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Combinatorial optimization problems have applications in a variety of sciences and engineering. In the presence of data uncertainty, these problems lead to stochastic combinatorial optimization problems which result in very large scale combinatorial optimization problems. In this paper, we report on the solution of some of the largest stochastic combinatorial optimization problem consisting of over a million binary variables. While the methodology is quite general, the specific application with which we conduct our experiments arises in stochastic server location problems. The main observation is that stochastic combinatorial optimization problems are comprised of loosely coupled subsystems. By taking advantage of the loosely coupled structure, we show that decomposition-coordination methods provide highly effective algorithms, and surpass the scalability of even the most efficiently implemented backtracking search algorithms.

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The increased demand for medical diagnosis procedures has been recognized as one of the contributors to the rise of health care costs in the U.S. in the last few years. Nuclear medicine is a subspecialty of radiology that uses advanced technology and radiopharmaceuticals for the diagnosis and treatment of medical conditions. Procedures in nuclear medicine require the use of radiopharmaceuticals, are multi-step, and have to be performed under strict time window constraints. These characteristics make the scheduling of patients and resources in nuclear medicine challenging. In this work, we derive a stochastic online scheduling algorithm for patient and resource scheduling in nuclear medicine departments which take into account the time constraints imposed by the decay of the radiopharmaceuticals and the stochastic nature of the system when scheduling patients. We report on a computational study of the new methodology applied to a real clinic. We use both patient and clinic performance measures in our study. The results show that the new method schedules about 600 more patients per year on average than a scheduling policy that was used in practice by improving the way limited resources are managed at the clinic. The new methodology finds the best start time and resources to be used for each appointment. Furthermore, the new method decreases patient waiting time for an appointment by about two days on average.

In this article, the authors discuss modeling and simulation of forest fire spread and suppression using the discrete event system specification (DEVS) cell space approach in DEVSJAVA. The event-based modeling approach enables efficient simulation of cell space and allows one to obtain timely simulation-based predictions of forest fire spread and suppression in uniform and nonuniform environmental conditions. This model represents an advance toward developing a real-time decision support simulation system for predicting forest fire spread and the effects of water-based suppression attempts.

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Simulating wildfire spread and containment remains a challenging problem due to the complexity of fire behavior. In this paper, the authors present an integrated simulation environment for surface wildfire spread and containment called DEVS-FIRE. DEVS-FIRE is based on the discrete event system specification (DEVS) and uses a cellular space model for simulating wildfire spread and agent models for simulating wildfire containment. The cellular space model incorporates real spatial fuels data, terrain data and temporal weather data into the prediction of wildfire behavior across both time and space. DEVS-FIRE is designed to be integrated with stochastic optimization models that use the scenario results from the simulation to determine an optimal mix of firefighting resources to dispatch to a wildfire. Preliminary computational experiments with fuel, terrain and weather data for a real forest demonstrate the viability of the integrated simulation environment for wildfire spread and containment.

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establish finite convergence for binary first-stage. Second, we derive FD cuts based on the second-stage variables only and use an idea from disjunctive programming to lift the cuts to the higher dimension space including the first-stage variables. We then devise an alternative algorithm (FD-L algorithm) based on the lifted FD cuts. Finally, we report on computational results based on several test instances from the literature. The results are promising and show that both algorithms can outperform a standard direct solver and a disjunctive decomposition algorithm on some large-scale instances. Furthermore, the FD-L algorithm provides better performance than the FD algorithm in general.