Decision-making On Emergency Medical Services Facility Location Under Uncertainties

Recently,with the background of highly frequent and world-wide natural disasters and emergencies,our government has issued a series of rules and policies to attach the importance of Emergency Medical Services(EMS)system from national-macro perspective.In this research,we incorporate different sources of uncertainties revealed in EMS process,such as emergency demand,time-dependent parameters,transportation cost and facility disruptions and so on,to address facility location decisions problems in EMS.Using the recent advances and techniques in stochastic programming,robust optimization and chance constrained programming,we propose a set of novel mathematical models for related EMS facility location problems,and design a class of enhanced decomposition algorithms,based on the real-life data,to determine the optimal,robust and reliable decisions of EMS facility location and allocation.Specifically,we mainly discuss the following three points with respect to the contributions of theory,modeling and practical applications.Firstly,Emergency Medical Services network design under demand uncertainty.Considering emergency demand uncertainty,we propose a single-stage and static EMS network design problem.On the basis of deterministic formulation,we introduce chance constraint to provide a probabilistic guarantee for each emergency site while minimizing the total cost.We deal with chance constraint by using the most two popular optimization tools under uncertainty(stochastic programming and robust optimization),and derive the equivalent counterparts of mixed integer linear programming and second order cone programming.In robust model,unlike these existing simple interval,box,polyhedron and budget uncertainty set in literature,we construct two types of uncertainty sets(symmetric and asymmetric uncertainty set respectively)by considering the skewness of available distribution information for uncertain parameters;In stochastic programming framework,we capture uncertainty by plenty of discrete random scenarios,propose an enhanced Branch-and-Benders-Cut(B&BC)method to solve large-scale and real-life instances,and make a comparison to Benders strategy in CPLEX 12.71.To illustrate the proposed models,a practical study based on the EMS network in Northern Ireland is conducted.The computational results imply that,robust policy is much more conservative than the solution of stochastic model that highly depends on the probability distribution of uncertain parameters.Therefore,decision-makers should make a trade-off among conservativeness,optimality and system reliability of the EMS network,and choose a better modeling method for their problems,based on theirs risk preference to conservativeness and available information.Secondly,dynamic ambulance location.As an important extension of the proposed models in chapter 3,we extend the single-stage and static EMS location problem into a multi-period and dynamic ambulance location,and incorporate more realistic features,such as time-dependent emergency demand uncertainty,time-dependent cost parameters,timedependent decisions and the relocation of ambulances.We also introduce chance constraint to guarantee the given coverage to be satisfied,in which one big difference from chapter 3is that chance constraint is imposed on the whole EMS system,instead of each emergency demand node.Here,we also employ discrete random scenarios to describe uncertainty,partition the whole planning horizon into T time periods,derive the mixed integer programming reformulation for two-stage chance constrained stochastic programming model,propose an efficient B&BC algorithm with several enhancements to solve large-scale real problems,and also make a comparison to a benchmark solution method in literature.Then,we propose a generalized chance constraint,termed probabilistic envelope constraint(PEC),which addresses the coverage envelope for all the violated probabilities and captures how much degree the bound of violation is.We propose a novel two-stage probabilistic envelope constrained stochastic programming framework,which is reformulated as a large-scale two-stage mixed integer problem.To overcome the computational challenges,we derive a conservative approximation of PEC.Based on the real data from Northern Ireland EMS network and randomly generated data,a computational study is done to verify the proposed algorithm and models,especially in handling with trade-off between quality of system-wide coverage and cost management.Some managerial insights are also drawn for EMS managers.Lastly,two-stage robust facility location under different sources of uncertainty with application to humanitarian logistics.In this research,we incorporate multiple uncertainties of demand,transportation cost and facility disruption simultaneously,and propose a novel two-stage robust facility location framework and with application to humanitarian logistics.At the beginning,we employ budget uncertainty set to capture the uncertain demand and transportation cost,propose a novel robust facility location model that can be reformulated as mixed integer programming counterpart,in which these two uncertain parameters are multiplicative in the objective.Then,assuming facility disruptions,we do not rely on any distributional information of facility disruptions completely and employ budget uncertainty set to capture the disruptions,which is much different from the idea in current works that they assume a known facility disrupted probability.But in real-life,it is nearly impossible for us to know exactly or predict accurately the disrupted probability.Based on different sources of uncertainty,we propose two-stage robust facility location model,in which decisions under disrupted situation is made in recourse stage and decisions under normal case is decided in first stage.Moreover,we design a strengthened column-and-constraint generation(C&CG)method to solve the min-max bi-level reformulation.A practical study is also investigated for the Northwest Sichuan,and some managerial insights are drawn.All in all,not only alleviate the huge risk caused by uncertainties and improve the efficiency of current EMS network,this research can enrich the existing literature about EMS facility location problems,and also provides useful guidance for EMS department and government.In terms of both methodology and real application,to the best of our knowledge,this research is the first to address the probabilistic envelope constraint from stochastic programming perspective,and generalize the chance constraint into PEC,which is applied to EMS facility location problems successfully.