TutORial: A Guide to Optimization Based Multi-Period Planning

By Linus Schrage.

Many organizations use multi-period planning models that involve optimization to decide things like the best production or investment levels in multiple periods into the future. There are a wide variety of features a user would like to have in such models. How those features are represented affects both the usefulness of the results and the solvability of these models as you add more periods to the model, or add more products, or in general, increase the detail. This tutorial describes how to best represent some important features that are common to most long range planning models. (a) Planning horizon length. (b) Ending conditions. The final period of the planning model frequently needs special treatment. In some situations you may be able to actually use an infinite horizon plan. (c) Period length. (d) Uncertainty. What is the best way of representing it? Variance, downside risk, Value-at-Risk, a utility function of some sort? (e) “Nervousness” and “sliding” scheduling. Most planning models are used in a “rolling” or “sliding” fashion, e.g., solve a 12 period model this month, implement the first period, and then next month slide things forward and repeat. When this is done, “nervousness” may be a problem, i.e., the plan made in February for what to do in June may differ substantially from what the plan published in January suggested for June. (f) Changeover, startup and shutdown costs. (g) Precedence constraints. (h) Scarce resource constraints. (i) Taxes. These can be important in some planning models. How these are properly calculated, or at least approximated, in an optimization model can be a challenge in the presence of features such as depreciation and choice of FIFO vs. LIFO inventory valuation. (j) Nonlinearities.