Mozart B.C. Menezes

Facility location for large-scale emergencies

In the p-center problem, it is assumed that the facility located at a node responds to demands originating from the node. This assumption is suitable for emergency and health care services. However, it is not valid for large-scale emergencies where most of facilities in a whole city may become functionless. Consequently, residents in some areas cannot rely on their nearest facilities. These observations lead to the development of a variation of the p-center problem with an additional assumption that the facility at a node fails to respond to demands from the node. We use dynamic programming approach for the location on a path network and further develop an efficient algorithm for optimal locations on a general network.

Return-on-investment (ROI) criteria for network design

We develop a model for optimal location of retail stores on a network. The objective is to maximize the total profit of the network subject to a minimum ROI (or ROI threshold) required at each store. Our model determines the location and number of stores, allocation of demands to the stores, and total investment. We formulate a store’s profit as a jointly concave function in demand and investment, and show that the corresponding ROI function is unimodal. We demonstrate an application of our model to location of retail stores operating as an M/M/1/K queue and show the joint concavity of a store’s profit. To this end, we prove the joint concavity of the throughput of an M/M/1/K queue. Parametric analysis is performed on an illustrative example for managerial implications. We introduce an upper bound of an optimal value of the problem and develop three heuristic algorithms based on the structural properties of the profit and ROI functions. Computational results are promising.

Democratic elections and centralized decisions: Condorcet and Approval Voting compared with Median and Coverage locations

In this study, we focus on the quality of Condorcet and Approval Voting winners using Median and Maximum Coverage problems as benchmarks. We assess the quality of solutions by democratic processes assuming many dimensions for evaluating candidates. We use different norms to map multidimensional preferences into single values. We perform extensive numerical experiments. The Condorcet winner, when he/she exists, may have very high quality measured by the Median objective function, but poor quality measured by the Maximum Coverage problem. We show that the Approval Voting winner is optimal when the quality is measured by the Maximum Coverage objective and fairs well when the Median objective is employed. The analyses further indicate that the number of voters and the distance norm may increase, while the number of candidates and dimensions may decrease the quality of democratic methods.

Comparison of Condorcet and Weber solutions on a plane

This paper compares the quality of facility location resulting from voting and that of a centralized decision. The focus is on the quality of the Condorcet solution, which is measured by the ratio of the Condorcet solution value to the global Weber solution value. Prior work defined on networks showed that the ratio is bounded by 3. We attempt to reduce the impact of topology by investigating the problem on the plane. In this case, the ratio is smaller than 2 . The result suggests that, when reducing the impact of topology, although a solution originated via voting can be somewhat distant from the optimal solution obtained via a centralized system, it is much closer to optimality than previously suggested.

Constructing a Watts-Strogatz network from a small-world network with symmetric degree distribution

Though the small-world phenomenon is widespread in many real networks, it is still challenging to replicate a large network at the full scale for further study on its structure and dynamics when sufficient data are not readily available. We propose a method to construct a Watts-Strogatz network using a sample from a small-world network with symmetric degree distribution. Our method yields an estimated degree distribution which fits closely with that of a Watts-Strogatz network and leads into accurate estimates of network metrics such as clustering coefficient and degree of separation. We observe that the accuracy of our method increases as network size increases.

Coordinated lab-clinics: A tactical assignment problem in healthcare

Abstract In some medical outpatient settings, it is desirable to perform patient diagnostic testing just before the appointment with the physician, effectively linking the testing to the clinic appointment. If testing resources are shared by several physicians, it becomes difficult to assure that testing is completed in time (with some probability) due to the variation in testing requirements across patients and types of clinics held concurrently. To address this tactical-level doctor–clinic assignment problem, we develop a mixed-integer programming (MIP)-based approach for assigning time slots to the physician clinics. The approach maximizes the minimum service level across blocks of time to reduce the likelihood of a patient not completing testing in time for their clinic appointment. A branch-and-price heuristic procedure is proposed to solve practical problem instances, and numerical examples are presented to show the efficiency of this model. Two mini-cases based on clinics’ actual operations are provided. The results of the mini-cases suggest that the proposed scheduling method will bring important improvements to these systems.

The wisdom of voters: evaluating the Weber objective in the plane at the Condorcet solution

We investigate the quality of Condorcet solutions when compared to a central decision maker solution in the context of a facility location model in the plane. We perform an extensive set of experiments and conclude that if each population member votes according to his/her own self interest, then the Weber objective at the Condorcet solution point is very close to the optimal Weber objective value. Reducing the set of voters has little impact on the quality of the Condorcet solution. Being short of a good candidate has some impact but the final decision is still a good one. The distance metric seems to be of little relevance as well. As long as candidates are diverse, the Condorcet solution results in a good decision when compared to the decision by a benevolent dictator.

General asymptotic and submodular results for the Median Problem with Unreliable Facilities

The Median Problem with Unreliable Facilities ( M P U F ) consists of locating facilities such that the expected cost of serving the customers, considering possibility of failure, is minimized. We consider a general version of M P U F where facility disruptions may have non-zero correlation while the current approaches assume independence. We express the problem as a two-stage stochastic program and show that, independently of correlation values, some previous asymptotic and submodular results remain valid.