This research considering a non-linear decreasing demand inventory policies considering shortage backorders problem, in which the demand isknown and decreases exponentially, the instantaneous replenishment is made at time ti ( i = 1, 2,..., n ) where 1 t = 0 , the quantity received at i t is used partly to meet accumulated shortages in the
previous cycle from time i 1 s - to i t ( i 1 i s t - < ) (i = 2,...,n), and no shortages at the
beginning ( 1 t = 0 ) and the end of the planning horizon ( n s = H ).
An algorithm based on particle swarm optimization is proposed in this research for solving the defined problem. The algorithm is consist of an enumerative procedure to find
optimal number of replenishment (n*) over a particle swarm optimization to find the optimal set of shortage starting point of each cycle ({si*}) and the set of replenishment
time ({ti*}). The particle representation of the problem for fixed value of n is a random key of (n – 1) elements, in which particle is consists of (n – 1) dimensions and each dimensions position is limited from 0 to 1.
Computational testing results indicate that the proposed algorithm is outperformed well known method in the past for solving the same problem, i.e. Wee’s method (1995) in
which the proposed method is able to provide smaller total cost across various testing problem.