Besides service level and mean physical stock, customer waiting time is an important performance characteristic for an inventory system. In this paper we discuss the calculation of this waiting time in case a periodic review control policy with order-up-to-level S is used and customers arrive according to a Poisson process. For the case of Gamma distributed demand per customer, we obtain (appro...

Retailers facing uncertain demand can use observed sales to update demand estimates. However, such learning is limited by the amount of inventory carried; when demand exceeds inventory (i.e., when a stock-out event occurs), a retailer in general cannot observe actual demand. We propose using observations on the timing of sales occurrences in a Bayesian fashion to learn about demand, and we anal...

some servers are to be located at nodes of a network. demand for services of these servers is located at each node and a subset of the nodes is to be chosen to locate one server in each. each customer selects a server with a probability dependent on distance and a certain amount of benefit is achieved after giving service to the customer. customers may waive receiving service with a known proba...

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable W satisfies a certain negative dependence assumption, then W is smaller (in the convex sense) than a Poisson variable of equal mean. Such W include those which may be written as a sum of totally negatively dependent indicators. This is generalised to other stochastic orderings. Application...

The arrival process of bidders and bids in online auctions is important for studying and modelling supply and demand in the online marketplace. A popular assumption in the online auction literature is that a Poisson process is a reasonable approximation. This approximation underlies theoretical derivations, statistical models and simulations used in field studies. However, there has been much e...