Bounds in multi-horizon stochastic programs

In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in Kaut et al. (Comput Manag Sci 11:179–193, 2014) relevant in many industry-life applications typically 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 based on an energy planning application are finally presented.