The multi-period supplementary supply-order system: An inventory game

This paper considers a supplementary supply-order system in which a retailer has an opportunity to place an additional order with a supplier after the demand is realized during each selling period, besides her first order according to the prediction of demand. We formulate this multiperiod problem as an inventory game between the supplier and the retailer, derive the optimal decision policies for both parties, and prove the existence of Nash Equilibrium. A closed-form Nash Equilibrium solution is derived when the parameters are stationary over the planning horizon. We also investigate the benefits of the supplementary supply-order system and the parameterpsilas influence by numerical study.