Dynamic supplier competition and cooperation for buyer loyalty on service

Abstract

A firm’s service-driven always-a-share behavior may have a significant effect on the competitive and cooperative inventory policies of its suppliers. To explore this effect, we consider a model of a repeat buyer (she) sharing her patronage among two heterogeneous newsvendor-type suppliers over an infinite horizon. To enjoy the best service advantage, the buyer plays one supplier (him) against the other by rewarding product availability with repurchase (loyalty) and punishing stockouts with switching (disloyalty) in the next period. Faced with this behavior, the optimal ordering policy of each supplier is a basestock policy with a non-negative “active” basestock level when the supplier has the buyer’s loyalty and a zero basestock level when he does not. Under competition, the optimal active basestock level of each supplier is greater than his myopic basestock level and increases in the other supplier’s active basestock level. Under a mild condition, the active basestock levels of both suppliers have at least one pure-strategy Nash equilibrium solution. If the suppliers cooperate, the optimal active basestock level of the supplier with the highest/lowest myopic profit is greater/smaller than his myopic basestock level. To better comprehend these results, we apply them to the case where the buyer’s demand is exponentially distributed. This allows us to obtain exact expressions for the optimal active basestock levels and payoff functions, which we then use in a numerical sensitivity analysis. We conclude with a discussion of the extension of the results to more than two suppliers.