Optimal inventory policies with an exact cost function under large demand uncertainty

In this paper we investigate the minimization process of the exact cost function for a continuous review (Q,R) inventory model with non-negative reorder point and fixed lead-time. Backorders are allowed and the unit shortage cost is used to determine the expected annual shortage cost. Provided that the lead-time demand has J-shaped or unimodal distribution satisfying specific assumptions we derive the general condition when the minimum cost is attained at a positive reorder point or at a reorder point equal to zero. Based on this condition a general algorithm is developed. Some numerical experimentation based on this algorithm using parameter values from the relevant literature indicates that with large demand uncertainty measured by the coefficient of variation the optimal inventory policies lead to excessively large orders and zero reorder points.