Optimal allocation of resources across sub-units in the context of centralized decision-making systems such as bank branches or supermarket chains is a classical application of operations research and management science. In this paper, we develop quantile allocation models to examine how much the output and productivity could potentially increase if the resources were efficiently allocated between units. We increase robustness to random noise and heteroscedasticity by utilizing the local estimation of multiple production functions using convex quantile regression. The quantile allocation models then rely on the estimated shadow prices instead of detailed data of units and allow the entry and exit of units. Our empirical results on Finland's business sector reveal a large potential for productivity gains through better allocation, keeping the current technology and resources fixed.

翻译：在诸如银行分支机构或超市连锁等集中决策系统中，跨子单元的资源最优分配是运筹学与管理科学的一项经典应用。本文开发了分位数分配模型，用以探究若资源在各单元间高效分配时，产出与生产率可能提升的程度。我们通过采用凸分位数回归对多个生产函数进行局部估计，增强了对随机噪声与异方差性的鲁棒性。分位数分配模型随后依赖估计出的影子价格而非单元的详细数据，并允许单元的进入与退出。基于芬兰商业部门的实证结果表明，在保持现有技术与资源固定的前提下，通过优化资源分配可实现巨大的生产率提升潜力。