Competition in the upstream and downstream market with lexicographic allocation policy

Abstract

In this thesis, we consider a supply chain in which two buyers share the same upstream source of supply that may be insufficient and then engage in quantity competition in the downstream market. When the total order quantity of the buyers exceeds the supplier's total supply, the limited inventory is allocated based on the lexicographic allocation policy, and the priority is given to the buyer who is willing to pay more. In such a setting, a three-stage game-theoretical model is established and solved backward to study the strategic behavior of every supply chain member and the effect of the demand risk level and competition intensity on their optimal strategy. Given the revealed demand, we analyze the pattern for the buyers' order quantity equilibrium as a function of the supplier's inventory level and the wholesale prices. Before the demand is realized, we derive the wholesale price equilibrium and the optimal inventory strategy of the supplier and study the interaction between them. We find that when the wholesale prices are not high enough, the two buyers' total order quantity experiences a drop when the supplier's inventory level crosses a critical value and keeps constant afterward. Therefore, the supplier has the incentive to limit his inventory level and lexicographic policy may now become a factor that causes insufficient supply. Moreover, the wholesale price equilibria are asymmetric with one buyer obtaining the control power while the other one grabbing the benefit of low purchasing cost, even though the two buyers are symmetric.