A common technical challenge encountered in many operations management models is that decision variables are truncated by some random variables and the decisions are made before the values of these random variables are realized, leading to non-convex minimization problems. To address this challenge, we develop a powerful transformation technique which converts a non-convex minimization problem to an equivalent convex minimization problem. We show that such a transformation enables us to prove the preservation of some desired structural properties, such as convexity, submodularity, and L-convexity, under optimization operations, that are critical for identifying the structures of optimal policies and developing efficient algorithms. We then demonstrate the applications of our approach to several important models in inventory control and revenue management: dual sourcing with random supply capacity, assemble-to-order systems with random supply capacity, and capacity allocation in network revenue management.

Fatigue is a status of human brain activities, and driving fatigue detection is a topic of great interest all over the world. In this paper, we propose a measure of fatigue produced by eye tracking glasses, and use it as the ground truth to evaluate driving fatigue detection algorithms. Particularly, PERCLOS, which is the percentage of eye closure over the pupil over time, was calculated from eyelid movement data provided by eye tracking glasses. Experiments of a vigilance task were carried out in which both EOG signals and eyelid movement were recorded. The evaluation results of an effective EOG-based fatigue detection algorithm convinced us that our proposed measure is an appropriate candidate for evaluating driving fatigue detection algorithms.

Various studies have shown that the traditional electrooculograms (EOGs) are effective for driving fatigue detection. However, the electrode placement of the traditional EOG recording method is around eyes, which may disturb the subjects' activities, and is not convenient for practical applications. To deal with this problem, we propose a novel electrode placement on forehead and present an effective method to extract horizon electrooculogram (HEO) and vertical electrooculogram (VEO) from forehead EOG. The correlation coefficients between the extracted HEO and VEO and the corresponding traditional HEO and VEO are 0.86 and 0.78, respectively. To alleviate the inconvenience of manually labelling fatigue states, we use the videos recorded by eye tracking glasses to calculate the percentage of eye closure over time, which is a conventional indicator of driving fatigue. We use support vector machine (SVM) for regression analysis and get a rather high prediction correlation coefficient of 0.88 on average.

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In many operations management problems, the decisions are truncated by random variables. Take a dual sourcing inventory management problem as an example: the suppliers may have random capacities, and the actual received quantity from ordering is truncated by this random capacity. Often the random capacities of different suppliers may be dependent. An interesting challenge is that due to the truncation, the optimization problem may not be convex. In “Stochastic Optimization with Decisions Truncated by Positively Dependent Random Variables”, X. Chen and X. Gao propose a transformation technique to convert the original nonconvex minimization problem to an equivalent convex one. They demonstrate the application of their method using an inventory substitution problem with dependent random supply capacities and a two-part fee cost structure. In addition, their method can also incorporate the decision maker’s risk attitude.