TMP production scheduling under uncertainty: Methodology and case studies

Operational decisions are influenced not only by the data and models available for the decision maker but also by the uncertainty within them. The decision maker must take an attitude towards risk and balance that against the expectation value of performance. This paper presents methods to manage rationally operational decision making tasks under uncertainty with an example taken from the paper industry, the scheduling of thermo-mechanical pulp (TMP) production with uncertainty in production cost and demand. The stochastic problem is analytically transformed into a deterministic optimization task, and the probability distributions of the stochastic variables are calculated directly rather than with Monte Carlo simulations. The objective is formulated in two alternative ways: either the decision maker's attitude towards risk is modeled with exponential utility function or the expected cost is minimized subject to an additional constraint for probability of exceeding user specified maximum cost allowed. The role of the constraints in a dynamic, stochastic case is also discussed.