Approximation schemes for the joint inventory selection and online resource allocation problem

In this paper, we introduce and study the joint inventory selection and online resource allocation problem, which is characterized by two sequential sets of decisions that are irrevocably linked. First, a decision maker (DM) must select starting inventory levels for a set of available resources. Subsequently, the DM must match arriving customers to available resources in an online fashion so as to maximize expected reward. We first study the problem in its most general form, before focusing on a specific version that arises at Anheuser Busch InBev (ABI). This particular application of our general setting is referred to as the ABI Trailer Problem, and it considers how ABI ships its beer to vendors via third‐party delivery trucks. In this problem, ABI must select the weights of preloaded trailers of beer, which are then matched in an online fashion to the arriving third‐party delivery trucks. For the general setting, we develop simple and easy‐to‐implement approaches that come with robust worst‐case performance guarantees. For the ABI setting, we reveal a simplifying structural property related to the optimal matching policy, which gives rise to a natural adaptation of our original approach. We test the efficacy of these policies through extensive numerical experiments, where we find that our approaches are either near‐optimal or improve upon state‐of‐the‐art benchmarks. In particular, using a data set from ABI, we are able to generate instances of the ABI Trailer Problem, on which our algorithm has the potential to yield revenue improvements in the range of millions of dollars per year.