Simulation-optimization approach for a continuous-review, base-stock inventory model with general compound demands, random lead times, and lost sales

A continuous-review, base-stock inventory model considering lost sales is proposed for general compound demands and random lead times. This model is a generalized form of the (S, d) policy, which has already been shown to be the best modified base-stock policy (MBSP) for Poisson demand and fixed lead times. In this paper, customers' inter-arrival times, demand sizes, and lead times are extended in a probabilistic situation with free distributions. Then, a hybrid simulation-optimization approach is developed to handle these generalized conditions. This approach uses design of experiments, a simulation model, and regression analysis to obtain the long-run cost function of the system under this extended MBSP. The optimal settings of this policy are achieved using a mathematical optimization model. Employing a simulation model, a cost function, and mathematical models makes this approach applicable for finding the optimal settings even in the presence of realistic restrictions and uncertainties. Moreover, a simulation-based procedure is introduced to find the optimal stock level for the traditional base-stock policy. The applicability of the proposed approach is illustrated through a real-world case study. Finally, a sensitivity analysis is applied using a series of benchmark instances, and some robustness properties are shown.