Computing optimal (s, S) policies in inventory models with continuous demands

Special algorithms have been developed to compute an optimal (s, S) policy for an inventory model with discrete demand and under standard assumptions (stationary data, a well-behaved one-period cost function, full backlogging and the average cost criterion). We present here an iterative algorithm for continuous demand distributions which avoids any form of prior discretization. The method can be viewed as a modified form of policy iteration applied to a Markov decision process with continuous state space. For phase-type distributions, the calculations can be done in closed form.