We analyze the price competition between two suppliers offering two different lead times and two different prices to a buyer. The buyer chooses its inventory replenishment policy in order to minimize its infinite-horizon average cost. In essence, the fast and expensive supplier is used only in emergencies, while the slow and cheap supplier receives the bulk of the orders. Thus, despite a higher price, the fast supplier is able to capture a part of the buyer's orders. We analyze the price competition between the asymmetric suppliers, where the market share of each supplier is derived from the buyer's inventory problem. We find equilibria that differ significantly from the Bertrand price-only competition. In particular, for some cost parameters, the fast supplier is able to charge a premium for faster delivery, and stay in business even with a higher production cost. We obtain in some cases closed-form formulas for the price difference in equilibrium. Hence, our results show that high cost suppliers may not be driven out of business if they can offer fast delivery.
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