Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

scholarly journals An inventory model for multiple items assuming time-varying demands and limited storage

2021 ◽  
Author(s):  
Luis A. San-José ◽  
Manuel González-De-la-Rosa ◽  
Joaquín Sicilia ◽  
Jaime Febles-Acosta
Keyword(s):  
Inventory Model ◽  
Inventory Systems ◽  
Decision Makers ◽  
Time Dependent ◽  
Time Varying ◽  
Limited Capacity ◽  
Inventory Policy ◽  
Numerical Examples ◽  
Multiple Products ◽  
Theoretical Results

AbstractA model for inventory systems with multiple products is studied. Demands of items are time-dependent and follow power patterns. Shortages are allowed and fully backlogged. For this inventory system, our findings provide the efficient inventory policy that helps decision-makers to obtain the initial inventory levels and the reorder points that maximize the profit per unit time. Moreover, when it is assumed that the warehouse used for the storage of products has a limited capacity, the optimal inventory policy is also developed. The model presented here extends some inventory systems studied by other authors. Numerical examples are introduced to illustrate the applicability of the theoretical results presented.

The behaviour of logistic equation in fuzzy environment: fuzzy differential equation approach

2021 ◽  
Vol 2 (1) ◽  
pp. 26
Author(s):  
Animesh Mahata ◽  
Sachindra Nath Matia ◽  
Banamali Roy ◽  
Shariful Alam ◽  
Hirak Sinha
Keyword(s):  
Differential Equation ◽  
Logistic Equation ◽  
Fuzzy Differential Equation ◽  
Equation Approach ◽  
Fuzzy Environment

scholarly journals TWO-STORAGE FUZZY INVENTORY MODEL WITH TIME DEPENDENT DEMAND AND HOLDING COST UNDER ACCEPTABLE DELAY IN PAYMENT

2020 ◽  
Vol 25 (3) ◽  
pp. 441-460
Author(s):  
Boina Anil Kumar ◽  
Susanta Kumar Paikray ◽  
Umakanta Mishra
Keyword(s):  
Solution Procedure ◽  
Inventory Model ◽  
Time Dependent ◽  
Peak Time ◽  
Fuzzy Environment ◽  
Holding Cost ◽  
Variable Holding Cost ◽  
Fuzzy Inventory ◽  
End Stage ◽  
Dependent Demand

If we observe a real business market, the demand for items in each cycle is not in the same pattern, that is, for specific business cycle it may increase, stable or decrease (for instance, cool drinks from end stage of the summer to winter; the demand goes on decreasing, and from the end of winter to peak time of summer; the demand goes on increasing). Also, if the supplier permits for delay in payment, retailer wishes to buy more goods, and for which the retailer may need extra storage (in terms of a rented warehouse). Moreover, the retailer has always wished to sell the items before they expire and accordingly order is placed. Mostly the parameters in a real world inventory model are imprecise. Thus, in the proposed study an inventory model having decreasing time dependent demand pattern with variable holding cost for TwoStorage facility under acceptable delay in payment has been developed. Mathematical model of the problem and its solution procedure is discussed for both crisp and fuzzy environment in order to obtain the optimal replenishment time and cost. Also, numerical examples are discussed to validate the study. Finally, sensitivity analysis is also studied to describe the fluctuating scenario of associated parameters.

A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment

2020 ◽  
Vol 54 (1) ◽  
pp. 267-286 ◽  
Author(s):  
Suman Maity ◽  
Avishek Chakraborty ◽  
Sujit Kumar De ◽  
Sankar Prasad Mondal ◽  
Shariful Alam
Keyword(s):  
Sensitivity Analysis ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Centroid Method ◽  
Numerical Examples ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Non Linear ◽  
Demand Rate ◽  
Comprehensive Study

This paper deals with an adaptation of an application of nonlinear heptagonal dense fuzzy number. The concept of linear and as well as non-linear for both symmetric and asymmetric heptagonal dense fuzzy number is introduced here. We develop a new ranking method for non-linear heptagonal dense fuzzy number also. Considering a backorder inventory model with non-linear heptagonal dense fuzzy demand rate we have utilized a modified centroid method for defuzzification. For decision maker’s aspects, numerical examples, comparative study with other dense fuzzy numbers and a sensitivity analysis show the superiority of the nonlinear heptagonal dense fuzzy number. Finally, graphical illustrations are made to justify the model followed by a conclusion.

The behaviour of logistic equation in fuzzy environment: fuzzy differential equation approach

2021 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Hirak Sinha ◽  
Shariful Alam ◽  
Animesh Mahata ◽  
Banamali Roy ◽  
Sachindra Nath Matia
Keyword(s):  
Differential Equation ◽  
Logistic Equation ◽  
Fuzzy Differential Equation ◽  
Equation Approach ◽  
Fuzzy Environment
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