This grant supports the development of advanced statistical methods'called constrained ranking and selection (R&S) procedures'for selecting the best of a large number of alternative system designs. These competing designs are typically evaluated via computer simulation with respect to the expected value of a primary performance measure, subject to constraints on acceptable expected values of several secondary performance measures. All the relevant expected values of the selected primary and secondary performance measures must be estimated by sufficiently long runs of the corresponding simulation models. Further, this research investigates how to extend the resulting constrained R&S procedures for use within each search step of a simulation optimization algorithm; and how to combine the extended constrained R&S procedures with optimization search algorithms to handle a large search space. Finally, findings from this research will be applied to a real-world problem, namely, groundwater resource allocation in water resource planning and management.
If successful, this research will develop generally applicable, statistically valid R&S procedures for discrete optimization under uncertainty both on objectives and constraints; help industry to reduce costs and improve overall decision-making processes; and provide a solid foundation for applying the new procedures to areas in which these techniques are not yet popular'in particular, the filed of environmental and water resources management, whose problems have an enormous impact on public policy/health. More specifically, the groundwater resource allocation problem for the Savannah Georgia region will be investigated from the perspective of environmental water resources planning. Therefore, the completion of the proposed work will have a significant impact not only on the theory and methodology of industrial engineering and operations research but also on environmental and water resources management.
Constrained ranking and selection (R&S) is to find the best simulated system under a primary performance measure, while also satisfying stochastic constraints on secondary performance measures. A constraint is called a stochastic constraint when its corresponding secondary performance measure needs to be estimated by simulation in order to determine feasibility. As a simulation model of a complicated or large-scale manufacturing or service system may take long to obtain one observation, statistically valid yet efficient selection procedures are needed. Classical R&S focuses on a single performance. However, we often encounter selection problems with multiple performance measures. Thus there have been emerging needs for constrained R&S. We successfully develop efficient procedures for constrained R&S. Solving this problem requires the identification and removal from consideration of infeasible systems (Phase I) and of systems whose primary performance measure is dominated by that of other feasible systems (Phase II). We propose two approaches, namely, carrying out Phases I and II sequentially and carrying out Phases I and II simultaneously. In a sequentially running procedure, a feasibility check procedure eliminates infeasible systems in Phase I and then a comparison procedure finds the best among the survived systems from the completed Phase I. On the other hand, a simultaneously running procedure performs feasibility and comparison procedures at the same time and eliminates a system if it turns out to be infeasible or inferior to a system which is already declared to be feasible. We also improve upon existing simultaneously running procedures by allowing certain systems to become dormant, halting sampling for those systems as the procedure continues. A system goes dormant when it is found inferior to another system whose feasibility has not been determined, and returns to contention only if its superior system is eliminated. If found feasible, the superior system will eliminate the dormant system. By making systems dormant, we avoid collecting unnecessary observations from interior systems, which results in big savings in terms of the number of observations needed until a decision is made. We also introduce a new procedure that minimizes the number of such switches, while still making a valid selection of the best constrained system, hoping to minimize the total sampling and switching costs. Constrained R&S procedures are useful when all alternatives can be simulated (no more than 1000). When the number of alternatives is large or infinite, it becomes impossible to simulate them all and instead an optimization search algorithm is needed. A number of optimization via simulation (OvS) algorithms have been presented, but they consider a single performance measure possibly with deterministic constraints only. Thus, similar to constrained R&S, we need new OvS methods to handle stochastic constraints. We present the penalty function with memory (PFM) method which enables any existing OvS algorithm to handle stochastic constraints. Moreover, we improve the efficiency of the combined PFM+OvS algorithm by utilizing constrained R&S procedures. The use of constrained R&S procedures for feasibility check or assigning computing budgets among visited solutions greatly help assigning a good penalty value to solutions. Finally, the combined PFM+OvS algorithm is applied to the problem of designing a water quality monitoring network for river systems. We want to find the optimal location of a finite number of monitoring devices that minimizes the expected detection time of a contaminant spill event while guaranteeing good detection reliability under uncertainties in spill and rain events. The performance of the method is tested on a real river system, the Altamaha River. We show that our method finds a better solution a lot faster than a heuristic method often used in the environmental management field. To summarize, we introduce a formal formulation of a general constrained R&S problem for the first time and a completely new way of constructing combined R&S techniques by running two statistical comparison procedures simultaneously. Also, a new method to handle stochastic constraints in optimization search is proposed. Our applications to water quality monitoring network design should help constructing bases for resulting methods to be transferred to the areas in which these techniques are not yet popular—such as environmental management whose problems have a huge impact on public policy/health. We reported our results and discoveries in peer-reviewed journals (seven articles published, two under review, five refereed conference proceedings, and three doctoral theses) and presented our work at scientific conferences such as INFORMS and Winter Simulation Conferences. One of our papers received a KUHN Award from Naval Research Logistics. Three PhD students were partially supported by this grant. Two are currently in industry and the 3rd one is a faculty member in a university.
