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Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.

In an era focusing on performance management, finding the right key performance indicators (KPIs) can aid the implementation of company goals. By monitoring and managing these indicators, the effects of prevention, continual improvements, and innovations are achieved to shape the core competitiveness. This study used the Delphi method to interview 18 field experts. Through their rich experiences and ideas, the study investigated the KPIs of new product development (NPD). Through qualitative and quantitative analysis, this study provides managers with effective management suggestions, including communication and contacts, information sharing, analysis and judgment, decision-making, goal planning, improved control, and pay-for-performance. After empirical analysis, the NPD process was found to have a total of 9 constructs with 43 important in relation to KPIs. To analyze the cause and effect relationships and importance of these constructs, decision-making trial and evaluation laboratory (DEMATEL) was utilized. The order of importance was as follows: Project schedule management, operational risk management, total quality management and life cycle cost management, demonstrating that the schedules, risks, quality and costs are valued team aspects during product research and development. Therefore, the results can provide the manager to build a more complete KPIs system and reduce product development risks. Key words: Key performance indicators, new product development, Delphi method, knowledge maps, decision-making trial evaluation laboratory

We consider a reservoir which has a single linear cost function with penalty. The release rules can be modeled as a sequential Markov decision process (MDP). By applying policy-iteration algorithm and value-iteration algorithm, we obtain the optimal state-dependent release policies and prove some corollaries for the problem.