Goal-driven optimization

Abstract

We develop a goal-driven stochastic optimization model that considers a random objective function in achieving an aspiration level, target, or goal. Our model maximizes the shortfall-aware aspiration-level criterion, which encompasses the probability of success in achieving the aspiration level and an expected level of underperformance or shortfall. The key advantage of the proposed model is its tractability. We can obtain its solution by solving a small collection of stochastic linear optimization problems with objectives evaluated under the popular conditional-value-at-risk(CVaR) measure. Using techniques in robust optimization, we propose a decision-rule-based deterministic approximation of the goal-driven optimization problem by solving subproblems whose number is a polynomial with respect to the accuracy, with each subproblem being a second-order cone optimization problem(SOCP). We compare the numerical performance of the deterministic approximation with sampling-based approximation and report the computational insights on a multiproduct newsvendor problem. © 2009 INFORMS.