关键词: 产品服务系统；服务水平；消费者满意度；极大值原理

Abstract: The actual service levels provided by firms in the product aftermarket may be different from what were promised, which affects customer satisfaction and realized demand in both product primary market and service aftermarket. Therefore, it is worth studying the service level decisions dynamically during the whole product life cycle. In this paper, service level dynamic models are developed to investigate the firm’s service level decisions during the whole product life cycle. Firms usually promise a service level before product release, but could shift to a different one in product life cycles. The difference between the actual service level and the promised service level affects customer satisfaction and realized demand. The problem when the marginal cost of service correlates and does not correlate to service level, respectively is investigated. When the marginal cost of service does not correlate to service level, the optimal strategy of the firm is solved and analyzed by Pontryagin Maximum Principle; when the marginal cost of service correlates to service level, a numerical study is performed and the properties of the optimal strategy is discussed. Our results show that when firms make decisions of the actual service level provided during the product life cycle, they will not consider their promises made in the past. With the time passes, the actually provided service level decreases and drops to the lowest level when the product life cycle ends. The optimal strategy of the initial service level promise is a threshold policy. Firms will offer the highest service level promises only if the product life cycles are short enough. On this basis, however, firms may actually provide a low service level during the product life cycle. Our work helps practitioners in making decisions on both the initially promised and the actually provided service levels during the whole product life cycle.

Key words: product service system; service level; customer satisfaction; maximum principle