOT

An interactive possibilistic programming for fuzzy multi objective solid transportation problem

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.

Many problems appear to be arising in the present as a result of variations in transportation networks. The stochastic fixed-charge transportation problem (SFCTP) is one such problem. The SFCTP is transformed into a chance-constrained programming (CCP) problem where supply and demand are stochastic and objective functions are in a rough interval. In this model, to analyze the multi-objective rough interval stochastic fixed-charge transportation problem (MORISFCTP), where the objective function coefficients are represented by rough intervals and the supply and destination factors are probabilistic constraints. This model operates an expected value operator to deal with uncertainty, in which the coefficient of the objective functions in the fuzzy is changed to a crisp form, and the probabilistic constraints are converted to a deterministic form by the Weibull distribution. To produce the optimal compromise solutions of the proposed model, three distinct methods are used: the fuzzy programming approach, the method of a linear weighted sum, and the €-constraint method. Lastly, the paper delivers a practical illustration of a MORISFCTP to demonstrate the usefulness and feasibility of the suggested methodology.

Multi-choice stochastic transportation problem involving extreme value distribution

In classical fractional transportation programming problem, we want to optimize the objective function in the form of one or several ratios subject to some linear constraints. If in multi-objective transportation problem, objective function is in ration of two linear function under some linear restrictions, then the problem is called multi-objective linear fractional transportation problem (MOLFTP). In this paper we propose a new method to solve multi-objective linear fractional transportation problem which is extension of Nomani et al. (Int J Manag Sci Eng Manag (2016) [9]). Two numerical problems are presented to validate the proposed algorithm.

Recently, Resende and Veiga [{\it SIAM J. Optim.}, 3 (1993), pp. 516--537] proposed an efficient implementation of the dual affine (DA) interior-point algorithm for the solution of linear transportation models with integer costs and right-hand-side coefficients. This procedure incorporates a preconditioned conjugate gradient (PCG) method for solving the linear system that is required in each iteration of the DA algorithm. In this paper, we introduce an incomplete $QR$ decomposition (IQRD) preconditioning for the PCG algorithm. Computational experience shows that the IQRD preconditioning is appropriate in this instance and is more efficient than the preconditioning introduced by Resende and Veiga. We also show that the primal dual (PD) and the predictor corrector (PC) interior-point algorithms can also be implemented by using the same type of technique. A comparison among these three algorithms is included and indicates that the PD and PC algorithms are more appropriate for the solution of transportation problems with well-scaled cost and right-hand-side coefficients and assignment problems with poorly scaled cost coefficients. On the other hand, the DA algorithm seems to be more efficient for assignment problems with well-scaled cost coefficients and transportation problems whose cost coefficients are badly scaled.

The study addresses a dynamic multi-objective multi-item solid transportation problem (MOMISTP) within the framework of a real-world fertilizer supply chain with varying cost and time. Unlike traditional static approaches, the problem is formulated dynamically to reflect monthly fluctuations in supply, demand, and conveyance availabilities. A feedforward neural network (FNN) is trained over the real-world historical data of supply, demand and conveyance availabilities to forecast monthly transportation cost and time. These forecasts are utilized as dynamic parameters in the objective functions, resulting in a sequence of dynamic optimization problems. Each monthly instance of the MOMISTP is solved using a dynamic NSGA-II framework. The variability along each time step is quantified using the Frobenius norm, which captures the intensity of environment change between two consecutive time steps. The quantified value is integrated with an ensemble-inspired prediction strategy to produce new solutions based on the changed environment along the time step. The ensembled approach comprises center-based prediction, knee-based prediction, random prediction and boundary population inclusion strategies. These methods are combined in the ratio of 3:3:3:1 to form an initial population for dynamic NSGA-II for further optimization over 12 months. This integrated approach enables effective adaptation to environmental changes and accurate forecasting of transportation parameters over 12 months. The strong correlation between cost and time across months suggests limited trade-offs; thus, a representative solution can be chosen for each time step. Overall, this methodology offers a robust decision-support tool for dynamic and resource-constrained supply chain environments, particularly those requiring time-sensitive logistics planning.

Solving transportation problems is essential in engineering and supply chain management, where profitability depends on optimal traffic flow. This study proposes risk-control approaches for two bottleneck transportation problems with random variables and preference levels to objective functions with risk parameters. Each proposed model is formulated as a multiobjective programming problem using robust-based optimization derived from stochastic chance constraints. Since it is impossible to obtain a transportation pattern that optimizes all objective functions, our proposed models are numerically solved by introducing an aggregation function for the multiobjective problem. An exact algorithm that performs deterministic equivalent transformations and introduces auxiliary problems is also developed.

This paper is to integrate among solid transportation problem, budget constraints and carbon emission with probable maximum profit. The range of air pollution and climate change are effected by \({\text {CO}_2}\) gas emission and other greenhouse gases from myriad transportation systems. Henceforth, our target is to minimize carbon emission for pollution-free environment. 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 real-life transportation problem. Due to time pressure, data limitation, lack of information or measurement errors in practical problems, there exist some hesitations. Based on the fact, decision maker considers indeterminacy in the designed problems. To overcome such hesitancy of occurrence and non-occurrence in 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 is utilized here to find the compromise solution of the multi-objective transportation problem. 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.

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.

Weakly admissible transformations are introduced for solving algebraic assignment and transportation problems, which cover so important classes as problems with sum objectives, bottleneck objectives, lexicographical objectives and others. A transformation of the cost matrix is called weakly admissible, if there are two constants α and β in the underlying semigroup that for all feasible solutions the composition of α and the objective value with respect to the original cost coefficients is equal to the composition of β and the objective value with respect to the transformed cost coefficients. The elements α and β can be determined by shortest path algorithms. An optimal solution for the algebraic assignment problem can be found after at most n weakly admissible transformations, therefore the proposed method yields an O(n 3) algorithm for algebraic assignment problems.

Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters: source, destination, and conveyance. The objectives such as transportation cost, transportation time, transportation safety level, and objectives in terms of environmental and social issues are generally in conflict with each other. In this paper, we present a fuzzy approach to bring these conflicting objectives together as high as possible. Instead of using the linear membership function, which is frequently used in the literature for ease of use, we use the hyperbolic membership function in our approach. Also, while most of the papers in the literature deal with the standard equality constrained form of MSTP, the mixed constrained form is addressed in this paper. Finally, a numerical example from the literature is used to illustrate the construction of the hyperbolic membership function and how well it represents the objective functions’ degree of satisfaction.

This paper introduces a grey quadratic programming (GQP) method asa means for decision making under uncertainty. The method improves upon existing grey linear programming (GLP) methods by allowing the consideration of the effects of economies of scale on cost coefficients in the objective function. The approach also has advantages over a grey nonlinear programming method, since a global optimum is obtainable and the model is moderately easy to solve through commercially available quadratic programming packages. The modelling approach is applied to a hypothetical problem of waste flow allocation within a municipal solid waste management system. The results indicate that, compared with the GLP method, GQP provides a more effective means for reflecting system cost variations and may therefore generate more realistic and applicable solutions.