In this thesis, we present models for the design, analysis and control of integrated production and inventory systems. A focus of the thesis is the important interaction between the production and inventory functions. A differentiating feature of production-inventory systems is the load-dependent nature of replenishment lead-times. We show how this load dependency affects in important (and sometimes counter-intuitive) ways the distribution of lead-time demand. In particular, we show that variability in lead-time demand is decreasing in the variability of end demand and in system loading. We also show that strategies used to cope with demand variability, such as holding safety stock, pooling inventory, reducing product variety, or using advanced order information can become (relatively) less valuable when either demand variability or utilization increases.
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