Goal-Driven Optimization

• Published in: Operations research Vol. 57; no. 2; pp. 342 - 357
• Main Authors: Chen, Wenqing, Sim, Melvyn
• Format: Journal Article
• Language: English
• Published: Hanover, MD INFORMS 01-03-2009; Institute for Operations Research and the Management Sciences
• Subjects: Analysis; Applied sciences; Approximation; Decision theory. Utility theory; Decision-making; Determinism; Exact sciences and technology; Financial risk; Goal programming; Linear programming; Mathematical optimization; Mathematical programming; Mathematical vectors; Operational research and scientific management; Operational research. Management science; Optimal solutions; Optimization; Optimization techniques; Portfolio theory; programming; Random variables; Risk aversion; Risk theory. Actuarial science; Robust optimization; Standard deviation; stochastic; Stochastic models; Stochastic programming; Studies; United States; Stochastic model; Cone; Probabilistic approach; Decision making; Expert system; programming: stochastic; Newsboy problem; Financial management; Linear programming; Modeling; Optimization; Goal programming; Stochastic programming; Decision rule; Multi item management; Problem solving; Aspiration level; Random function; Objective function; Sampling; Risk management
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1080.0570

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.