A modelling and simulation approach to assessment of a negative binomial approximation in a multi-echelon inventory system

Some studies in the multi‐echelon inventory systems literature have used a negative binomial distribution to approximate a critical random variable arising in the model. Graves (1996) developed a multi‐echelon inventory 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 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: 1) probability of no stockout; 2) fill rate. A separate analytical evaluation of the negative binomial approximation has been preliminarily reported elsewhere. In the current study, we apply a modelling and simulation approach to assess whether the approximation‐based search procedures, in fact, lead to optimal or near‐optimal stock levels.