Seller - buyer supply chain games where shortage are permitted

In the area of seller-buyer supply chain management, researchers have been very active in seeking optimal policies for both players to achieve a favorable outcome. Most studies are based on somewhat unrealistic assumptions such as deterministic demand and unpermitted shortages. In reality, due to factors such as irregular production capacity or unanticipated demands, shortages will occur, and it will influence both players' decisions. In this paper, we include shortage as a decision variable determined by the seller, and demand is assumed sensitive to both selling price and marketing expenditure. The interaction between seller and buyer will be investigated as non-cooperative Stackelberg game, and the cooperation between seller and buyer will be explored based on Pareto-efficient solution concept. Consequences of the non-cooperative and cooperative aspects of these games will be compared and finally, numerical examples and sensitivity analysis will be presented to compare between models with and without shortages.