Bi-objective multi-period planning with uncertain weights: a robust optimization approach

Decisions resulting from multi-objective planning models are quite sensitive to objective weights, and the latter are hard to determine accurately. We describe a robust formulation of a bi-objective multi-period planning problem where objective weights are random, independent and uniformly distributed in a predetermined range. We apply this model to a 245,090 ha forest in British Columbia, Canada, where the amount of employment and the proportion of old forest through the planning horizon are the two management objectives. Evaluated under simulated scenarios of weights, robust solutions produce more stable weighted sum of the objectives through the planning periods than traditional deterministic solutions. In other words, no large changes in the weighted sum of the objectives are expected even when the weights change over time. With this approach, we envision that these types of decisions will be better accepted by stakeholders and other social actors involved in the decision-making process.