Effects of System Parameters on the Optimal Cost and Policy in a Class of Multidimensional Queueing Control Problems

• 成果类型: Article
• 署名作者: Vercraene, Samuel; Gayon, Jean-Philippe; Karaesmen, Fikri
• 署名单位: Institut National des Sciences Appliquees de Lyon - INSA Lyon; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1600
• 发表日期: 2018
• 页码: 150-162
• 关键词: production-inventory system; structural-properties; queues

摘要

We consider a class of Markov Decision Processes frequently employed to model queueing and inventory control problems. For these problems, we explore how changes in different system input parameters (transition rates, costs, discount rates etc.) affect the optimal cost and the optimal policy when the state space of the problem is multidimensional. To address a large class of problems, we introduce two generic dynamic programming operators to model different types of controlled events. For these operators, we derive sufficient conditions to propagate monotonicity and supermodularity properties of the value function. These properties allow to predict how changes in system input parameters affect the optimal cost and policy. Finally, we explore the case when several parameters are changed at the same time.