Joint Replenishments Optimization for the (Rn, Sn) policy

This paper considers the periodic-review nonstationary stochastic joint replenishment problem (JRP) under Bookbinder and Tanu0027s static-dynamic uncertainty control policy. According to a static-dynamic uncertainty control rule, the decision maker fixes timing of replenishments once and for all at the beginning of the planning horizon, inventory position is then raised to a predefined order-up-to-position at the beginning of each replenish period. We present a mixed integer linear programming (MILP) model for approximating optimal static-dynamic uncertainty policy parameters. We further demonstrate that our MILP model can be used to approximate the optimal control rule for the JRP, also known as $(sigma, vec{S})$ policy. An extensive computational study illustrates the effectiveness of our approach when compared to other competitor approaches in the literature.