Optimal pricing policy for a deteriorating product by dynamic tracking control
研究了有限时间范围内易逝品的最优定价问题，通过动态跟踪控制方法推导出状态反馈形式的定价策略，并讨论了时间范围已知和未知两种情况。
Abstract We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed. Keywords: deteriorating itemspricing policyinventory controltracing problemmaximum value principle Acknowledgements We are grateful to the editor-in-chief and the referees for their constructive comments and suggestions to help improve our work. We gratefully acknowledge the support of grants from (i) Research Grants Council of Hong Kong, General Research Fund No. 410509, and NSFC Key Program Grant No. 70932005, for X.Q. Cai.; (ii) NSFC Research Fund No. 71101147 for Y.Feng; (iii) the Fundamental Research Funds for the Central Universities of China No. NKZXZD1103, and Program for New Century Excellent Talents in University of China(NCET-11-0252) for Y.J. Li, and (iv) the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (12JJD630004), and NSFC Research Fund No. 70971069, for D. Shi.