The Applications Of Generalized Maximal Covering Model In Emergency Facility Location Problem

The most important function in emergency management is that choosing the positions of emergency service facilities, so as to provid abundant emergency resources immediately to the places where the accidents happened. For example, in city programming, the policy-maker always decide where to open the emergency service facilities such as police station, fire brigade,emergency treatment station, traffic control ing centre and so on, to ensure that for each emergency node could be served by some facility as soon as possible when emergency occured on this node. Service facility location decision is extremely important to emergency management, for opening facilities on appropriate sites could not only decrease the cost, but also ensure that the goods can be provided efficiently so as to avoid more possible losts.So far, many relevant models of emergency facility location problem have been proposed by researchers, including absolute centre-point model, median model, set covering model and maximal covering model and a wide variety of extensions. There also has been some applications of queueing theory, analytical hierarchy process (AHP)and DEA(data envelopment analysis)methord in emergency facility location, and have obtained many accomplishments.On the base of emergency facility maximal covering location problem (MCLP),this paper applies generalized maximal covering model into emergecy facility location problem, improves the assumption that the coverage is binary in maximal covering model,and considers the coverage as a decreasing step function between 0～1; in addition, in view of the reques-ts of urgency and efficiency in emergency service, this paper replaces distiance which was used to measure coverage levels in generalized maximal covering model with response time, then presents an emergency facility generalized maximal covering location problem(GMCLP).As a result of the assumption that the coverage is binary in traditional maximal covering model, a few of certain emergency nodes might not be covered. However, in fact, all of the emergency nodes should be served no matter whether the times from facilities to these nodes exceed the restricted time. Therefore, this paper introduces the following generalization of the MCLP model; we assume that for each emergency node i corresponds a multiple set of response times(different response time is generated by different emergency facility), with corresponding coverage levels, are specified, then the degree of coverage is assumed to be a decreasing step function of the response time to the closest facility, the notion of partially covered"is proposed between full covered and not covered. Thus, each of the emergency node i can be covered just with different coverage levels. The GMCLP model resolved the problem of which certain nodes might not be covered in traditional MCLP model, and realized covering all nodes in net with finite resources. In the end, the branchand-bound algorithm and heuristic algorithm based on lagrangian relaxation are developed to solve the model, and a computational instance is presented to illustrate how GMCLP model has improved MCLP model.In addition, on the base of response time which was considered merely before,this paper also considers the processing ability of emergency facility. We assume that the emergency system consists of two types of service facilities with different capabilities, each type of facility corresponds specified restricted times, and also consider the standard whether a node is served adequately. According to this, we establish double-goal programming formulations for emergency facility location problem, including double-goal MCLP formulation and double-goal MCLP-GMCLP formulation. Computational results are presented for comparing two types of formulations.