This paper proposes new location models for emergency medical service stations. The models are generated by incorporating a survival function into existing covering models. A survival function is a monotonically decreasing function of the response time of an EMS vehicle to a patient that returns the probability of survival for the patient. The survival function allows for the calculation of tangible outcome measures-the expected number of survivors in case of cardiac arrests. The survival-maximizing location models are better suited for EMS location than the covering models which do not adequately differentiate between consequences of different response times. We demonstrate empirically the superiority of the survival-maximizing models using data from the Edmonton EMS system.

a b s t r a c tBicycle sharing systems can significantly reduce traffic, pollution, and the need for parking spaces in city centers. One of the keys to success for a bicycle sharing system is the efficiency of rebalancing operations, where the number of bicycles in each station has to be restored to its target value by a truck through pickup and delivery operations. The Static Bicycle Rebalancing Problem aims to determine a minimum cost sequence of stations to be visited by a single vehicle as well as the amount of bicycles to be collected or delivered at each station. Multiple visits to a station are allowed, as well as using stations as temporary storage. This paper presents an exact algorithm for the problem and results of computational tests on benchmark instances from the literature. The computational experiments show that instances with up to 60 stations can be solved to optimality within 2 hours of computing time.

The Generalized Vehicle Routing Problem (GVRP) consists of finding a set of routes for a number of vehicles with limited capacities on a graph with the vertices partitioned into clusters with given demands such that the total cost of travel is minimized and all demands are met. This paper offers four new integer linear programming formulations for the GVRP, two based on multicommodity flow and the other two based on exponential sets of inequalities. Branch-and-cut algorithms are proposed for the latter two. Computational results on a large set of instances are presented.

This study introduces the Static Bicycle Relocation Problem with Demand Intervals (SBRP-DI), a variant of the One Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP). In the SBRP-DI, the stations are required to have an inventory of bicycles lying between given lower and upper bounds and initially have an inventory which does not necessarily lie between these bounds. The problem consists of redistributing the bicycles among the stations, using a single capacitated vehicle, so that the bounding constraints are satisfied and the repositioning cost is minimized. The realworld application of this problem arises in rebalancing operations for shared bicycle systems. The repositioning subproblem associated with a fixed route is shown to be a minimum cost network problem, even in the presence of handling costs. An integer programming formulation for the SBRP-DI are presented, together with valid inequalities adapted from constraints derived in the context of other routing problems and a Benders decomposition scheme. Computational results for instances adapted from the 1-PDTSP are provided for two branch-and-cut algorithms, the first one for the full formulation, and the second one with the Benders decomposition.

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