Supply interruptions in a lost-sales inventory system with random lead time

This paper presents an analytical model for computing the stationary distribution of the on-hand inventory in a continuous-review inventory system with compound Poisson demand, Erlang distributed lead time, and lost sales, where the supplier can assume one of the two “available” and “unavailable” states at any point in time according to a continuous-time Markov chain. Exact analytical expressions are derived for the special case where demand sizes are exponentially distributed, and some cost minimization numerical results are presented. One of the main factors that greatly influence the efficiency of every production and/or inventory control operation in a highly competitive environment is the reliability of its supply process. Many organizations, due to various reasons ranging from equipment breakdowns to political crises, are often faced with the challenge of managing their inventories in the presence of randomly occurring supply interruptions. The significance of modeling such interruptions is undoubtedly due to the severity of their potential negative impacts on the customer service level and the operating cost of virtually every supply chain in today's business market. The problem has motivated a considerable body of research in recent years. However, within the context of inventory control theory, very little has appeared in the literature that focuses on the issue of random supply interruptions in inventory systems with non-zero replenishment lead times, owing to the inherent analytical complexity of such systems. The main purpose of this work is to expand some of our earlier research findings in lost-sales inventory systems with variable lead times to address the supply interruption problem in a similar setting.