The joint stochastic lot sizing and pricing problem

We consider a joint stochastic lot sizing pricing problem where period demands are price dependent and stochastic. Herein, we propose an alternative joint inventory control pricing policy for the profit-optimal (s,S,p) policy. The proposed policy – referred to as (R,S,p) is an order-up-to policy where replenishment schedule and price levels for each period are set before the planning horizon starts. As such, this policy can be considered as rather static as compared to the dynamic (s,S,p) policy. We also provide a quadratic mixed integer programming formulation in order to obtain the optimal (R,S,p) policy parameters. Furthermore, (R,S,p) policy is compared against the profit-optimal (s,S,p) policy on an extensive numerical study where several different benchmark policies are additionally used. The results show that the proposed policy exhibits a competitive profit performance with respect to the profit-optimal policy especially for low or moderate levels of demand uncertainty. The results also reveal that the relative benefit of using dynamic pricing policy, as compared to that of using dynamic inventory control, diminishes as demand uncertainty escalates.