Goutam Panigrahi

An imperfect EPQ model for deteriorating items with promotional effort dependent demand

In this paper, a multi-item economic production quantity (EPQ) model for deteriorating seasonal products is developed with stock and promotional effort dependent demand in an imperfect production process. The promotional efforts are advertising, delivery facilities, better services, etc. The production process produces some imperfect quality units which are instantly reworked at a cost to bring back its quality to the perfect ones. Here, the rate of production is time dependent. Unit production cost is a function of production rate including the defective ones and the deterioration rate is considered as constant. The model is formulated as a profit maximization problem with space and budget constraints in the form of an optimal control problem. The total profit function with the effect of inflation and time-value of money is expressed as a finite integral over a finite planning horizon. The problem is solved using variational calculus to determine the minimum defective rates of the production process for which the total profit is maximum. Another three models are developed considering the constraints as uncertain (fuzzy, random and rough) in nature. For fuzzy model, three types of fuzzy numbers are considered. To deal with the fuzzy constraints, fuzzy possibility measure is used. Also, stochastic and rough constraints are reduced to the approximate crisp ones following chance constrained approach and rough expectation respectively. Numerical experiments are performed to illustrate the models. Also, some sensitivity analyses are performed and presented.

Constrained covering solid travelling salesman problems in uncertain environment

In this paper, we introduce some constrained covering solid travelling salesman problems (CCSTSPs). In CCSTSPs, a salesman begins from an initial city, visits a subset of cities exactly once using any one of available vehicles at each step on the tour such that all other cities are covered within an imprecise predetermined distance and comes back to the initial city within a restricted time. Here, the travelling costs between the cities are considered as rough variables where the covering distance is taken as fuzzy and rough variable separately. A travel time constraint has been imposed where the time variable may be represented as rough variable. We develop an RID-MGA heuristics to solve the proposed model in trust measure and justify its performance by comparing some best known result of some benchmark problems and then solve experiment with some randomly generated data. Sensitivity analyses on RID-MGA are also performed with respect to different population size and number of generations. Finally, following the proposed model, some near optimal paths which could have been implemented for humanitarian delivery service due to the earthquake of Nepal (

Solving a Solid Transportation Problems Through Fuzzy Ranking

25{\text {th}}

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

25th April, 2015) is obtained by RID-MGA.

A Study towards Building An Optimal Graph Theory Based Model For The Design of Tourism Website

This paper deals with nonlinear transportation problem where one part of unit transportation cost varies with distance from some origin, and the problems consist one more impurity restriction. Moreover, the fixed unit transportation costs are imprecise ones. In model I, some parameters (i.e. production cost, transport cost, supply, demand and unit of impurity at demand point) are considered as Gaussian type-2 fuzzy variable, while model II considered only the supply and demand which are deterministic. The type-2 fuzzy variables are transformed into type-I fuzzy variables with the help of CV-based reduction method. Genetic algorithm (GA) has been applied to solve the proposed models. Finally, an illustration is presented numerically to demonstrate the experimental results.

A study to increase effectiveness of distance learning websites in India with special reference to the state West Bengal to increase the present GER of higher education through incorporation of Elearning facility in a better way

A solid transportation problem (STP) with imprecise cost coefficients is modeled in this paper. The proposed fuzzy STP (FSTP) is optimized by the Vogel approximation method (VAM). For different types of imprecise operations and comparisons in VAM, fuzzy ranking method is used. The proposed FSTP is also converted to a crisp one using fuzzy expectation (mean value) and then solved using generalized reduced gradient (GRG) method. Finally, a numerical illustration is performed to support the methods, and optimum results by two methods are compared.

Web Attributes Offered by Websites of Universities of West Bengal to Run E-Learning System: A Hierarchical Clustering Based Study

In this article, we model an “Imprecise Constrained Covering Solid Travelling Salesman Problem with Credibility” (ICCSTSPC), a generalization of Covering Salesman Problem (CSP), in fuzzy environment. A salesman begins from an initial node, visits a subset of nodes exactly once using any one of appropriate vehicles available at each step, so that unvisited nodes are within a predetermined distance from the visited nodes, and returns to the initial node within a restricted time. Here the travelling costs and travelling times between any two nodes and the covering distance all are considered as fuzzy. Thus the problem reduces to find the optimal tour for a set of nodes with the proper conveyances so that total travelling cost is minimum within a restricted time. The ICCSTSPC is reduced to a set of Imprecise Constrained Covering Solid Travelling Salesman Problems by solving Unicost Set Cover Problem (USCP) using Random Insertion-Deletion (RID). These reduced Constrained Solid Travelling Salesman Problems (CSTSPs) are solved by an Improved Genetic Algorithm (IGA), which consists of probabilistic selection, order crossover, proposed generation dependent inverse mutation. A random mutation for vehicles is proposed to get a better cost at each generation of IGA by choosing an alternative vehicle for each node. Hence the ICCSTSPC is solved by a random insertion-deletion (RID) for covering set and IGA, i.e., RID-IGA. To justify the performance of the RID-IGA, some test problems are solved. The model is illustrated with some randomly generated crisp and fuzzy data.

An Approach To Propose A Model For E-Learning Content Up-Gradation For Increasing Ger Of Higher Education In West Bengal

Abstract 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.