(604d) Selecting Optimal Frequency of Visit for Vendor-Managed Customers

For industrial gases companies, which operate massive supply chain networks, last mile delivery is a crucial part for customer profitability. To that end, capabilities that efficiently plan last mile delivery and decrease transportation costs constitute a constant area of focus. In this context, the concept of vendor-managed (VM) customer has been introduced, where the supplier is in charge of maintaining and replenishing the customer’s inventory [1]. However, many clients still prefer the traditional retail-managed (RM) approach and proactively contact the supplier to place orders. Generally, VM clients have a fixed frequency of visit (FOV) that is usually appointed by some tactical replenishment planning optimization solution. The delivery amounts to these customers are then decided based on their FOVs and average consumption rates over time. In many situations, FOVs are designated at a higher level, without considering routing aspects and the effect that these FOV decisions will have on the routing costs, which in turn leads to suboptimal distribution planning [2,3].

Integrating routing into FOV selection results in a problem known as the Periodic Vehicle Routing Problem with Service Choice (PVRP-SC) [4]. If the provided quantity to a VM customer is an independent decision for the planner, then inventory management needs to be incorporated as well, leading to an Inventory Routing Problem [5]. However, all these variants fail to take into consideration the effect of RM customers. As is commonly the case that a depot is in charge of serving both types of customers, a visiting scheme that does not consider RM customers would definitely have ignored a crucial part of the distribution operation. In this work, we try to address this gap.

In previous work [6], we created a simulation engine that closely mimics the real-world operation of a distributor, who offers service to a portfolio of VM customers while also operating a call center through which it receives additional ad-hoc orders placed by RM customers. Our simulation engine utilizes historic data to build a forecast regarding the potential for RM customer orders to materialize in the near future, allowing for both in-sample and out-of-sample realizations of such orders. Based on the service policy selected by the user, the simulation engine solves the corresponding routing optimization problem at each day with its exact, branch-and-cut solver and assigns all pertinent customers to delivery routes. The resulting schedule is then adopted in a rolling horizon fashion, while the probabilities of RM customer placing orders are suitably updated based on the exact materialization of recent orders.

In this work, we utilized our simulation engine as the basis for a metaheuristic framework that can optimize the FOV selection for VM customers collectively, at the depot level. An initial visiting scheme can be obtained by solving the associated PVRP-SC, where RM clients are ignored. In order to evaluate the merit of a depot-level FOV assignment in light of RM customers, the engine will recreate the distribution operation that would have occurred at the depot-level based on the historic data and applicable visiting scheme for VM clients. The cost associated with the proposed FOV assignment is thus assessed. In order to yield high-quality FOV assignments, we conduct a variable neighborhood search (VNS) procedure [7], which guides the local search on the FOV decision space. For this, we suitably define a set of local search neighborhoods, which constitute structured switches and swaps of the FOV of select VM customer subsets that are based on demand and cost information. Candidate local search moves are swiftly evaluated with a reduced version of our simulation engine, while the full version of the latter is reserved to assess each new plan selected. By dynamically changing hyperparameters, the VNS procedure shifts its focus between diversified and intensified search, while the process will keep iterating until termination criteria asserting local neighborhood optimality are met.

Using representative data from Linde PLC spanning four years of distribution records, we conduct a comprehensive case study to designate the best FOV scheme for VM customers at the depot level. We also demonstrate the vital role of RM customers in the real-world setting, where ignoring them will result in highly suboptimal FOV schemes. Furthermore, our analysis allows us to quantify the effect of specific VM customer visit frequency on overall transportation costs, providing strategic information on which customers in the portfolio should maintain—or be assigned—VM status.

References:

[1]. Archetti, C., Bertazzi, L., Laporte, G., & Speranza, M. G. (2007). A branch-and-cut algorithm for a vendor-managed inventory-routing problem. Transportation Science, 41(3), 382-391.

[2]. Hemmelmayr, V. C., Doerner, K. F., Hartl, R. F., & Vigo, D. (2014). Models and algorithms for the integrated planning of bin allocation and vehicle routing in solid waste management. Transportation Science, 48(1), 103-120.

[3]. Agatz, N., Campbell, A., Fleischmann, M., & Savelsbergh, M. (2011). Time slot management in attended home delivery. Transportation Science, 45(3), 435-449.

[4]. Coelho, L.C., Cordeau, J.F. and Laporte, G., 2013. Thirty years of inventory routing. Transportation Science, 48(1), pp.1-19

[5]. Francis, P., Smilowitz, K., & Tzur, M. (2006). The period vehicle routing problem with service choice. Transportation Science, 40(4), 439-454.

[6]. Izadkhah, A., Subramanyam, A., Laínez-Aguirre, J. M., Pinto, J. M., & Gounaris, C. E. (2020). Multi-period Vehicle Routing: Effect of Customer Flexibility in Delivery Day Window. Under review

[7]. Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11), 1097-1100.