Modeling and simulation of a one-warehouse, N-retailer inventory System: reassessing a negative binomial approximation

Some studies in the multi-echelon inventory systems literature have used a negative binomial distribution to approximate that of a critical random variable arising in the inventory model. Graves (1996) developed a model with fixed replenishment intervals where each site follows a base stock policy. He proposed - in the one-warehouse, N-retailer case - a negative binomial distribution to approximate a random variable which he referred to as "uncovered demand". Computational evidence was provided to demonstrate the effectiveness of the approximation. Graves then suggested search procedures for approximately optimal base stock levels at the warehouse and N identical retailers under two customer service criteria: (i) probability of no stockout and (ii) fill rate. A separate analytical evaluation of the negative binomial approximation has also been reported elsewhere. In the current study, we apply a modeling and simulation approach to assess whether the approximation-based search procedures, in fact, lead to optimal stock levels.