Competitive Strategies for Two Firms with Asymmetric Production Cost Structures
研究一家面临凸生产成本和线性库存持有成本的生产平滑企业与一家线性生产成本且无库存的接单企业之间的竞争策略，分析均衡策略的时间特征，并发现生产平滑企业的最优库存策略及其对接单企业定价生产决策的影响。
We model joint production-marketing strategies for two firms with asymmetric production cost structures in competition. The first firm, called the “Production-smoother,” faces a convex production cost and a linear inventory holding cost. The second firm, called the “Order-taker,” faces a linear production cost and holds no inventory. Each firm is assumed to vary continuously over time both its production rate and its price in view of an unstable “surge” pattern of demand. The underlying theoretical motivation is to investigate the temporal nature of the equilibrium policies of two competing firms, one operating at or near capacity (the Production-smoother), and one operating significantly below capacity (the Order-taker). We characterize and compare the equilibrium strategies of the two competing firms. Among our results, we show that if the duopolistic Production-smoother finds it optimal to hold inventory, then he will begin the season by building up inventory, continue by drawing down inventory until it reaches zero, and conclude by following a “zero inventory” policy until the end of the season. This result, which is robust with respect to the market structure, is compared with a monopolistic Production-smoother policy. We also show that due to the “coupling” effect between the two competing firms, the time at which the Production-smoother begins his zero inventory policy is also critical for the Order-taker who divides his production and pricing strategies into two parts determined by the Production-smoother's zero inventory point. Numerical examples that illustrate certain aspects of our analyses are provided as well.