Compound Poisson disorder problem with uniformly distributed disorder time


Quickest detection of a change in the customer arrival times and/or their shopping mix at some unknown and unobserved time is crucial for adjusting service system promptly for maximum customer satisfaction and profitability. We formulate customer types and arrivals with a marked point process and assume that its mean measure changes abruptly at some random time with uniform distribution over a wide time interval. The latter is an approximation for our little knowledge about when the change may happen. The aim is to find an optimal alarm time based solely on the observed history of types and times of customer arrivals so as to minimize the expected cost of a false alarm and detection delay time. We show that the problem is equivalent to a finite-horizon optimal stopping problem of a finite-dimensional piecewise-deterministic Markov sufficient statistic. We describe the solution and illustrate it on some numerical examples. Joint work with Cagin Uru, Duke University and Semih O. Sezer, Sabanci University, Turkey.


S. Dayanik is a full professor teaching at Bilkent since 2009. He had taught at Princeton University between 2002 and 2009. He earned his PhD degree in operations research with concentration in applied probability from Columbia University in 2002. He received INFORMS Nicholson Student Paper, INFORMS JFIG, IMS Tweedie New Researcher awards early in his career. His research interests are in stochastic modeling and data analytics.