Decentral allocation planning in multi-stage customer hierarchies

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.