Browsing by Subject "Poisson arrivals"

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Open Access
A note on "continuous review perishable inventory systems: models and heuristics"
(2003) Gürler, Ü.; Özkaya, B. Y.
In a recent paper, Lian and Liu (2001) consider a continuous review perishable inventory model with renewal arrivals, batch demands and zero lead times. However, the main analytical result they provide holds only for some special cases such as Poisson arrivals with exponential interarrival times. In this note we generalize Theorem 1 of Lian and Liu (2001) for the case where the arrivals follow an arbitrary renewal process.
Open Access
State-dependent control of a single stage hybrid system with poisson arrivals
(2011) Gokbayrak, K.
We consider a single-stage hybrid manufacturing system where jobs arrive according to a Poisson process. These jobs undergo a deterministic process which is controllable. We define a stochastic hybrid optimal control problem and decompose it hierarchically to a lower-level and a higher-level problem. The lower-level problem is a deterministic optimal control problem solved by means of calculus of variations. We concentrate on the stochastic discrete-event control problem at the higher level, where the objective is to determine the service times of jobs. Employing a cost structure composed of process costs that are decreasing and strictly convex in service times, and system-time costs that are linear in system times, we show that receding horizon controllers are state-dependent controllers, where state is defined as the system size. In order to improve upon receding horizon controllers, we search for better state-dependent control policies and present two methods to obtain them. These stochastic-approximation-type methods utilize gradient estimators based on Infinitesimal Perturbation Analysis or Imbedded Markov Chain techniques. A numerical example demonstrates the performance improvements due to the proposed methods. © 2011 Springer Science+Business Media, LLC.