Sujit Kumar De

An EOQ model with backlogging

This paper deals with a new approach of linguistic dichotomous fuzzy variables for a classical backordered EOQ (Economic Order Quantity) model with PE (Promotional Effort) and selling price dependent demand rate. In practice, we have observed that the demand rate during a shortage period decreases with time. Based on these assumptions, we have developed a cost minimization problem (a crisp model) by trading off setup cost, inventory cost, backordering cost and cost for promotional effort. Then, we have studied a fuzzy model by considering the coefficient vectors as pentagon fuzzy numbers associated with some co-ordinates. Defuzzification is made with the help of the center-of-gravity method followed by a ranking index and the Euclidean distance of the objective function. Considering a numerical example, phi- (φ-)coefficients have been computed for each method and a decision is made according to the natural characteristics of the decision variables. Finally, conclusions are drawn, explaining the justification of the model.

A Replenishment Policy for Items with Finite Production Rate and Fuzzy Deterioration Rate

In order to solve the economic production quantity (EPQ) inventory model, we always consider the deterioration rate as a constant quantity. But in the real situation, the deterioration rate will have little disturbances from the actual constant value. Therefore, we have developed an EPQ inventory model with fuzzy deterioration rate and finite production rate. The effect in the loss in production quantity due to faulty/aged machine have also been considered. The methodology for obtaining the optimum value of fuzzy total cost is also derived and the solution procedure is explained with one numerical example. To study the effect of changes in the system parameters on the decision variables, a sensitivity analysis is carried out by one numerical example.

A deteriorating EOQ model for natural idle time and imprecise demand: hesitant fuzzy approach

This paper deals with managerial decision-making for a deteriorating economic order quantity (EOQ) inventory model for natural idle time and imprecise demand under hesitant fuzzy environment. Also,...

The (p, q, r, l) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean

This paper investigates a hill type economic production-inventory quantity (EPIQ) model with variable lead-time, order size and reorder point for uncertain demand. The average expected cost function is formulated by trading off costs of lead-time, inventory, lost sale and partial backordering. Due to the nature of the demand function, the frequent peak (maximum) and valley (minimum) of the expected cost function occur within a specific range of lead time. The aim of this paper is to search the lowest valley of all the valley points (minimum objective values) under fuzzy stochastic demand rate. We consider Intuitionistic fuzzy sets for the parameters and used Intuitionistic Fuzzy Aggregation Bonferroni mean for the defuzzification of the hill type EPIQ model. Finally, numerical examples and graphical illustrations are made to justify the model.

Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers

In supply chain inventory models, it was assumed that the retailers and their customers must pay for the items as soon as the items are received. However, in practice the supplier is usually willing to provide the retailer a full trade credit period for payments and the retailer just offers the partial trade credit period to his/her customers. In addition, many products such as blood for blood banks, pharmaceuticals, fruit, vegetables, volatile liquids and others deteriorate constantly and have their expiration dates. In this paper, we established optimal lot-sizing policies for a retailer who sells a deteriorating item to credit-risk customers by offering partial trade credit to reduce his/her risk. The objective is to maximize the total profit per unit time of the retailer with respect to the optimal purchase quantity during the optimal cycle time. The concavity of the total profit per unit time is demonstrated using inventory parametric values. Sensitivity analysis is carried out to advise the decision maker to keep an eye on critical inventory parameters.

Triangular dense fuzzy lock sets

This article deals with a triangular dense fuzzy set having special property on Cauchy sequence. In this set, the normality will never be attained unless we unlock by a special key on triangular dense fuzzy set at its final defuzzified state. We give several definitions on triangular dense fuzzy lock sets first and then discuss its locking unlocking property for single-key, double-key, and multiple keys environments with special reference to the convergence of Cauchy sequence. The non-membership function of the proposed lock set has also been studied. The graphical representations of the (non-)membership functions are developed, and the defuzzifications are done by existing methods of dense fuzzy sets as well as cloudy fuzzy sets implicitly. However, we have extended this fuzzy lock set into fuzzy lock matrix to generalize the concept. Finally, we discuss the fields of its practical application and draw a conclusion for better motivation.Graphical Abstract of the Triangular Dense fuzzy lock sets

An intelligent decision for a bi-objective inventory problem

This article deals with the bi-objective manufacturing inventory problems. We know that the present world economy is very much competitive and nobody leaves a pace to the other company for their profit-seeking enterprises. However, every company has a specific demand curve for selling their commodities or products which may intersect each other or not. Under these circumstances it is troublesome to get an optimum solution for bi-objective problems in the business arena that maximises their individual average total profit. To overcome these situations, we have used seven methods, namely goal programming, goal attainment, utility function, individual optimisation, geometric mean, global criteria, and mini–max method extensively. Moreover, we have studied the cases of two book producers problems along with their parabolic and linear several demand positions, respectively. Numerical examples and graphical illustrations are made to justify the model.

An economic order quantity model under two-level partial trade credit for time varying deteriorating items

ABSTRACTIn general, supplier/retailer frequently offers trade credit to its credit-risk downstream member in order to stimulate their respective sales. This trade credit may either be full or parti...

Adaptive noise risk modelling: fuzzy logic approach

ABSTRACT Recently, noise pollution has taken place as one of the most human health disorders. The main sources of noise are coming from human malpractices on reckless car driving and the use of loud speakers in different festivals at different places. Behavioural study explores that in many places the local usual road traffic noise level exceeds the normal standards. However, few people have adaptive capacity to ignore the effect of ambient noise pollution within considerable limits. Thus, in this article, we have developed an adaptive traffic noise model over the vulnerable society of a specific noise-prone zone. We develop a fuzzy logic to analyse the noise risk, and then it has been compared by the odds ratio of the experimental data. Moreover, we have considered the normality and non-normality in participation for various noise parameters, namely noise level, exposure time and affected age group of the people of a particular place as well. Finally, graphical illustrations are made for global justification of the model.

Two-layer supply chain model for Cauchy-type stochastic demand under fuzzy environment

Purpose The purpose of this paper is to deal with profit maximization problem of two-layer supply chain (SC) under fuzzy stochastic demand having finite mean and unknown variance. Buyback policy is employed from the retailer to supplier. The profit of the supplier solely depends on the order size of the retailers. However, the loss of shortage items is related to loss of profit and goodwill dependent. The authors develop the profit function separately for both the retailer and supplier, first, for a decentralized system and, second, joining them, the authors get a centralized system (CS) of decision making, in which one is giving more profit to both of them. The problem is solved analytically first, then the authors fuzzify the model and solve by fuzzy Hausdorff distance method. Design/methodology/approach The analytical models are formed for both centralized and decentralized systems under non-cooperative and cooperative environment with suitable constraints. A significant assumption on density function, namely Cauchy-type density function, is introduced for demand rate because of its wider range of the retailers’ satisfactions. Fuzzy Hausdorff metric is incorporated within the fuzzy components of the fuzzy sets itself. Using this method, the authors find out closure values of both centralized and decentralized policies, which is an essential part of any cooperative and non-cooperative two-layer SC models. Moreover, the authors take care of the profit values with corresponding ambiguities for both the systems explicitly. Findings It is found that the centralize policy of SC could only be able to maximize the profit of both the retailers and suppliers. All analytical results are illustrated numerically along with sensitivity analysis and side by side comparative studies between Hausdorff and Euclidean distance measure are done exclusively. Research limitations/implications The main focus of attention of the proposed model is given to usefulness of Hausdorff distance. Unlike other distances, Hausdorff distance can take special care on the similarity measures of different fuzzy sets. Researchers have been engaged to use Hausdorff distance on the different fuzzy sets but, in this study, the authors have used it within the components of a same fuzzy set to gain more closure values than other methods. Originality/value The use of this Hausdorff distance approach is totally new as per literature survey suggested yet. However, the Cauchy-type density function has not been introduced anywhere in SC management problems by modern researchers still now. In crisp model, the sensitivity on goodwill measures really provides a special attention also.