Discrete-time EOQ with lost sales, binomial demand, and geometric lead time: inventory level distribution and performance analysis

This paper presents a stochastic analytical model for the discrete-time EOQ (DT-EOQ) with lost sales, where both consumption and supply processes are modelled as Bernoulli trials. This approach allows for the representation of binomial daily demand and geometrically distributed lead time, capturing various demand patterns, including smooth, intermittent, or rare occurrences. The study provides a comprehensive mathematical derivation of the closed-form expression for the steady-state probabilities of on-hand inventory levels. This leads to concise and exact formulations for key performance measures such as the average inventory level, inventory cycle length, stock-outs per cycle, and fill rate. Notably, the proposed estimator for the average inventory level shows improved accuracy over existing formulas. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed modelling approach.