Cyclic inventory routing with dynamic safety stocks under recurring non-stationary interdependent demands

Abstract

We consider the Inventory Routing Problem (IRP) with one vendor replenishing the inventories of many retailers who face stochastic demands. To hedge against demand uncertainty, dynamic lot-sizing and safety stock planning are integrated using chance-constrained programming to adapt to the varying demand uncertainty across planning periods and allow for variable replenishment periods. We present a tactical approach towards obtaining cyclic delivery schedules that avoid given starting inventories and account for non-stationary interdependent demands. The assumption of independent, identically distributed (i.i.d.) demands often oversimplifies the stochasticity of the underlying demand time series by neglecting, among other things, seasonality and correlation. In IRPs, the evolution of the demand time series highly affects the consolidation of retailer replenishments in delivery routes. The problem is modeled as a mixed-integer linear program (MILP), including several real-world characteristics. To obtain solutions faster than by using MILP solvers, we propose a multi-start adaptive local search and an adaptive large neighborhood search (ALNS) heuristic. The influence of several problem parameters on the solutions is investigated. The benefit of an integrated planning of lot-sizing and routing over sequential planning is assessed. The results show that the proposed approach for cyclic delivery schedules allows a (de-)synchronization of retailer replenishments and their consolidation in vehicle routes while meeting real-world constraints in both routing and inventory management. Under non-stationary demands, it yields savings of 2.8% and 1.9% on average compared to given or zero starting inventories by setting initial inventories endogenously. The presented heuristics render near-optimal results. The ALNS deviates by only 0.6% from optimal on instances where cv=0, and by an average of 1.6% from optimal on all small-sized instances. On larger problems, it outperforms the other heuristics and obtains an average deviation from the best solution found of only 0.1%.