D demand rate per year
P production rate per year
q ¼ 1 D
P P 0
h stock-holding cost per unit per year excluding interest
charges
A ordering cost per order
c unit purchasing cost per item
s unit selling price per item of good quality
a customer’s fraction of the total amount owed payable at
the time of placing an order offered by the retailer,
0 6 a 6 1
M retailer’s trade credit period offered by the supplier in
years
N customer’s trade credit period offered by the retailer in
years
3538 G.C. Mahata / Expert Systems with Applications 39 (2012) 3537–3550
Ie interest earned per $ per year
Ic interest charged per $ per year by the supplier
h constant deterioration rate, where 0 6 h < 1
t1 the time at which the production stops in a cycle
T cycle time in years
TRC(T) annual total cost, which is a function of T
T⁄ optimal cycle time
Q⁄ = DT⁄ optimal order quantity