Highlights► We investigated dispatching and relocation decisions of emergency service providers. ► ADP is powerful in solving the underlying stochastic and dynamic optimization problem. ► Average response time can be improved by using more flexible dispatching rules. ► Relocating ambulances proactively improves service quality. ► Essential to take into account time-dependent information.

Emergency service providers are facing the following problem: how and where to locate vehicles in order to cover potential future demand effectively. Ambulances are supposed to be located at designated locations such that in case of an emergency the patients can be reached in a time-efficient manner. A patient is said to be covered by a vehicle if (s)he can be reached by an ambulance within a predefined time limit. Due to variations in speed and the resulting travel times it is not sufficient to solve the static ambulance location problem once using fixed average travel times, as the coverage areas themselves change throughout the day. Hence we developed a multi-period version, taking into account time-varying coverage areas, where we allow vehicles to be repositioned in order to maintain a certain coverage standard throughout the planning horizon. We have formulated a mixed integer program for the problem at hand, which tries to optimize coverage at various points in time simultaneously. The problem is solved metaheuristically using variable neighborhood search. We show that it is essential to consider time-dependent variations in travel times and coverage respectively. When ignoring them the resulting objective will be overestimated by more than 24%. By taking into account these variations explicitly the solution on average can be improved by more than 10%.

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Demographic change towards an ever aging population entails an increasing demand for specialized transportation systems to complement the traditional public means of transportation. Typically, users place transportation requests, specifying a pickup and a drop off location and a fleet of minibuses or taxis is used to serve these requests. The underlying optimization problem can be modeled as a dial-a-ride problem. In the dial-a-ride problem considered in this paper, total routing costs are minimized while respecting time window, maximum user ride time, maximum route duration, and vehicle capacity restrictions. We propose a hybrid column generation and large neighborhood search algorithm and compare different hybridization strategies on a set of benchmark instances from the literature.