(195a) Developing Periodic Replenishment Plans for Vendor Managed Inventory Customers in the Context of Mixed Networks

Last-mile distribution, the crucial final leg of product delivery, often represents a major cost burden for businesses [1]. Consequently, there is a pressing need to streamline these operations, particularly through optimal vehicle routing [2]. In Vendor-Managed Inventory Customer (VMIC) networks, suppliers have more control over delivery schedules and quantities, but such flexibility is absent in Customer-Managed Inventory Customer (CMIC) setups. While research has focused on co-optimizing routes and periodic replenishment schedules within both exclusively VMIC [3, 4] or CMIC networks, the reality is that many networks contain a mix of both customer types. Optimizing long-term delivery policies for such hybrid networks proves challenging due to the inherent variability and the computationally complex nature of the underlying Vehicle Routing Problem (VRP) [5].

In our previous work [6], we developed an iterative algorithm to drive cost savings through coordination (i.e., correlating delivery dates and quantities) of VMICs. At each iteration, we grow a cluster of VMICs and sample various network demand realizations [7]. Using this information, we determine the optimal coordination for the cluster such that it reduces distribution costs in the long run. The resulting coordinations result in significant cost savings without affecting the service levels of any customer. While this work modeled each representative day of distribution as a Capacitated Vehicle Routing Problem (CVRP) [8], the framework can be easily and modularly adapted to any other VRP variant as its basis.

In this work, we focus on converting the optimal coordinations into a periodic replenishment plan. The optimal coordinations usually cannot be easily interpreted as a practical (feasible) periodic replenishment plan and this can arise due to several factors such as the fraction of days of visits not matching up with periodic visit frequencies and/or the otherwise optimal delivery quantities not being able to be bin-packed into the fleet. To this end, we develop an MILP model to determine the optimal replenishment plan and the resulting demand correlations where we seek to minimize the deviation of the periodic replenishment plan from the previously determined optimally coordinated plan. We conduct extensive computational studies on augmented benchmark instances from the literature and show efficacy of our methodology to generate periodic replenishment plans that can reduce long-term average network costs.

References

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