Erhan Erkut

Technical Note---Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location

To calculate many of the important performance measures for an emergency response system, one requires knowledge of the probability that a particular server will respond to an incoming call at a particular location. Estimating these “dispatch probabilities” is complicated by four important characteristics of emergency service systems. We discuss these characteristics and extend previous approximation methods for calculating dispatch probabilities to account for the possibilities of workload variation by station, multiple vehicles per station, call-and station-dependent service times, and server cooperation and dependence.

Scheduling ambulance crews for maximum coverage

This paper addresses the problem of scheduling ambulance crews in order to maximize the coverage throughout a planning horizon. The problem includes the subproblem of locating ambulances to maximize expected coverage with probabilistic response times, for which a tabu search algorithm is developed. The proposed tabu search algorithm is empirically shown to outperform previous approaches for this subproblem. Two integer programming models that use the output of the tabu search algorithm are constructed for the main problem. Computational experiments with real data are conducted. A comparison of the results of the models is presented.

Designing New Electoral Districts for the City of Edmonton

Every few years, the city of Edmonton, Canada must review and evaluate changes to its electoral district boundaries. The review process that was completed in 2009 resulted in modifying the district plan from a six-ward system with two council members in each to a single-member 12-ward system. The authors of this paper designed the redistricting plan. This paper describes the algorithm we applied to solve the problem and the decision support system we used. The algorithm is based on a multicriteria mathematical model, which is solved by a tabu search heuristic embedded within a geographic information system (GIS)-based decision support system. The resulting district plan meets districting criteria, including population balance, contiguity, compactness, respect for natural boundaries, growth areas, and integrity of communities of interest. This plan was formally approved as a city bylaw and used in the municipal elections in 2010.

Telecommunications network design with multiple technologies

In this paper we consider a telecommunications network design problem allowing for multiple technologies. The problem arises in wide-area network and metro-area network design for which a combination of technologies may be necessary due to high traffic volumes, long-distance transmission, and design restrictions. The network design problem builds the best network to channel traffic between a set of origins and destinations, which requires selecting links, equipping them with fiber, deciding on the type of technology, and locating switches. The goal is to minimize the total cost of the network, which accounts for the flow cost, the fiber and technology costs, and the switch-location cost. We model the problem using a multicommodity network design formulation with side constraints. We apply Benders decomposition to the problem and develop a two-phase solution method that uses a number of improvements over the basic Benders algorithm. We present promising results on randomly generated test problems.

A Lagrangian relaxation approach to large-scale flow interception problems

The paper presents a tight Lagrangian bound and an efficient dual heuristic for the flow interception problem. The proposed Lagrangian relaxation decomposes the problem into two subproblems that are easy to solve. Information from one of the subproblems is used within a dual heuristic to construct feasible solutions and is used to generate valid cuts that strengthen the relaxation. Both the heuristic and the relaxation are integrated into a cutting plane method where the Lagrangian bound is calculated using a subgradient algorithm. In the course of the algorithm, a valid cut is added and integrated efficiently in the second subproblem and is updated whenever the heuristic solution improves. The algorithm is tested on randomly generated test problems with up to 500 vertices, 12,483 paths, and 43 facilities. The algorithm finds a proven optimal solution in more than 75% of the cases, while the feasible solution is on average within 0.06% from the upper bound.