@article{Cui2026,
title = {Coordinating supply chains with order smoothing and cooperative game theory},
journal = {Accepted for publication in the International Journal of Production Economics},
volume = {},
issue = {},
pages = {},
year = {17th May, 2026},
doi = {},
url = {},
author = {G. Cui and S.M. Disney and N. Imura and K. Nishinari},
abstract = {We examine the use of cooperative game approaches to allocate profit in a three-echelon collaborative supply chain, focusing on order smoothing. Order smoothing involves altering the order-generating process in a supply chain to mitigate the bullwhip effect. This is facilitated by the well-known proportional order-up-to replenishment policy. We quantify the benefits of order smoothing and show that it reduces costs across all possible partial coalitions as well as in a fully centralised supply chain. However, it also introduces cost asymmetry: the upstream stages benefit, while the downstream stage—where order smoothing is implemented—incurs additional costs. We demonstrate that profit redistribution using cooperative game approaches can eliminate this imbalance. Our findings hold across two different cost metrics and a wide range of demand patterns.}
}