In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

This paper studies an unequal area layout problem whose objective is to find a flexible bay layout with the best shortest single loop. The problem can be used for production systems in which material handling is carried out by automated guided vehicles (AGVs) that move along a single-loop path. The designed layout is robust against future changes in material flows, which are caused by different factors such as demand fluctuations, technology advancement, and new product introduction. It is first proved that there exists a feasible single loop for any bay layout, which indicates the problem is well-defined and always has a feasible solution. Then, a powerful hybrid algorithm based on Memetic and Simulated Annealing is developed. The algorithm is tested on many randomly generated instances and well-known instances from the literature. The numerical experiment shows that the proposed heuristic is both efficient and effective. The new layout-design approach significantly improves the loop-length when compared with the traditional approach in which the layout is first determined based on rectilinear distances, and then the best single loop is found. Our study highlights the importance of adequately incorporating the material handling system into the layout design phase.

Currently, stroke patients are transported to the nearest stroke center, following specific protocols. Yet, these protocols do not consider many factors, including the spatial variation in population density, the stroke’s severity, the time since stroke onset, and the congestion level at the receiving stroke center. We develop an analytical framework that enriches the stroke transport decision-making process by incorporating these factors. Our research contributes to the literature of stroke care systems by (i) developing the first analytical framework to determine the optimal primary hospital destination in a regional stroke network and (ii) comparing the impact of incorporating prehospital triaging on health outcomes. To this end, we develop an efficient reformulation for allocation problems with stochastic demand and multiserver system under congestion. We derive data-driven outcome prediction models embedded in mixed integer second-order cone programming formulation. Our framework is applied to two real-life cases: Montreal and Quebec City Stroke Networks. We show that adopting a triage strategy could lead to significantly improved health outcomes, where the magnitude of these improvements varies with the networks’ sizes and congestion levels. In the Montreal case, our proposed policy may increase the ratio of patients for therapeutic intervention eligibility by 12.5% while improving by 69% the number of patients with more than two days of emergency department boarding delays. Our results reveal that it is important to consider the network’s characteristics in making a decision for or against implementing a prehospital triage strategy. Finally, we propose a heuristic policy that provides a promising performance while also being easy to implement.This paper was accepted by Stefan Scholtes, healthcare management.