Assumptions:-
a) The deterioration rate is proportional to time.
b) Demand rate is function of selling price.
c) Shortage whenever allowed, are partially backlogged.
d) Holding cost h(t) per item per time- unit is time dependent and is assumed to be
where δ>0,h>0.
e) Selling price p follows an increasing trend, demand rate possess the negative derivative throughout
its domain where demand rate is , a>0, b>0.
f) Backlogging rate for negative inventory is
, is backlogging parameter and (T-t) is
waiting time
g) is the time when inventory will reach to zero level
h) is the time where shortages are not allowed.
i) T is the complete length of cycle(T= )
j) Replenishment is instantaneous and lead time is zero.
k) The selling price per unit item is p.
l) Inventory is depleted due to deterioration and demand of the item.
m) To control the deterioration preservation technology is used.