Abstract
This paper considers an EOQ inventory model with varying demand and holding costs. It suggests minimizing the total cost in a fuzzy related environment. The optimal policy for the nonlinear problem is determined by both Lagrangian and Kuhn-tucker methods and compared with varying price-dependent coefficient. All the input parameters related to inventory are fuzzified by using trapezoidal numbers. In the end, a numerical example discussed with sensitivity analysis is done to justify the solution procedure. This paper primarily focuses on the aspect of Economic Order Quantity (EOQ) for variable demand using Lagrangian, Kuhn-Tucker and fuzzy logic analysis. Comparative analysis of there methods are evaluated in this paper and the results showed the efficiency of fuzzy logic over the conventional methods. Here in this research trapezoidal fuzzy numbers are incorporated to study the price dependent coefficients with variable demand and unit purchase cost over variable demand. The results are very close to the crisp output. Sensitivity analysis also done to validate the model.
Highlights
In today’s competitive scenario, organizations face immense challenges for meeting the transitional consumer's demand, and maintaining the inventory plays a major role
K - Ordering cost a - constant demand rate coefficient b - price-dependent demand rate coefficient P - selling price Q - Order size c - unit purchasing cost g - constant holding cost coefficient Let’s consider the total cost [15] and modify in a fuzzy environment The total cost per cycle is given by Partially differentiating w.r.t Q, Equating the economic order quantity in crisp values obtained as Inventory Model For Fuzzy Order Quantity By using trapezoidal numbers, fuzzified input parameters are as follows
The fuzzified output varies at a larger rate than crisp output while varying the demand
Summary
In today’s competitive scenario, organizations face immense challenges for meeting the transitional consumer's demand, and maintaining the inventory plays a major role. K - Ordering cost a - constant demand rate coefficient b - price-dependent demand rate coefficient P - selling price Q - Order size c - unit purchasing cost g - constant holding cost coefficient Let’s consider the total cost [15] and modify in a fuzzy environment The total cost per cycle is given by Partially differentiating w.r.t Q, Equating the economic order quantity in crisp values obtained as Inventory Model For Fuzzy Order Quantity By using trapezoidal numbers, fuzzified input parameters are as follows. Available Online Partially differentiating w.r.t ‘Q’ and equating to zero, the optimal economic order quantity for crisp values is derived, Applying the graded mean representation partially differentiating w.r.t Q1, Q2, Q3, Q4 and equating to zero, The above derived results depict that Q1 > Q2 > Q3 > Q4 failing to satisfy the constraints 0 ≤ Q1 ≤ Q2 ≤ Q3 ≤ Q4.
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