Showing papers by "Sankar Kumar Roy published in 2017"
TL;DR: The approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP are proposed and compared and two numerical examples are presented to show the feasibility and usefulness of the paper.
Abstract: 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.
79 citations
TL;DR: The mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) is formulated where the feasibility space is designed based on the selection of goal values and a utility function for selecting the goals of the objective functions is introduced.
Abstract: 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.
75 citations
57 citations
TL;DR: In this article, a multi-item inventory model for deteriorating items is proposed, where a two-level supply chain policy is formed based on manufacturer's and retailer's perspective, and the deterioration rate is considered as constant.
Abstract: This article is concerned with a multi-item inventory model for deteriorating items. The model is formed on the basis of a two-level supply chain policy, i.e., based on manufacturer's and retailer's perspective. The deterioration rate is considered as constant. The demand factor of any items suffer from a large amount of stock level; so, we consider stock-dependent demand function. The demand of any item is also dependent on its selling price; thus, a price-dependent demand function is introduced here. The retailer adopts the trade-credit policy for his customers in order to promote market competitiveness. He can earn revenue and interest after the customer pays the amount of purchasing cost to the retailer until the end of the trade-credit period, offered by the supplier. Shortages are allowed in the retailer's model as it is a very realistic item, too. A price discount on backordered commodities is offered for those customers who are willing to backorder their demand. Thereafter, we present an easy analytical solution procedure to find the total profit for both manufacturer and retailer. We also use the classical game theory and Nash equilibrium approach to find an optimal solution of the joint profit. The results are discussed with several numerical examples to illustrate our model and to provide some managerial insights related to the model. Furthermore, a parametric sensitivity analysis of the optimal solutions is provided and a concavity figure of our profit function is supplied to stabilize our model. The paper ends with a conclusion and an outlook to future research projects.
55 citations
TL;DR: A procedure is shown for converting from MCITP to deterministic TP and then solve it, and a case study is included to illustrate the usefulness of the paper.
Abstract: This paper explores the study of Transportation Problem (TP) under the light of multi-choice environment with interval analysis. The parameters of TP follow multi-choice interval-valued type so this form of TP is called Multi-Choice Interval Transportation Problem (MCITP). Introduction of time is an important notion in TP of this paper. Transportation time and cost, both are minimized through single objective function of TP, which is the main aim of this paper. A procedure is shown for converting from MCITP to deterministic TP and then solve it. A case study is included to illustrate the usefulness of the paper. Finally, concluding remarks and an outlook for future study are presented to this paper.
39 citations
TL;DR: In this paper, the authors developed an inventory model for deteriorating items with stock dependent demand rate and presented an easy analytical closed-form solution to find the optimal order quantity so that the total cost per unit time is minimized.
Abstract: In this study, we develop an inventory model for deteriorating items with stock dependent demand rate. Shortages are allowed to this model and when stock on hand is zero, then the retailer offers a price discount to customers who are willing to back-order their demands. Here, the supplier as well as the retailer adopt the trade credit policy for their customers in order to promote the market competition. The retailer can earn revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. Besides this, we consider variable holding cost due to increase the stock of deteriorating items. Thereafter, we present an easy analytical closed-form solution to find the optimal order quantity so that the total cost per unit time is minimized. The results are discussed with the help of numerical examples to validate the proposed model. A sensitivity analysis of the optimal solutions for the parameters is also provided in order to stabilize our model. The paper ends with a conclusion and an outlook to possible future studies.
34 citations
TL;DR: This paper considers that the parameters of the Fixed-Charge Transportation Problem (FCTP) are imprecise, and in this proposed problem, uncertainties are considered in terms of interval and RI.
Abstract: In this paper, we analyze the interval programming using interval and rough interval (RI) Interval programming is one of the tools to tackle uncertainty in mathematical programming In the real world situations, we often encounter the cases where the data cannot be determined with certainty So, the value of the data is assessed using an interval Here, we consider that the parameters of the Fixed-Charge Transportation Problem (FCTP) are imprecise In our proposed problem, uncertainties are considered in terms of interval and RI We present a study of the FCTP using the interval programming An example of the FCTP is included to show the effectiveness and usefulness of our proposed study Finally, concluding remarks and future scopes of our paper are discussed
27 citations
TL;DR: The paper is formulated with the Holling–Tanner prey–predator model with Beddington–DeAngelis functional response including prey harvesting with the help of normal theory and center manifold theorem to verify the validity of analytic results of the proposed model.
21 citations
TL;DR: The concepts of upper and lower approximations of a subset in a lattice are depicted based on this soft congruence relation and their related properties are given with examples to investigate their characterizations.
Abstract: In this paper, we first describe soft congruence relation over a lattice. We then define the concepts of complete soft congruence relation. Besides this, the concepts of upper and lower approximations of a subset in a lattice are depicted based on this soft congruence relation. We then give their related properties with examples to investigate their characterizations.
15 citations
TL;DR: In this article, the effects on prey of two predators which are also related in terms of prey-predator relationship were investigated and different types of functional responses were considered to formulate the mathematical model for predator and generalist predator of the proposed model.
Abstract: In this paper, we investigate the effects on prey of two predators which are also related in terms of prey–predator relationship. Different types of functional responses are considered to formulate the mathematical model for predator and generalist predator of our proposed model. Harvesting effort for the generalist predator is considered and the density-dependent mortality rate for predator and generalist predator is incorporated in our proposed model. Local stability as well as global stability for the system is discussed. We analyze the different bifurcation parameters to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Finally, some numerical simulations and graphical figures are provided to verify our analytical results with the help of different sets of parameters.
14 citations
TL;DR: A new formulation of mathematical model of MOFTP with fuzzy goal of each objective function is enlisted and the solution technique of the formulated model is described through multi-choice goal programming approach.
Abstract: 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 a...
TL;DR: The proposed approach is not only improved the applicability of goal programming in real world situations but also provided useful insight about the solution of a new class of TP.
Abstract: This paper explores the study of fuzzy transportation problem (FTP) using multi-choice goal-programming approach. Generally, the decision variable in transportation problem (TP) is considered as real variable, but here the decision variable in each node is chosen from a set of multi-choice fuzzy numbers. Here, we formulate a mathematical model of FTP considering fuzzy goal to the objective function. Thereafter, the solution procedure of the proposed model is developed through multi-choice goal programming approach. The proposed approach is not only improved the applicability of goal programming in real world situations but also provided useful insight about the solution of a new class of TP. A real-life numerical experiment is incorporated to analyze the feasibility and usefulness of this paper. The conclusions about our proposed work including future studies are discussed last.
TL;DR: In this paper, 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).
Abstract: In this paper, we study Stackelberg game as a multi-choice stochastic bi-level programming problem. In Stackelberg game, we have introduced the concept of leader at the higher level and the followers at lower level of the problem. We have considered the parameters of the constraints follow normal distribution and the cost coefficients of the objective functions are multi-choice types. To solve the problem, at first all the probabilistic constraints are transformed into deterministic constraints. 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 bi-level programming problem. Finally, a case study is presented to illustrate the usefulness of the paper.
TL;DR: The nested sequence of equivalence relations in rough approximation produces a multi-level partitions of the universe which partition the universe into different nested granules which form a bounded lattice.
Abstract: This paper deals with the successive rough approximation to lattice theory. The nested sequence of equivalence relations in rough approximation produces a multi-level partitions of the universe which partition the universe into different nested granules. Based on the hierarchy of the granules in the different level of stratified rough set approximation, they form a bounded lattice. Some important results are investigated to illustrate the paper.