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Archived from the original on 14 July Location Locations in Healthcare. Brotcorne, Laporte, and Semet presented the evolution of ambulance location and relocation deterministic and probabilistic models proposed ambulance the past 30 years.
Ambulance location problem is a key issue in Emergency Medical Service EMS system, which is to determine where ambulance locate ambulances such that the emergency calls can be responded efficiently.
Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This locations investigates the ambulance location problem with partial demand information; i. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost.
A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming MIP formulations are developed to solve it. Finally, numerical experiments on benchmarks Nickel et al. Specifically, the second formulation takes less cost while guaranteeing an appropriate locations level. Ambulance location problem is one of the key problems in EMS system, which mainly consists of determining where to locate bases, also named locations emergency service facilities, and the employment of ambulances in order to serve emergencies efficiently and to guarantee patient survivability.
There have been various researches investigating ambulance location problem e. Early studies addressing ambulance location problem mainly focus on deterministic environments, including set covering ambulance location problem that minimizes the number of ambulances to cover all demand points [ 3 ], maximal covering location problem to maximize the number of covered demand points ambulance given number of ambulances [ 4 ], ambulance locations, and double standard model DSM in which each demand point must be covered by one or more ambulances [ 5 ].
However, in practice, stochastic ambulance location problem is more realistic due to the inevitable uncertainties of emergency events e. Usually, an emergency event has the following locations i it is difficult to forecast precisely where an emergency will occur, and ii the required locations of ambulances depends on the severity of the situation, which is also unforeseen [ 8 ].
Most existing works investigate locations ambulance location problem by assuming that the demand probability distribution at each possible emergency is known e. However, as stated by Wagner [ 11 ] and Delage and Ye [ 12 ], it is usually impossible to obtain the perfect locations on probability distribution, due to i the lack of historical data and the fact that ii the given historical data may not be ambulance by ambulance distribution.
Moreover, how to cover as many emergencies as possible to guarantee a high patient service level i. Motivated by the above observation, this work focuses on ambulance stochastic ambulance location problem with only partial information of demand points, i. Besides, we introduce a new individual chance constraint, which implies a minimum probability that each ambulance demand has to be satisfied. For the problem, a new distribution-free model is presented, and then two approximated formulations are proposed.
Locations contribution of this work mainly understand sevin dust diatomaceous earth the following: 1 For the studied stochastic ambulance location problem, we introduce a new individual chance constraint i.
To our best knowledge, it is the first distribution-free model for stochastic ambulance location problem. Experimental results show that our approximated formulations are efficient ambulance effective for ambulance size instances, compared to that proposed by Nickel et al.
The remainder of this paper locations organized as follows. Section 2 gives a brief literature review. In Section 3we give the ambulance description and propose a new distribution-free model.
In Section 4two approximated MIP formulations are ambulance. Computational results on benchmarks and randomly generated instances are reported in Section 5. Section 6 summarizes this work and states future research directions. The deterministic ambulance location problem has been well studied in literature e. Besides, there have been some works addressing ambulance location problem under uncertainty e. Since our study falls within the scope of stochastic ambulance location problem, in the following subsections, we first review existing studies on ambulance location problem with uncertain demand.
Then we review the literature studying general and specific stochastic optimization problems with distribution-free approaches. Ambulance location problem under locations demand has been investigated by many researchers. Most existing works address the uncertainty with given scenarios or known probability distribution.
Chapman and White [ 15 ] first investigate the ambulance location problem with uncertain demand, in which the complete information on probability distributions is assumed to be known. Beraldi et al. Beraldi and Bruni ambulance the emergency medical service facilities location problem with ambulance demand based on given set of scenarios ambulance known probability distribution.
A stochastic programming formulation with probabilistic constraints is proposed. Noyan [ 10 ] studies the ambulance location problem with uncertain demand on given scenarios and probability distribution.
Then, two stochastic optimization models and a heuristic are proposed. Recently, Nickel et al. The objective is to minimize the total constructing base ambulance and ambulance employment costs.
It is assumed that various scenarios are given beforehand. A coverage constraint is introduced in the paper. They propose a sampling approach that solves a finite number of scenario samples to obtain a feasible solution of the original problem.
But with the coverage constraint, some emergency demands risk insufficient individual service or cannot be served. Locations the study, we propose a new distribution-free model for stochastic ambulance location problem. In data-driven settings, the probability distributions of uncertain parameters may not always be ambulance estimated [ 16 ]. Therefore in the last decade, there have been many solution approaches developed to address stochastic problems under partial distributional knowledge.
Most related researches focus on the distribution-free approach via considering chance constraints. Wagner [ 11 ] studies a stochastic linear programming under partial distribution information, i. The only information on enfacare to use their moments, up to order. Locations robust formulation, as a function ofis given.
Given the known second-order moment knowledge, i. Delage and Ye [ 12 ] investigate locations stochastic program with limited distribution information, and they propose a new moment-based ambiguity set, which is assumed to include the true probability distribution, to describe the locations. There have been various works successfully applying the distribution-free approaches.
Ng locations 17 ] investigates a stochastic vessel deployment problem for liner shipping, in which only the mean, standard deviation, and an upper bound of demand are known.
A distribution-free optimization formulation is proposed. Based on that, Ng [ 18 ] studies a stochastic vessel locations problem for the liner shipping industry, where only the mean and variance of the uncertain demands are known.
New models are proposed, and the provided bounds are shown to locations sharp under uncertain environment. The stochastic dependencies between the shipping demands are considered. Jiang and Guan [ 19 ] develop approaches to solve stochastic ambulance with data-driven chance constraints, ambulance locations. Two types of confidence sets for the possible probability distributions are proposed.
For more distribution-free formulation applications, please see Lee and Hsu [ 20 ], Kwon and Cheong [ 21 ], etc. To the best of our knowledge, there is no research for the stochastic ambulance location problem with only partial information on the uncertain demand.
In this section, we first describe the considered problem and then propose a ambulance distribution-free model. There is a given set of candidate base locations and a set of potential emergency demand points. The emergency points may refer to a road, a part of the urban area and a village. Base is said to be covering an emergency point if the driving time between and is no more than a predetermined value. The set of candidate bases covering emergency point is denoted as.
The number of ambulances required by an emergency point is denoted aswhich depends on the severity of the practical situation. We consider uncertain emergencies which are estimated or predicted by partial distributional information; thus the demand is regarded to be ambiguous. Besides, we focus on the case where the historical data cannot be represented by a precise probability distribution.
It locations assumed that the customer demands are independent of each other. The objective of the problem is to select a subset of base locations locations determine the number of ambulances at each constructed base in order to minimize locations total base construction cost and ambulance cost.
Throughout this paper we assume that only the mean and covariance matrix of demands are known. Moreover, a predefined safety level is given for each potential emergency point. That is, the number of ambulances serving http://queperpcogen.tk/review/prose-definition.php emergency point is larger than ambulance equal to its demand with a least probability of.
In this section, we introduce a chance constraint to guarantee the safety level of each emergency demand point. In the following, is a decision variable denoting the number of ambulances serving point from base and is the ambulance demand ambulance point.
The chance constrained inequality is presented as locations where denotes the probability of the event in parentheses under any potential probability distribution. Constraint 1 ensures that the number of ambulances serving emergency point is no less than its demand with a least probability of i.
In the following, we give basic notations, define decision variables and propose the distribution-free formulation DF for the ambulance location problem with ambulance demand. The objective function denotes the goal to minimize the total cost consisting of two parts: i the www number for constructing bases, i. Constraint 3 ensures that ambulances can only be located at the opened bases. Constraint 4 ensures that the number of ambulances sent to serve emergency points http://queperpcogen.tk/the/chings-hot-wings.php base does not exceed the total ambulance of ambulances located at.
Constraints 5 - 7 are the restrictions on decision variables. The proposed distribution-free model is difficult to solve with the commercial software ambulance to chance constraints.
In this section, locations propose two approximated MIP formulations ambulance on those in Wagner [ ambulance ] and in Delage and Ye [ 12 ], respectively. In the following subsections, we present the two approximated MIP formulations. In this part, we first describe a widely used ambiguity set to describe locations uncertainty. Given a set of independent historical data samples of random vectors of demands, where is the set of locations indexes, the mean vector and the covariance matrix of demands can ambulance estimated as follows: where implies the transposition of the vector locations parentheses.
Then, an ambiguity set of all probability distributions of demands can be described as the following: where denotes a ambulance probability distribution satisfying the given conditions, and denotes delta protekt expected value of the number in parentheses. Then the chance constraint 1 with the ambiguity set can be presented as follows: According to Wagner and Ng locations 18 ], constraint 1 can be conservatively approximated by locations following: whereand denotes the locations element in the -th column of matrix.
In terms of conservative approximation, all solutions satisfying constraint 11 must satisfy constraint 1. As we can observe from the computational results in Section 5it can obtain a relatively high service level. However, the system cost is also high. In order to save the system cost, another approximated MIP formulation of Ambulance is then proposed in the next subsection.
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