Chase Rainwater

Social network analysis via multi-state reliability and conditional influence models

This paper incorporates multi-state reliability measures into the assessment of a social network in which influence is treated as a multi-state commodity that flows through the network. The reliability of the network is defined as the probability that at least a certain level of influence reaches an intended target. We consider an individuals influence level as a function of the influence levels received from preceding actors in the network. We define several communication functions which describe the level of influence a particular actor will pass along to other actors within the network. Illustrative examples are presented, and the network reliability under the various communication influence levels is computed using exhaustive enumeration for a small example and Monte Carlo simulation for larger, more realistic sized examples.

Robust facility location: Hedging against failures

While few companies would be willing to sacrifice day-to-day operations to hedge against disruptions, designing for robustness can yield solutions that perform well before and after failures have occurred. Through a multi-objective optimization approach this paper provides decision makers the option to trade-off total weighted distance before and after disruptions in the Facility Location Problem. Additionally, this approach allows decision makers to understand the impact on the opening of facilities on total distance and on system robustness (considering the system as the set of located facilities). This approach differs from previous studies in that hedging against failures is done without having to elicit facility failure probabilities concurrently without requiring the allocation of additional hardening/protections resources. The approach is applied to two datasets from the literature.

Analysis of a parallel machine scheduling problem with sequence dependent setup times and job availability intervals

In this study, we propose constraint programming (CP) model and logic-based Benders algorithms in order to make the best decisions for scheduling non-identical jobs with availability intervals and sequence dependent setup times on unrelated parallel machines in a fixed planning horizon. In this problem, each job has a profit, cost and must be assigned to at most one machine in such a way that total profit is maximized. In addition, the total cost has to be less than or equal to a budget level. Computational tests are performed on a real-life case study prepared in collaboration with the U.S. Army Corps of Engineers (USACE). Our initial investigations show that the pure CP model is very efficient in obtaining good quality feasible solutions but, fails to report the optimal solution for the majority of the problem instances. On the other hand, the two logic-based Benders decomposition algorithms are able to obtain near optimal solutions for 86 instances out of 90 examinees. For the remaining instances, they provide a feasible solution. Further investigations show the high quality of the solutions obtained by the pure CP model.

A constraint programming approach for the team orienteering problem with time windows

We propose a constraint programming (CP) model to solve the TOPTW.Our model obtains the best known solutions for 122 out of 304 benchmark instances.It also finds 49 optimal solutions out of 66 known optimal solutions.It improves the solution for 1 instances and proves 2 new optimal solutions. The team orienteering problem with time windows (TOPTW) is a NP-hard combinatorial optimization problem. It has many real-world applications, for example, routing technicians and disaster relief routing. In the TOPTW, a set of locations is given. For each, the profit, service time and time window are known. A fleet of homogenous vehicles are available for visiting locations and collecting their associated profits. Each vehicle is constrained by a maximum tour duration. The problem is to plan a set of vehicle routes that begin and end at a depot, visit each location no more than once by incorporating time window constraints. The objective is to maximize the profit collected. In this study we discuss how to use constraint programming (CP) to formulate and solve TOPTW by applying interval variables, global constraints and domain filtering algorithms. We propose a CP model and two branching strategies for the TOPTW. The approach finds 119 of the best-known solutions for 304 TOPTW benchmark instances from the literature. Moreover, the proposed method finds one new best-known solution for TOPTW benchmark instances and proves the optimality of the best-known solutions for two additional instances.

Optimal Dredge Fleet Scheduling Within Environmental Work Windows

The U.S. Army Corps of Engineers oversees dredging in hundreds of navigation projects annually, through its fleet of government equipment and through individual contracts with private industry. The research presented here sought to examine the decision to allocate dredge resources to projects systemwide under necessary constraints. These constraints included environmental restrictions on when dredging could take place in response to the migration patterns of turtles, birds, fish, and other wildlife; dredge equipment resource availability; and varying equipment productivity rates that affected project completion times. The paper discusses problem definition and model formulation of optimal dredge fleet scheduling within environmental work windows. In addition, a sensitivity analysis was conducted to provide decision makers with quantitative insights into dredging program efficiency gains that could be realized systemwide if environmental restrictions were relaxed. Opportunities exist to provide decision makers with quantitative insights into how efficiencies might be obtained if targeted research were to show that particular restricted periods could be relaxed without adverse consequences to sensitive and endangered species.

A bi-objective analysis of the r-all-neighbor p-center problem

Abstract In this paper we consider a generalization of the p -center problem called the r -all-neighbor p -center problem (RANPCP). The objective of the RANPCP is to minimize the maximum distance from a demand point to its r th-closest located facility. The RANPCP is applicable to facility location with disruptions because it considers the maximum transportation distance after ( r - 1 ) facilities are disrupted. While this problem has been studied from a single-objective perspective, this paper studies two bi-objective versions. The main contributions of this paper are (1) algorithms for computing the Pareto-efficient sets for two pairs of objectives (closest distance vs r th-closest distance and cost vs. r th-closest distance) and (2) an empirical analysis that gives several useful insights into the RANPCP. Based on the empirical results, the RANPCP produces solutions that not only minimize vulnerability but also perform reasonably well when disruptions do not occur. In contrast, if disruptions are not considered when locating facilities, the consequence due to facility disruptions is much higher, on average, than if disruptions had been considered. Thus, our results show the importance of optimizing for vulnerability. Therefore, we recommend a bi-objective analysis.

A facility neighborhood search heuristic for capacitated facility location with single-source constraints and flexible demand

We consider a generalization of the well-known capacitated facility location problem with single source constraints in which customer demand contains a flexible dimension. This work focuses on providing fast and practically implementable optimization-based heuristic solution methods for very large scale problem instances. We offer a unique approach that utilizes a high-quality efficient heuristic within a neighborhood search to address the combined assignment and fixed-charge structure of the underlying optimization problem. We also study the potential benefits of combining our approach with a so-called very large-scale neighborhood search (VLSN) method. As our computational test results indicate, our work offers an attractive solution approach that can be tailored to successfully solve a broad class of problem instances for facility location and similar fixed-charge problems.

Models for reducing the risk of critical networked infrastructures

In this paper, we review the literature studying how to reduce the disruption risk to critical networked infrastructures. This is an important area of research because huge consequences result from infrastructure disruptions. As a result, this research area has grown a lot in the last decade. In this review we discuss articles from the literature, place them into categories, and suggest topics for future research. Our review shows that although this area is growing in popularity, there are still many important opportunities for future work.

Assessing multi-layered social networks using reliability models

In this paper we introduce the first model to determine how best to make connections amongst a multi-layer network so to ensure a specified level of reliability amongst the components (actors) in the various levels of the system. This work is broadly applicable to any relationship in ma nufacturing, business organization or social networks in which the communication structure between independent subsystems is to be determined. Our approach utilizes concepts from the fields of reliability and network optimization to provide decision makers with the first tool for measuring the tradeoff between system reliability and the degree of information sharing in a system. Using an intelligent enumeration scheme, we provide solutions and analysis for an example network. The results support the con clusion that a significant decrease in reliability accompanies even moderate increases in the requirements of participating components (actors). They also emphasize that given the level of network design flexibility allowed in our model, numerous communication paths of equivalent system reliability are available that would be difficult to obtain without mathematical modeling.

Strategic level proton therapy patient admission planning: a Markov decision process modeling approach

A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated from different categories satisfy desired mix percentages. Deviations from these percentages and their impacts on operational capabilities are of particular interest to healthcare planners. In this study, we investigate intelligent ways of admitting patients to a proton therapy facility that maximize the total expected number of treatment sessions (fractions) delivered to patients in a planning period with stochastic patient arrivals and penalize the deviation from the patient mix restrictions. We propose a Markov Decision Process (MDP) model that provides very useful insights in determining the best patient admission policies in the case of an unexpected opening in the facility (i.e., no-shows, appointment cancellations, etc.). In order to overcome the curse of dimensionality for larger and more realistic instances, we propose an aggregate MDP model that is able to approximate optimal patient admission policies using the worded weight aggregation technique. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI).