THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Aspectos estratégicos e econômicos da política de bonificação em quantidade de produto

ste trabalho objetiva identificar a percepção dos gestores de controladoria de indústrias sobre os aspectos estratégicos e econômicos da decisão de bonificação em quantidade de produto. A premissa é que os resultados econômicos gerados pela decisão de desconto no preço e de bonificação em quantidade de produto são iguais, considerando a mesma quantidade de produto entregue ao cliente. Com base no banco de dados da FIPECAFI- FEA-USP, analisaram-se 91 questionários encaminhados a controllers atuantes em diversos setores. Os resultados revelam: 1) um número muito significativo de empresas da amostra selecionada adota a bonificação em produtos; 2) a área comercial é a principal responsável por essa decisão; e 3) identificação da percepção dos controllers sobre aspectos decisórios de bonificação em quantidade de produtos.