Abstract:
In this paper, an EOQ model is developed for a deteriorating item with quadratic time dependent demand rate under trade credit. Mathematical models are also derived under two different situations i.e. Case I; the credit period is less than the cycle time for settling the account and Case II; the credit period is greater than or equal to the cycle time for settling the account. The numerical examples are also given to validate the proposed model. Sensitivity analysis is given to study the effect of various parameters on ordering policy and optimal total profit. Mathematica 7.1 software is used for finding optimal numerical solutions.
Machine summary:
"2. Notations and Assumptions The following notations and assumptions are used: R R(t) a bt ct 2 : a > 0, 0 < b < 1, 0 ≤ c ≤ 1; the annual demand θ: deterioration rate A: the ordering cost per order C: the unit purchase cost p: the unit selling price M: the permissible credit period offered by the supplier to the retailer for settling the account Ic : interest rate at which the interest is charged Ie : interest rate at which the interest is earned Q: the order quantity I (t): inventory level at any instant of time T: replenishment cycle time Ki (T): total profit per time unit; i =1, 2.
From Table 1(E), we see that, increase of unit selling price ‘p’ results slight decrease in optimal cycle time T = T1*, and optimal order quantity Q = Q1* and increase in optimal total relevant profit K1(T1*).
From Table 1(F), we wee that, increase of deterioration rate ‘θ’ results decrease in optimal cycle time T = T1*, and optimal order quantity Q = Q1* and increase in optimal total relevant profit K1(T1*).
Case II From Table 2(A), we see that increase of parameter ‘a’ results decrease in optimal cycle time T = T2*, increase in optimal order quantity Q = Q2* and optimal total relevant profit K2(T2*).
From Table 2(F), we see that, increase of deterioration rate ‘θ’ results decrease in optimal cycle time T = T2*, optimal order quantity Q = Q2* and optimal total relevant profit K2(T2*)."