Showing papers by "Sankar Kumar Roy published in 2016"

Multi-objective Transportation Problem with Cost Reliability Under Uncertain Environment

Abstract: This paper analyzes the study of a Multi-Objective Transportation Problem (MOTP) under uncertain environment. Assuming the uncertainty in real-life decision making problems, the concept of reliability is incorporated in the transportation cost and the effectiveness is justified through the proposed MOTP. Again, considering the real phenomenon in the MOTP, we consider the transportation parameters, like as supply and demand as uncertain variables. Also, we consider the fuzzy multi-choice goals to the objective functions of the MOTP; and Fuzzy Multi-Choice Goal Programming (FMCGP) is used to select the proper goals to the objective functions of the proposed MOTP. Here, the proposed study is not only confined to obtain the compromise solution but also to fix up the proper goals to the objective functions of the MOTP. A numerical example is presented to illustrate and justify the proposed study. Finally, the paper ends with the conclusion and future study.

Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand

Abstract: This study develops a mathematical model for a transportation problem consisting of a multi-objective environment with nonlinear cost and multi-choice demand. The objective functions of the proposed transportation problem are non-commensurable and conflict with each other. The focus of the paper is on objective functions of nonlinear type, which occur due to the extra cost of supplying goods remaining at their points of origin to various destinations, and on demand parameters that are considered to be of multi-choice type. Thus, the mathematical model is formulated by considering nonlinear cost and multi-choice demand. Multi-choice programming models cannot be solved directly. A general transformation technique is developed to make multi-choice demand tractable with the help of binary variables. Therefore, an equivalent multi-objective decision making model is established in order to find the optimal solution of the problem. The outcome from a numerical example demonstrates the feasibility of the proposed...

Solving matrix game with rough payoffs using genetic algorithm

Abstract: In this paper, we analyze a matrix game using a rough programming approach. The combination of a matrix game and a rough programming approach represents a new class defined as a rough matrix game. The pay-off elements are characterized by rough variables, and the uncertainties of the rough variables are measured using a measure known as trust. Based on this trust measure, we defined trust equilibrium strategies and a rough expected value. We derived a series of optimal solutions to a rough matrix game using a genetic algorithm. We present a numerical example that illustrates the effectiveness of our rough matrix game.

Analysis of Prey-Predator Three Species Fishery Model with Harvesting Including Prey Refuge and Migration

Abstract: In this article, a prey-predator system with Holling type II functional response for the predator population including prey refuge region has been analyzed. Also a harvesting effort has been considered for the predator population. The density-dependent mortality rate for the prey, predator and super predator has been considered. The equilibria of the proposed system have been determined. Local and global stabilities for the system have been discussed. We have used the analytic approach to derive the global asymptotic stabilities of the system. The maximal predator per capita consumption rate has been considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Also, we have used fishing effort to harvest predator population of the system as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent is earned from the resource. Finally, we have presented some numerical simulations to verify the analytic results and the system has been analyzed through graphical illustrations.

An inventory model with declining demand market for deteriorating items under a trade credit policy

Abstract: The main purpose of this paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items under a trade credit policy to reflect more realistic situations within an economic product quantity framework. In this paper, we analyse an inventory model when the supplier offers the retailer a credit period to settle the account, if the ret ailer orders a large quantity. The proposed study is meant for a declining demand market in which shortages are not allowed. The demand rate is a decreasing function of time and the deterioration rate is a constant fraction of the on-hand inventory. The mathematical formulation is explored by numerical examples. An analysis of the sensitivity of parameters on the optimal solution of our proposed study is carried out.

Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply

Abstract: This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice parameters. Assume that the supply parameters of the constraints in a transportation problem (TP) follow logistic distribution. The main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required demand. Using stochastic programming, the stochastic supply constraints of the TP are transformed into deterministic constraints. Finally, a non-linear deterministic model is formulated. Using Lingo software, the optimal solution of the proposed problem is derived. To illustrate the methodology, a real-life problem on the TP is considered.

Solving multi-objective transportation problem with interval goal using utility function approach

Abstract: This paper presents the study of transportation problem (TP) with interval goal under multiple objective environment. Most of the multi-objective transportation problems (MOTP) are solved by goal programming (GP) approach. Using GP, the solution of MOTP may not be satisfied all 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, a real-life problem on TP is considered to show the feasibility and usefulness of our paper.

An approach to solve fuzzy interval valued matrix game

Abstract: The conventional game theory is based on known payoffs. In the real situations, usually the payoffs are not known and have to be approximated. The aim of this paper is to develop a simple and an effective fuzzy multi-objective linear programming method for solving matrix game in which the payoffs are expressed with fuzzy intervals. Since, the payoffs of the matrix game are fuzzy intervals, the value of the matrix game is also fuzzy interval. Using upper and lower bounds of the payoffs, we obtain upper and lower bounds of the value of the matrix game by fuzzy multi-objective linear programming method. Lastly, a numerical example is given to illustrate the method.

Multi-choice stochastic bi-level programming problem in cooperative nature via fuzzy programming approach

Abstract: In this paper, a Multi-Choice Stochastic Bi-Level Programming Problem (MCSBLPP) is considered where all the parameters of constraints are followed by normal distribution The cost coefficients of the objective functions are multi-choice types At first, all the probabilistic constraints are transformed into deterministic constraints using stochastic programming approach Further, a general transformation technique with the help of binary variables is used to transform the multi-choice type cost coefficients of the objective functions of Decision Makers(DMs) Then the transformed problem is considered as a deterministic multi-choice bi-level programming problem Finally, a numerical example is presented to illustrate the usefulness of the paper

A comprehensive study on transportation problems under multi-choice environment

Abstract: Transportation problems sustain economic and social activity and are treated as central nerve system to operations research and management science. Based on day-by-day competitive market scenario several types of decision making problems are introduced using the classical sense of transportation problem to find better decisions. Although, the classical transportation problem defines the way to minimize total cost of a transportation system, but nowadays it is used for several objectives like optimizing profit, minimizing transportation time, fixing of cost of goods, etc. by using several methodologies. Considering the real-world situations, transportation problems are developed in many decision making problems under several uncertain environments. Optimization under multi-choice environment is also a kind of uncertain programming problem which mainly occurred due to the presence of multi-choice parameter in optimizing function or in the feasibility conditions or in both. Incorporating the daily-life transportation situations for selection of route under multiple choice possibilities in a transportation problem, the multi-choice TP is developed. This thesis is devoted to transportation problem under the different environments considering the multi-choice programming framework. The single-objective TP is not adequate to handle real-life decision making problems, owing to present competitive market scenario, we consider our study in multi-objective window. To cover all real-life situations on TPs, we introduce the multi-objective function in our considered TP in this thesis. Again, linear programming problems are not sufficient for formulating all types of decision making problem in real-life situations. As a result, non-linear programming problems have been incorporated into the multi-objective TPs. Here, in the thesis, the non-linear objective function is occurred in the TP due to some goods are left after distributing the goods from the origin to the destination points. An optimization problem becomes a goal programming problem if the objective functions have some specific aspiration level of satisfaction which are known as the goal of the objective functions. Goal programming approach is a well known technique to solve multi-objective transportation problems. But GP is not always producing better optimal solutions. Here, we propose a new way to solve MOTP by revised multi-choice goal programming and utility function approach. In this study, we present a better result of MOTP using utility function approach in compare to GP or RMCGP. Again, conic scalarization function is incorporated to solve the multi-choice MOTP. The CSF is presented as much better technique in compare to GP and RMCGP technique. Transportation time is also an important factor in a TP and so it is also required to minimize transportation time along with the minimization of transportation cost. In this research contents, we introduce a new procedure to solve bi-objective transportation problem namely time and cost minimizing TP under multi-choice interval cost parameters. Considering the real-life situations, we develop a transportation problem under fuzzy decision variable. Considering the fuzzy multi-choice goal corresponding to each of the allocations, we incorporate a new class of TP namely FTP. We extend the study into multi-objective environment for better results of FTP. We initiate the study of cost reliability in the multi-objective transportation problem under uncertain environment. Assuming the uncertainty in real-life decision making problems, the concept of reliability is incorporated in the transportation cost and the effectiveness is justified through the proposed MOTP. Furthermore, considering the real phenomenon in the MOTP, we treat the transportation parameters, like as supply and demand as uncertain variables and obtain a better solution in compare to traditional TPs. In this thesis, we attempt to formulate the mathematical model of Two-Stage multi-objective transportation problem where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate the interval grey parameters for supply and demand in the Two-Stage MOTP, and a procedure is applied to reduce the interval grey numbers into real numbers. Choosing several modes of transportation in a TP, a new method is designed for solving transportation problem by introducing the multi-modal transport systems. Here we incorporate the situation of multi-mode of transportation and analyze the way to solve TP under this situation and propose a better mode of transportation for optimal solution. Again, we consider the study of multi-choice multi-item TP in the inventory optimization problem. Two different classes of TP such as inventory optimization and transportation optimization made under the consideration of a single mathematical model and noted as a new model namely IOIT. The proposed mathematical models and methodologies are justified by con-