Optimising reorder intervals and order-up-to levels in guaranteed service supply chains

We consider the problem of determining the optimal reorder intervals R and order-up-to levels S in a multi-echelon supply chain system where all echelons are assumed to have fixed ordering costs and to operate with a (R, S) policy with stationary nested power-of-two reorder intervals. By using the guaranteed service approach to model the multi-echelon system facing a stochastic demand, we formulate the problem as a deterministic optimisation model in order to simultaneously determine the optimal R and S parameters as well as the guaranteed service times. The model is a non-linear integer programming (NLIP) problem with a non-convex and non-concave objective function including rational and square root terms. Then, we propose a sequential optimisation procedure (SOP) to obtain near-optimal solutions with reasonable computational time. The numerical study demonstrates that for a general acyclic multi-echelon system with randomly generated parameters, the SOP is able to obtain near-optimal solutions of about 0.46% optimality gap in average in a few seconds. Moreover, we propose an improved direct approach using a global optimiser, bounding the decision variables in the NLIP model and considering the SOP solution as an initial solution. Numerical examples illustrate that this reduces significantly the computational time.