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In today’s highly competitive marketplace, selecting an appropriate set of projects from a portfolio of candidate projects is vital for enterprises. An accurate selection of projects can steer a company to great success, while a careless selection may lead it to bankruptcy. Variability of project parameters such as benefit, cost, risk (failure probability), etc. during planning horizon makes this selection more complicated and increases the importance of an elaborate analysis. In this article, we studied a multi-objective R&D project portfolio selection problem. There is a conflicting desire to maximize expected net benefit and minimize risk in companies. From a novel perspective, the authors considered repetitive projects and variable amounts for aforementioned project parameters during planning horizon that could be an effect of sanctions, in our model that are features of real world problems. Due to NP-hardness of the problem and its high computational effort especially when the number of projects grows, we solved test problems of different sizes using a Multi-Objective Differential Evolution (MODE) algorithm to find pareto optimal solutions.

The required time for surgical interventions in operating rooms (OR) may vary significantly from the predicted values depending on the type of operations being performed, the surgical team, and the patient. These deviations diminish the efficient utilization of OR resources and result in the disruption of projected surgery start times. This paper proposes a two-stage chance-constrained model to solve the OR scheduling problem under uncertainty. The goal is to minimize the costs associated with OR opening and overtime as well as reduce patient waiting times. The risk of OR overtime is controlled using chance constraints. Numerical experiments show that the proposed model provides a better trade-off between minimizing costs and reducing solution variability when compared to two existing models in the literature. It is also shown that the three models converge as the overtime probability threshold approaches one. Moreover, it is observed that the individual chance constraints result in the opening of fewer rooms, lower waiting times, and shorter solution times when compared to that of joint chance constraints. A decomposition algorithm is applied that solves large test instances of the OR scheduling problem, that of which is known to be NP-hard. Strong valid inequalities are derived in order to accelerate the convergence speed. The proposed approach outperformed both a commercial solver and a basic decomposition algorithm after solving all test instances with up to 89 surgeries and 20 ORs in less than 48 minutes. INDEX TERMS Chance constraints, mixed-integer programming, operating room scheduling, two-stage stochastic programming, uncertainty.