Competitive strategies for two firms with asymmetric production cost structures

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.