Dataset on optimizing ambulance deployment and redeployment in Fez-Meknes region, Morocco

Emergency Medical Services (EMS) are crucial for saving patients' life, attenuating disabilities, and improving patients' satisfaction. Optimal deployment and redeployment of ambulances over a territory reduce response times for serving emergencies. Thus, rapid interventions and transport to a hospital are guaranteed. Optimizing ambulance deployment and redeployment is achieved by conceptualizing and formulating mathematical programming models and simulation models. Mathematical models maximize the proportion of the population that can be reached by ambulance in a response time less than a threshold value. In contrast, simulation models assess a given ambulance deployment and redeployment configuration. The application of mathematical and simulation models require data related to demand areas (geographic territories), demand value at each demand area, locations of potential sites for ambulance bases, X and Y geographic coordinates of demand areas and potential sites, travel times between potential sites and demand areas, etc. All these data are essential in deciding which potential sites to choose for locating ambulance bases and how many ambulances to allocate to each base per period. Beside elaborating and constructing ambulance deployment and redeployment models, researchers in Operations Research (OR) are challenged when collecting data for executing, testing, and proving the performance of their proposed models. This paper provides data about medical transport in Morocco's Fez-Meknes region, which can be accessed at https://zenodo.org/record/6416058. They were collected from the field, estimated based on the population size, and obtained by computer programs. The dataset includes 199 demand areas and their respective demand value per ambulance type and per period, the travel times between 18, 22, 40 potential sites and the 199 demand areas per period, and the travel times between the potential sites. Also, the dataset comprises the minimum number b of ambulances required by each demand area for α-reliable coverage, which was computed using a MATLAB program. The number b of ambulances required by each demand area is mandatory to apply reliability models such as the MALP and the Q-MALP models. These data would be used by the research community interested in EMS, especially pre-hospital emergency issues addressed by deploying mathematical programming and simulation tools.

elaborating and constructing ambulance deployment and redeployment models, researchers in Operations Research (OR) are challenged when collecting data for executing, testing, and proving the performance of their proposed models. This paper provides data about medical transport in Morocco's Fez-Meknes region, which can be accessed at https: //zenodo.org/record/6416058 . They were collected from the field, estimated based on the population size, and obtained by computer programs. The dataset includes 199 demand areas and their respective demand value per ambulance type and per period, the travel times between 18, 22, 40 potential sites and the 199 demand areas per period, and the travel times between the potential sites. Also, the dataset comprises the minimum number b of ambulances required by each demand area for α-reliable coverage, which was computed using a MATLAB program. The number b of ambulances required by each demand area is mandatory to apply reliability models such as the MALP and the Q-MALP models. These data would be used by the research community interested in EMS, especially pre-hospital emergency issues addressed by deploying mathematical programming and simulation tools.

Value of the Data
• Data on Emergency Medical Services (EMS) are crucial for optimizing ambulance deployment and redeployment. Indeed, researchers in Operations Research (OR) conceptualize and formulate optimization models for ambulance deployment and redeployment. They need data to solve their models, compare them with other models, and defend their proposals. • Data presented in this article would be helpful to OR researchers interested in developing simulation and mathematical programming models for optimizing ambulance deployment and redeployment. Several articles on EMS and ambulance deployment have pointed to a lack of data as the main limitation of applying optimization models [ 4 , 5 ]. Making these data available and accessible would help OR researchers focus on developing their models and improving their performance rather than collecting data to test them. • When a mathematical model is formulated, researchers need to test, compare and apply them to make them valuable. Researchers can use the provided data to study the behavior of their proposed models. They can also be used for simulation purposes. Based on the obtained results, researchers could compare the performance of their proposed models with previously developed models.

Data Description
Researchers incorporate several parameters when building simulation models or developing mathematical optimization models for ambulance deployment and redeployment [6] . These include the demand area's definition, the demand's value for each demand area, the identification of potential sites for ambulance base location, the estimation of travel times between potential sites and demand areas, etc. This section presents the data related to these parameters and the notations commonly associated with them. Note that the tables shown in the text ( Tables 1 to 16 ) are explanatory and illustrative. All indicated data are made accessible on the Zenodo repository data https://zenodo.org/record/6416058 [1] , containing complete tables.

Demand
EMS demand is at the heart of ambulance deployment and redeployment models. It allows making optimal decisions about locating ambulances to cover the maximum number of requests. For this purpose, it is necessary to know the exact location of the demand areas and the value of the demand at each demand area. Fig. 1 presents the territory for which the dataset presented in this article was collected, computed, and made available. The territory is Morocco's Fez-Meknes region, composed of 9 prefectures and provinces. Each of them is subdivided into municipalities and boroughs, corresponding to demand areas. In total, the territory includes 199 demand areas.  190; 191; 192; 193; 194; 195; 196; 197; 198; 199

Indexes of demand areas
For modeling purposes, an index i is assigned to each demand area as described in Table 1 . Mathematical programming models identify demand areas by their corresponding indexes and use them in equations and mathematical formulas.

X and Y geographic coordinates of demand areas
The associated X and Y geographic coordinates for each demand area were identified and reported in Table 2 . The geographic coordinates are essential because they are needed to identify demand areas and estimate travel times (see Section 2.4 ).

Demand values
The value of transport demand is the number of calls received and handled by the Civil Protection Alert Processing Center in the Fez-Meknes region. In our investigation, we found only the total number of interventions in the whole territory of the prefectures and provinces. The number of interventions in each demand area is not available. In the absence of data on demand history in each demand area, researchers propose substituting demand by the size of the resident population using a scale [4] .  Table 4 Values of demand in each demand area.

ALS Ambulances BLS Ambulances
Demand Areas Index  Table 3 provides the population size in each demand area extracted from the High Commission for Planning (HCP) 1 database, the primary data provider in Morocco.
In this data paper, we suggest substituting the history of interventions with the population size in each demand area using ratios calculated by dividing the actual number of Civil Protection interventions by the population size (see Section 2.1 ).
Multi-period redeployment models need to dispose of the demand value at each demand area per ambulance type and time period. Most EMS systems operate with two distinct ambulance types: AL S and BL S ambulances. Table 4 provides the demand value at each demand area per ambulance type (AL S and BL S) and per period ( t = 1 and t = 2). The two periods were defined based on the analysis conducted in Section 2.3 .
Data in Table 4 were estimated based on the population size in each demand area provided in Table 3 and using ratios described in Section 2.1 . Concerning the breakdown of demands per ambulance type, we hypothesized that 65% of demands requested BLS ambulances, and 35% requested ALS ambulances. Also, 70% of demands arrive during the first period ( t = 1) and 30% during the second period ( t = 2).
For example, for the first line of Table 4 corresponding to the first demand area ( i = 1), the demand value is obtained by multiplying the population size (141,168) by the ratio of 1.0470% (see Section 2.1 ), which gives a result of 1478 (the annual demand of demand area 1). 35% of this demand is ALS demand (517), and 75% is BLS demand (961). Then, the ALS demand during the first period ( t = 1) is 362 (0.7 × 517) and during the second period ( t = 2) is 155 (0.3 × 517). The same for BLS demand during the first period 673 (0.7 × 961) and during the second period 288 (0.3 × 961).

Arrival rates
The arrival rate is the average number of requests received per hour. For ambulance deployment and redeployment optimization, the arrival rates are needed per demand area ( i = 1, …199), per period ( t = 1, 2), and ambulance type (AL S, BL S). They were estimated from Table 4 , reporting the demand value in each demand area and using Eqs. (1) -(4) .
Demand Area Index Service Time (minutes) For instance, the arrival rate λ( i = 1, t = 1, ALS) for demand area i = 1 is calculated by dividing the annual demand (362) from Table 4 by the duration of the period t = 1 in hours (15 h) multiplied by 365 days of the year. Table 5 provides the arrival rates of demands requesting ambulances of type ALS and BLS per period.

Service time
When an ambulance is dispatched to serve demand, it becomes busy during an amount of time, called service time. It corresponds to the time it takes for the ambulance to get to the demand area, provide on-site care, transport the patient to a hospital, and return to the ambulance base.
Researchers developing probabilistic mathematical programming models and simulation models need to estimate the service time at each demand area. Table 6 provides service time at each of the 199 demand areas included in the dataset.

Potential sites
Potential sites correspond to some selected demand areas that can host ambulance bases. In this dataset, we have considered three cases of potential sites. The first case corresponds to the current ambulance base sites in the Fez-Meknes region (18 potential sites). The second case adds sites with hospitals (22 potential sites). The third case includes all urban municipalities (40 potential sites). For modeling purposes, we differentiate between potential sites and demand areas. For this, we used different indices: the i index for the demand areas ( i = 1, ..., 199) and the j index for the potential sites. For the first case of 18 potential sites j = 1, ... 18; the second case, j = 1, ... 22; the third case j = 1, …40. However, note that potential sites are also demand areas. Table 7 lists the potential sites considered in the three cases with their i and j indexes. Figs. 2-4 show the locations of the 18, 22, and 40 potential sites, respectively.

Number of ambulances
We provide in Table 8 different options concerning the maximum number of ambulances to be deployed per type and per period. These numbers constitute the upper bound of deployed ambulances.  The data in Table 8 can be used for testing purposes and analyzing the behavior of the optimization models based on the number of ambulances to be deployed.

Travel time
Travel times between the 18, 22, and 40 potential sites and the 199 demand areas per period are indicated in Table 9 , Table 10 , and Table 11 , respectively.
For multi-period redeployment, travel times are mandatory between each potential site and the other potential sites per period. Tables 12-14 give the travel time between the 18 potential sites, 22 potential sites, and 40 potential sites.

Number of ambulances for α-reliable coverage
When researchers base their ambulance deployment and redeployment models on αreliability models such as the MALP [7] model and the Q-MALP model [8] , the number b k it of ambulances is needed to solve these models. It refers to the minimum number of ambulances of type k that have to cover demand area i during period t for α-reliable coverage. In Table 15 we provide the b k it corresponding to α equal 90%.  Table 16 .

Definition of demand areas and estimation of demand values
The demand areas were extracted from the High Commission for Planning (HCP), Morocco's official producer and provider of statistics. Table 17 specifies the number of demand areas of the prefectures and provinces of the Fez-Meknes region.
The value of transport demand is the annual number of calls received and handled by the Civil Protection (CP) Alert Processing Center in the Fez-Meknes region. The history of transport interventions is often used to estimate the demand. This approach is widely adopted, especially since it is difficult to predict how much, where, and when transport demands will occur. Hence, we calculated a ratio corresponding to the total number of CP service interventions in each prefecture and province to its population size ( Table 18 ).
The ratios are then used to estimate the demand value in each demand area belonging to each prefecture and province. Indeed, the population size of each demand area was multiplied by the ratio for the prefecture/province to which it belongs.

Definition and location of potential sites
The first case of potential sites (18 potential sites) corresponds to the current location of the CP services in the Fez-Meknes region. The CP staff identified the 18 potential sites. The second case (22 potential sites) added to the 18 potential sites 4 other potential sites corresponding to hospitals identified by hospital managers. 2 The third case (40 potential sites) added to the 22 potential sites 18 other potential sites corresponding to urban areas identified by the HCP. 2 http://www.data.gov.ma/data/fr/dataset/la-liste-des-hopitaux

Definition of time periods
Due to the variation of travel time with traffic depending on the day time periods (i.e., peak hours), multi-period redeployment models suggest subdividing the day into homogeneous periods defined by observing the evolution of travel times. We used the Google Maps mobile application to capture the hourly variations in travel times between a sample of geographic areas in Fez and Meknes cities, the most populated urban areas in the Fez-Meknes region ( Table 19 ). Fig. 5 shows the variation in travel time per hour of the day. It can be observed that two principal periods characterized travel times. The first period is from 7 h to 22 h and the second from 22 h to 7 h.

Estimating travel time
To estimate travel times, we have used a VBA code that communicates with the Bing Map engine using an API.

Computation of the number b k it of ambulances
For α-reliable coverage, there must be at least b k it ambulances of type k covering demand area i during period t . The b k it is expressed using queuing theory formulas of a system M/G/Z/Z. b k it is the smallest integer satisfying Eq. (5) .

Table 19
Travel times between a set of urban areas.

Ethics Statements
This work did not include data involving human subjects, animal tests, or data acquired from social media platforms.