To generate continuing profits as well as to retain market share, companies need to regularly introduce new products into the market, replacing outdated products and enticing buyers to purchase new products. Thus, planning the product transition from the phase-out of a product to the phase-in of a product is a challenging task for both production planners and marketing managers. One significant concern in particular is how to account for the learning effect associated with the production of two successive products that share a single type of production resource. To address this problem of designing production plans for two successive products, we develop an MINLP (Mixed-Integer Non-Linear Programming) model that minimizes the total operating cost for managing the product transition. In doing so, we consider the number of production resources, the lengths of the product production periods, and the number of setups for both products during the ramp-down and ramp-up periods. We study the behaviors of the proposed model with the help of numerical experiments by varying the values of key parameters, including the learning effect and its impact on performance under different operational scenarios. Leveraging the results from the sensitivity analyses, the operational characteristics for managing the product transition are discussed.

为了产生持续的利润并保持市场份额，公司需要定期向市场推出新产品，更换过时的产品并吸引买家购买新产品。因此，规划从产品逐步淘汰到产品逐步引入的产品过渡对于生产计划人员和营销经理来说都是一项具有挑战性的任务。一个特别重要的问题是如何考虑与共享单一类型生产资源的两个连续产品的生产相关的学习效果。为了解决为两个连续产品设计生产计划的问题，我们开发了一个 MINLP（混合整数非线性规划）模型，该模型可以最大限度地降低管理产品转换的总运营成本。在这样做时，我们考虑了生产资源的数量，产品生产周期的长度，以及在减速和加速期间两种产品的设置数量。我们在数值实验的帮助下通过改变关键参数的值来研究所提出模型的行为，包括学习效果及其在不同操作场景下对性能的影响。利用敏感性分析的结果，讨论了管理产品转换的操作特征。