Decentral allocation planning in multi-stage customer hierarchies

•Novel approach to allocate scarce resources in multi-level customer hierarchies.•Applicable for decentral allocation decisions based on customer profitability.•Facilitates supply chain planning, e.g. allocation planning and demand fulfillment.•New application of standard econometric tools, e.g. Theil index and Lorenz curve.

This paper presents a novel allocation scheme to improve profits when splitting a scarce product among customer segments. These segments differ by demand and margin and they form a multi-level tree, e.g. according to a geography-based organizational structure. In practice, allocation has to follow an iterative process in which higher level quotas are disaggregated one level at a time, only based on local, aggregate information. We apply well-known econometric concepts such as the Lorenz curve and Theil’s index of inequality to find a non-linear approximation of the profit function in the customer tree. Our resulting Approximate Profit Decentral Allocation (ADA) scheme ensures that a group of truthfully reporting decentral planners makes quasi-coordinated decisions in support of overall profit-maximization in the hierarchy. The new scheme outperforms existing simple rules by a large margin and comes close to the first-best theoretical solution under a central planner and central information.