(301c) Estimation of Cost Savings By Co-Serving Customers in Vendor-Managed Inventory Distribution

Supply chain logistics forms an essential backbone in a plethora of businesses and represents a
sizeable portion of operational costs. This leads to increased research to improve and optimize
these operations. One area of research concentration is optimal vehicle routing [1] with a
particular focus in the context of vendor managed inventory (VMI) [2]. In VMI, the vendor
determines the quantity and timing of deliveries based on a few preset restrictions. This
paradigm allows for greater flexibility for the distributor but puts the dispatcher in the critical
role of determining which customers get deliveries and how much. Determining how to best
cluster customers and provide them with service on the same day is a challenging problem. It
entails solving a set of NP-Hard VRP problems and is exacerbated by the stochastic nature of
the delivery quantities each day. In this talk, we present the framework developed to
determine highly synergistic clusters of customers in a network.
Previous work [3-4] established a scenario sampling framework to estimate the marginal cost of
a single target customer within an existing network. Here, we extend this framework to account
for a cluster of target customers and quantify the possible synergies between these customers
to inform dispatching decisions. The new scenario sampling framework accounts for the
variations in delivery amounts. We define the joint probability for all combinations where each
individual customer in the cluster might or might not exert demand such that there are limited
degrees of freedom, which can be suitably selected to adjust the degree of co-serving the group
of customers. With the specified joint probability distributions of serving these cluster
customers individually as well as together, we sample realizations of the demands and generate
a collection of scenarios that collectively represent long-term depot-level operations. Each
resulting deterministic problem simplifies to a “Multi-Depot Vehicle routing problem with inter-
depot routes” (MDVRPI) [5]. The MDVRPI instance is formulated as a mixed-integer linear
program (MILP) with an exponential number of variables and solved using a Brach-Price-and-
Cut (BPC) solver [6-7]. Due to the stochastic demands, we repeat each set of scenarios with
several instances of non-cluster customer demands until we confirm the stabilization of long-
term average costs. We can then estimate the costs of serving customers clusters together,
separately, and independently by weighing them according to their corresponding sample
distribution.
We conduct extensive computational studies on benchmark instances drawn from the
literature with varying sizes of pre-selected clusters. We show how the framework can identify
clusters that are synergistic as well as other clusters that are antagonistic in nature, and we
quantify the average costs for operating under each dispatching paradigm. In this manner, we
identify opportunities for cost savings by suitably switching customers to different days of
service.

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Cost to Serve Individual Customers. Optimization Online
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