Abstract: This thesis is concerned with the mathematical analysis of situations where service must be provided to customers within a prespecified time after arrival, the delay-limit (e.g., due to a service contract). Customer arrivals are governed by a stochastic process, and customers can be served jointly to obtain economies of scale. In Part I a basic model is extensively analysed, using techniques from Markov decision theory and queueing theory. In Part II this model is extended to the context of the production of exchangeable items, leading to a general framework for inventory models with a delay-limit on backorders. Several models within this framework are then studied in detail, including lost-sales inventory models.
