Goal-Driven Optimization

Achieving a target objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion, which encompasses the probability of success in achieving the goal and an expected level of under-performance or shortfall. The key advantage of the proposed model is its tractability. We show that proposed model is reduced to solving a small collections 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 a polynomial number of subproblems 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 approximation and report the computational insights on a multi-product Newsvendor problem. ∗NUS Business School, National University of Singapore. Email: [email protected] †NUS Business School, National University of Singapore and Singapore MIT Alliance (SMA). Email: [email protected]. The research of the author is supported by SMA, NUS academic research grants R-314-000-066-122 and R-314-000-068-122.