Processes transforming input into output mostly consist of multiple interacting subprocesses, which require coordination to ensure the required output quality and -quantity. Likewise, supply chains consist of multiple organizations, which in turn consist of multiple units. Decision-making between these units and between organizations requires coordination. Within every organizational unit, decisions are constantly made based on expectations about the future, which are never completely correct. For example, it is normal that the standard deviation of the demand prediction error, the difference between the prediction of demand for a product and the actual demand for this product, is of the same order of magnitude as the average demand itself. In addition, the decisions are naturally related: you have to make purchases before you can make, you have to make before you can transport to the points of sale, and this in turn must precede the final sale to a customer. The time span between purchase and sale is usually weeks or months, depending on the part of the manufacturing chain that is being considered.
Decision-making is supported by transactional systems, which keep track of locations and states of items in real time. Often also decision support systems are used, which make a proposal for a decision (buy this quantity, produce that quantity, send a quantity there). These systems use algorithms based on what in control theory is called Model Predictive Control, and within Operations Management rolling scheduling. Because there is high uncertainty, rolling schedule formulations based on deterministic optimization methods do not yield optimal decisions. Demonstrating this suboptimality is not trivial, because the modeled (stochastic) situations are usually too complex for a formal mathematical analysis.
In this presentation we will discuss a number of generic decision problems and discuss a conceptual approach to the problem as a whole and mathematical formulations of some of these decision problems. Dealing with uncertainty is central to all problems. We discuss a number of practical properties of optimal solutions and the resulting insights into where uncertainty must be absorbed in complex systems.
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