In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in  relevant in many industry-life applications tipically involving strategic and operational decisions on two different time scales. After providing three general mathematical formulations of a multi-horizon stochastic program, we extend the definition of the traditional Expected Value problem and Wait-and-See problem from stochastic programming in a multi-horizon framework. New measures are introduced allowing to quantify the importance of the uncertainty at both strategic and operational levels. Relations among the solution approaches are then determined and chain of inequalities provided. Numerical experiments on a real-life application from energy planning are finally presented.
published in Annals of Operations Research 2020, 292(2), pp. 605–625.