domain: info sde

text:
Christophe Botella

Pierre Bonnet

François Munoz

Pascal Monestiez

Alexis Joly

Overview of GeoLifeCLEF 2018: location-based species recommendation

Keywords: LifeCLEF, biodiversity, big data, environmental data, visual data, species recommendation, evaluation, benchmark

The GeoLifeCLEF challenge provides a testbed for the systemoriented evaluation of a geographic species recommendation service. The aim is to investigate location-based recommendation approaches in the context of large scale spatialized environmental data. This paper presents an overview of the resources and assessments of the GeoLifeCLEF task 2018, summarizes the approaches employed by the participating groups, and provides an analysis of the main evaluation results.

Introduction

Automatically predicting the list of species that are the most likely to be observed at a given location is useful for many scenarios in biodiversity informatics. First of all, it could improve species identification processes and tools by reducing the list of candidate species that are observable at a given location (be they automated, semi-automated or based on classical field guides or flora). More generally, it could facilitate biodiversity inventories through the development of location-based recommendation services (typically on mobile phones) as well as the involvement of non-expert nature observers. Last but not least, it might serve educational purposes thanks to biodiversity discovery applications providing functionalities such as contextualized educational pathways.

The aim of the challenge is to predict the list of species that are the most likely to be observed at a given location. Therefore, we provided a large training set of species occurrences, each occurrence being associated to a multi-channel image characterizing the local environment. Indeed, it is usually not possible to learn a species distribution model directly from spatial positions because of the limited number of occurrences and the sampling bias. What is usually done in ecology is to predict the distribution on the basis of a representation in the environmental space, typically a feature vector composed of climatic variables (average temperature at that location, precipitation, etc.) and other variables such as soil type, land cover, distance to water, etc. The originality of GeoLifeCLEF is to generalize such niche modeling approach to the use of an image-based environmental representation space. Instead of learning a model from environmental feature vectors, participants may learn a model from k-dimensional image patches, each patch representing the value of an environmental variable in the neighborhood of the occurrence (see Figure 1 below for an illustration). From a machine learning point of view, the challenge will thus be treatable as a multi-channel image classification task.

Dataset

The participants were provided with a train and test set of species geolocated occurrences. Both were first composed of a .csv file with the occurrences spatial coordinates, the punctual values of environmental variables at the occurrence location, and, for the train table, the species name and identifier. Secondly, each row of the table (train and test) referred to a 33-channel image containing the environmental tensor extracted at that location.

Species occurrences

Occurrences data were extracted from the Global Biodiversity Information Facility platform (GBIF6 ). To achieve precise species prediction from a geolocation, the geolocations in question must be as precise as possible. However, a high number of occurrences from the GBIF have a spatially degraded geolocation for conservation reasons. Thus, we have chosen source datasets with undegraded geolocations in France, which are : Only observations falling in the metropolitan French territory were kept so as to focus on a region for which we had an easy access to rich and homogeneous environmental descriptors for the whole dataset. Occurrences with uncertain names, as notified by the GBIF, were removed. The full dataset is finally composed of 291,392 occurrences. The labels to be predicted within the challenge are the species identifier (field species glc id). There are 3,336 species identifiers in total, and their associated taxonomic names are provided by the field espece retenue bdtfx (bdtfx referential 4.1). Due to some unreferenced heterogeneity in the data collection protocol (naturalists checklists, conversion of site name to geolocation, etc), some geographical points accumulate several occurrences. Indeed, there are in total 75,668 distinct geolocations (with a maximum of 527 points in one geolocation). All occurrences geolocations are represented in Figure 2. It reveals the bias in the spatial distribution of the occurrences.

Environmental data

Each occurrence is characterized by 33 local environmental images of 64x64 pixels. These environmental images were constructed from various open datasets and include 19 bioclimatic quantitative variables at 1km resolution from Chelsea Climate [START_REF] Karger | Climatologies at high resolution for the earth's land surface areas[END_REF], 10 pedological ordinal variables at 1km resolution from ESDB soil pedology data [START_REF] Panagos | The european soil database[END_REF][START_REF] Panagos | European soil data centre: Response to european policy support and public data requirements[END_REF][START_REF] Van Liedekerke | Esdbv2 raster library-a set of rasters derived from the european soil database distribution v2. 0. European Commission and the European Soil Bureau Network[END_REF], one land cover categorical descriptor at 100 meters resolution from Corine Land Cover 2012 soil occupation data (version 18.5.1, 12/2016), one potential evapo-transpiration quantitative variable at 1km resolution from CGIAR-CSI evapotranspiration data ( [START_REF] Zomer | Trees and water: smallholder agroforestry on irrigated lands in Northern India[END_REF][START_REF] Zomer | Climate change mitigation: A spatial analysis of global land suitability for clean development mechanism afforestation and reforestation[END_REF]), one elevation quantitative variable at 90 meters resolution from USGS Elevation data (Data available from the U.S. Geological Survey and downloadable on the Earthexplorer7 ) and one indicator of fresh water proximity at 12,5m resolution from the BD Carthage hydrologic data. As each of those variables are stored in large raster covering the French geographical territory. For any occurrence, we crop a 64 × 64 pixels window centered on the occurrence geolocation from the raster of each environmental variable. This way, we make the 64 × 64 × 33 environmental tensor associated with this occurrence. Besides, the punctual environmental values associated with an occurrence, are simply the extracted cell's values from the rasters at the occurrence geolocation.

Train and test sets

The total of 291,392 occurrences were randomly split into a training set (218,543) and a test set (72,849) with the constraints that :

-For each species in the test set, there is at least one observation of it in the training set. -An observation of a species in the test set is distant of more than 100 meters from all observations of this species in the train set to avoid major reporting dependencies.

Thus, the final train set contained all of the 3,336 species, while the test set contained 3,209 species.

Task Description

For every occurrence of the test set, participants must supply a list of 100 species maximum, ranked without ex-aequo. The used evaluation metric is the Mean Reciprocal Rank (MRR). The MRR is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries ordered by probability of correctness. The reciprocal rank of a query response is the multiplicative inverse of the rank of the correct answer. The MRR is the average of the reciprocal ranks for the whole test set:

M RR = 1 Q Q q=1 1 rank q
where Q is the total number of query occurrences x q in the test set and rank q is the rank of the correct species y(x q ) in the ranked list of species predicted by the evaluated method for the occurrence x q .

4 Participants and methods 22 research groups registered to the GeoLifeCLEF challenge 2018. Among this large raw audience, 3 research groups finally succeeded in submitting run files. Details of the used methods and evaluated systems are synthesized below and further developed in the working notes of the participants ( [START_REF] Deneu | Location-based species recommendation using co-occurrences and environment -geolifeclef 2018 challenge[END_REF], [START_REF] Taubert | Species prediction based on environmental variables using machine learning techniques[END_REF] and [START_REF] Moudhgalya | Hierarchically embedded taxonomy with clnn to predict species based on spatial features[END_REF]). Table 1 reports the results achieved by each run as well as a brief synthesis on the methods used in each of them. Complementary, the following paragraphs give a few more details about the methods and the overall strategy employed by each participant.

FLO team, France, 10 runs, [START_REF] Deneu | Location-based species recommendation using co-occurrences and environment -geolifeclef 2018 challenge[END_REF]: FLO developed four prediction models, (i) one convolutional neural network trained on environmental tensors (FLO 3). The CNN implemented a customized architecture. It also treated the categorical land cover descriptor independantly from quantitative variables for the primary layers. Activation's of both variables types where then fused in deeper layers. (ii) one neural network (FLO 2) trained on species occurrences falling at the closest spatial point and two other models only based on the spatial occurrences of species: (iii) a closest-location classifier (FLO 1) and (iv) a random forest fitted on the spatial coordinates (FLO 4). Other runs correspond to late fusions of that base models, either by simply averaging either the output probabilities (FLO 5,FLO 6,FLO 7,FLO 8), or ranks with the Borda method (FLO 9,FLO 10).

ST team, Germany, 16 runs, [START_REF] Taubert | Species prediction based on environmental variables using machine learning techniques[END_REF]: ST experimented two main types of models, convolutional neural networks on environmental tensors with different data augmentations like rotation and flip of images (ST 1, ST 3, ST 11, ST 14, ST 15, ST 18, ST 19) and Boosted Trees (XGBoost) on vectors of environmental variables concatenated with spatial positions (ST 6, ST 9, ST 10, ST 12, ST 13, ST 16, ST 17). They also proposed a nearest-neighbor classifier based on the environmental variables of occurrences (ST 5), and two species cluster models (ST 17,ST 8) where groups of species are constituted by the similarity of the environmental variables where they occur. For analysis purposes, ST 2 corresponds to a random predictor and ST 7 to a constant predictor returning always the 100 most frequent species (ranked by decreasing value of their frequency in the training set). SSN, India, 4 runs, [START_REF] Nithish B Moudhgalya | Hierarchically embedded taxonomy with clnn to predict species based on spatial features[END_REF]: SSN attempted to learn a CNN-LSTM hybrid model, based on a ResNext architecture [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF] extended with an LSTM layer [START_REF] Gers | Learning to forget: Continual prediction with lstm[END_REF] aimed at predicting the plant categories at 5 different levels of the taxonomy (class, then order, then family, then genus and finally species). The four runs are derived from this model.

Results

We report in Figure 3 and Table 1 the main results achieved by the 33 submitted runs as well as some synthetic information about the used methods and variables for each run. The main conclusions we can draw from that results are the following:

Convolutional Neural Networks outperformed boosted trees: Boosted trees are known to provide state-of-the-art performance for environmental modelling. They are actually used in a wide variety of ecological studies [START_REF] Guisan | Habitat Suitability and Distribution Models: With Applications in R[END_REF][START_REF] De'ath | Boosted trees for ecological modeling and prediction[END_REF][START_REF] Messina | Mapping global environmental suitability for zika virus[END_REF][START_REF] Moyes | Predicting the geographical distributions of the macaque hosts and mosquito vectors of plasmodium knowlesi malaria in forested and non-forested areas[END_REF]. Our evaluation, however, demonstrate that they can be consistently outperformed by convolutional neural networks trained on environmental data tensors. The best submitted run that does not result from a fusion of different models (FLO 3), is actually a convolutional neural network trained on the environmental patches. It achieved a M RR of 0.043 whereas the best boosted tree (ST 16) achieved a M RR of 0.035. As another evidence of the better performance of the CNN model, the six best runs of the challenge result from the combination of it with the other models of the Floris'Tic team. Now, it is important to notice that the CNN models trained by the ST team (ST 1, ST 3, ST 11, ST 14, ST 15, ST 18, ST 19) and SSN team did not obtain good performance at all (often worse than the constant predictor based on the class prior distribution), which could be due to a mismatch of species identifiers, as noticed by the participant. For team ST, results can't be interpreted directly as a failure of the methods. The ranking of runs in the test set was not consistent with validation results and the learning process can be improved according to [START_REF] Taubert | Species prediction based on environmental variables using machine learning techniques[END_REF]. This illustrates the difficulty of designing and fitting deep neural networks on new problems without former references in the literature. Lastly, the approaches trying to adapt existing complex CNN architectures that are popular in the image domain (such as VGG [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], DenseNet [START_REF] Huang | Densely connected convolutional networks[END_REF], ResNEXT [START_REF] Xie | Aggregated residual transformations for deep neural networks[END_REF] and LSTM [START_REF] Gers | Learning to forget: Continual prediction with lstm[END_REF]) were not successfull. High difference of performances in CNN learned with homemade architectures (F LO 6, F LO 3, F LO 8, F LO 5, F LO 9, F LO 10 compared to ST 3, ST 1) could underline the importance of architecture choices.

Purely spatial models are not so bad: the random forest model of the FLO team, fitted on spatial coordinates solely (FLO 4), achieved a fair M RR of 0.0329, close to the performance of the boosted trees of the ST team (that were trained on environmental & spatial data). Purely spatial models are usually not used for species distribution modelling because of the heterogeneity of the observations density across different regions. Indeed, the spatial distribution of the observed specimens is often more correlated with the geographic preferences of the observers than with the abundance of the observed species. However the goal of GeoLifeClef is to predict the most likely species to observe given the real presence of a plant. Thus, the heterogeneity of the sampling effort should induce less bias than in ecological studies.

It is likely that the Convolutional Neural Network already captured the spatial information: The best run of the whole challenge (FLO 6) results from the combination of the best environmental model (CNN FLO 3) and the best spatial model (Random forest FLO 4). However, it is noticeable that the improvement of the fused run compared to the CNN alone is extremely tight (+ 0.0005), and actually not statistically significant. In other words, it seems that the information learned by the spatial model was already captured by the CNN. Besides, CNN uses the whole environmental tensor as input and is better than the XGBoost methods which used only the average of each environmental matrix as input. So it is likely that CNN captured more information than the average of the environmental image. It might be some patterns associated with a particular area, or more generic environmental patterns (a wet valley, etc.).

The learning of species communities patterns has potential: We first state that species have marked spatial patterns. Indeed, predicting the nearest species in space (FLO 1) or in the environmental space (ST 5) is much more efficient than simply listing species per global abundance (ST 7), which corresponds to a uniform prior on spatial distribution of each species. Second, methods that allow interactions between species abundance, either by building and predicting group of species that have similar environmental preferences (ST 17), or learning the association between species that co-occur in a close surrounding (FLO 2) perform better than simple nearest-neighbor approaches. However, these approaches are still limitating as, for example, FLO 2 only used the closest point as input information about surrounding species. Besides, even though the good performance of ST 17, there was very few groups of more than 1 species in their algorithm, which leaves small chances to predict non-common species while they represent the majority of species.

A significant margin of progress but still very promising results: even if the best MRR scores appear to be very low at a first glance, it is important to relativize them with regard to the nature of the task. Many species (tens to hundred) are actually living at the same location so that achieving very high MRR scores is not possible. The MRR score is useful to compare the methods between each others but it should not be interpreted as for a classical information retrieval task. In the test set itself, several species are often observed at exactly the same location. So that there is a max bound on the achievable MRR equal to 0.56. The best run (FLO 3) is still far from this max bound (MRR=0.043) but it is much better than the random or the prior distribution based MRR. Concretely, it retrieves the right species in the top-10 results in 25% of the cases, or in the top-100 in 49% of the cases (over 3, 336 species in the training set), which means that it is not so bad at predicting the set of species that might be observed at that location.

Complementary Analysis

Spatial heterogeneity of model performances: We computed the MRR restricted to occurrences that fall in spatial quadrats of 10×10 km all over the French territory. We projected this on a map in Figure 4. The global performances of the methods hide spatial heterogeneity, as shown in the map. Indeed, Paris is the best predicted area, then the Mediterranean region and the Alpes. Then other regions like the Loire, the Pyrenees and the Atlantic coastline. One could think this is due to the larger number of points available in these areas, but this is not exactly true. Complementary analysis showed that the importantly sampled areas had a more stable MRR but not higher in average. Thus, improving models predictions should pass by finding reasons of varying regional performances, in the hope to bring a solution. Rare species are not unpredictable: For each species and method, we calculated the MRR over the occurrences of this species in the test set. We ordered species per decreasing global occurrences count in the test set in order to compare the performances of each method along the gradient from common to rare species. The raw graphs were difficult to analyse because the MRR varies importantly for rare species, as there are very few occurrences. Thus, we operate a smoothing along the scarcity gradient. For each species we took the median of the MRR over the 40 species of closest rank on this scarcity gradient. Figures 5 and6 show the result for FLO 3 (environmental CNN), ST 16 (XGBoost), FLO 4 (spatial Random Forest) and ST 7 (Global frequency of species). One can see that ST 7 early cancels along the scarcity gradient. This is because more than 50% of the species over which the median is calculated have a null MRR, which correctly represents the tendancy we want to observe. First, it seems that non-common species have marked spatial preferences because FLO 4 is much better when getting scarcer than ST 7. Second, the progression of predictions of FLO 3 and ST 16 compared to FLO 4 for rare species (in the long tail) suggests that those species mainly have marked environmental preferences that is not easy to capture with a spatial model which doesn't have access to this information. The CNN is very good at predicting non-common species, which may be a bit surprising as (i) its predictions should be smooth in space according to the width of some environmental images (64x64km for climatic and pedological variables) and the chosen architecture and (ii) rare species often have a restricted niche.

Conclusion

We have analyzed the results of the 3 participants of GeoLifeCLEF 2018. CNN models learnt on environmental tensors revealed to be the most performing method, however challenging to operate. According to those results, they are more efficient than Boosted Trees a state of the art method in species distribution modeling. This might be because they may detect particular area or environmental patterns as they access to the full surrounding environment data, but that remain to be proved. Spatial and species association methods have shown reasonably good results, but there is room for improvement, especially for the use of interdependence. The complementary analysis revealed that all methods had the same areas of unreliability. Furthermore, the integration of environmental variables seems to be very beneficial to the prediction of noncommon species. The task of finding the species found at a precise location is difficult because many species co-exist at very small spatial scales (under the meter). The accuracy of current geolocation devices doesn't even allow to indicate with this precision the point where the specimen was observed. Thus, in the future, the evaluation process shouldn't penalize predictions of other species that have been observed in such a close surrounding regarding the precision of the reported geolocation.

Fig. 1 .

 1 Fig. 1. Example of 6 channels from the environmental tensor of an occurrence. Each channel is an environmental heatmap, i.e. a matrix representing the values of an environmental variable in a square spatial area centered at the occurrence location.

Fig. 2 .

 2 Fig. 2. Occurrences geolocations in GeoLifeCLEF 2018 and their source dataset over the metropolitan territory.

Fig. 3 .

 3 Fig. 3. MRR scores per submitted run and participant.

Fig. 4 .

 4 Fig. 4. MRR per 10×10km square spatial quadrat for FLO 3 over the study region.

Fig. 5 .

 5 Fig. 5. Smoothed MRR per species for FLO 3 and ST 16. Species are ordered by number of occurrences in the test set. Each species MRR is smoothed by taking the median over the MRR the 40 species of closest rank along the scarcity gradient.

Fig. 6 .

 6 Fig. 6. Smoothed MRR per species for FLO 4 and ST 7. Species are ordered by number of occurrences in the test set. Each species MRR is smoothed by taking the median over the MRR the 40 species of closest rank along the scarcity gradient.

  1. Carnet en ligne from Tela Botanica. 2. Cartographie des Leguminosae (Fabaceae) en France from Tela Botanica. 3. Naturgucker dataset. 4. iNaturalist Research-grade Observations.

Table 1 :

 1 Methods and results of runs submitted to GeoLifeCLEF2018.

	rank run-name	score algorithm type		variables		top1 top10 top30
	Perfect 0.5593					0.4214 0.854 0.97
	1 FLO 6 0.0435	fusion: CNN+Random Forest	Env.tensor, Geoloc	0.0116 0.100 0.25
	2 FLO 3 0.0430 CNN		Env.tensor		0.0110 0.098 0.25
	3 FLO 8 0.0423	fusion: CNN + Random Forest + NN	Env.tensor, Neighbors	Geoloc,	0.0111 0.097 0.24
	4 FLO 5 0.0422 fusion: CNN + NN		Env.tensor, Neighbors	0.0112 0.097 0.24
	5 FLO 9 0.0388	CNN + Random forest + NN	Env.tensor, Neighbors	Geoloc,	0.0099 0.088 0.22
	6 FLO 10	0.0365	CNN neighbors + Random Forest + nearest-(spatial)	Env.tensor, Neighbors, Geoloc	0.0116 0.074 0.20
	7 ST 16	0.0358	XGBoost model/species)	(1	Env.tensor, Geoloc	0.0111 0.077 0.18
	8 ST 13	0.0352 XGBoost		Env.tensor, Geoloc	0.0114 0.075 0.18
	9 ST 10	0.0348 XGBoost		Env.tensor, Geoloc	0.0113 0.073 0.18
	10 ST 9	0.0344 XGBoost		Env.tensor, Geoloc	0.0108 0.073 0.18
	11 ST 12	0.0343 XGBoost		Env.tensor, Geoloc	0.0110 0.072 0.18
	12 ST 6	0.0338	XGBoost model/species)	(1	Env.tensor, Geoloc	0.0104 0.072 0.18
	13 FLO 4 0.0329 Random forest		Geoloc		0.0098 0.071 0.17
	14 FLO 7 0.0327 NN + Random forest		Neighbors, Geoloc	0.0093 0.071 0.18
	15 ST 17	0.0326	Environmental cluster-ing of species	Env.tensor, Geoloc	0.0106 0.068 0.16
	16 FLO 2 0.0274 NN		Neighbors		0.0079 0.057 0.15
	17 ST 5	0.0271	nearest-neighbors (envi-ronment, spatial)	Neighbors		0.0098 0.051 0.14
	18 ST 8	0.0220	Environmental cluster-ing of species	Env.tensor, Geoloc	0.0087 0.043 0.08
	19 FLO 1 0.0199	nearest-neighbors (spa-tial)	Geoloc		0.0077 0.042 0.09
	20 ST 3	0.0153 CNN		Env.tensor		0.0047 0.029 0.08
	21 ST 1	0.0153 CNN		Env.tensor		0.0047 0.029 0.08
	22 ST 14	0.0144 CNN		Env.tensor		0.0040 0.030 0.07
	23 ST 7	0.0134 Global species frequency occurrences counts	0.0026 0.033 0.08
	24 ST 15	0.0103 CNN (vgg-like)		Env.tensor		0.0046 0.019 0.03
	25 ST 19	0.0099	standard DenseNet121 CNN	Env.tensor		0.0021 0.024 0.05
	26 ST 11	0.0096 CNN (vgg-like)		Env.tensor		0.0022 0.022 0.05
	27 ST 18	0.0096 ensemble CNN (vgg-like) Env.tensor		0.0019 0.023 0.05
	28 ST 4	0.0085 XGBoost		Env.tensor, spatial	0.0021 0.022 0.04
	29 SSN 3	0.0030 CNN(Resnext)-LSTM		Env.tensor, Taxonomy	0.0006 0.006 0.02
	30 SSN 4	0.0016 CNN(Resnext)-LSTM		Env.tensor, Taxonomy	0.0000 0.005 0.01
	31 ST 2	0.0016 Random list				0.0003 0.003 0.01
	32 SSN 2	0.0013 CNN(Resnext)-LSTM		Env.tensor, Taxonomy	0.0001 0.002 0.01
	33 SSN 1	0.0004 CNN(Resnext)-LSTM		Env.tensor, Taxonomy	0.0001 0.002 0.00

https://www.gbif.org/

(https://earthexplorer.usgs.gov/)


Aurelie Charles
email: aurelie.charles@mines-albi.fr

Matthieu Lauras

An enterprise modelling approach for better optimisation modelling: application to the humanitarian relief chain coordination problem

Keywords: Optimisation modelling, Humanitarian supply chains, Enterprise modelling, Coordination, Relief chains

HAL is

Introduction

The number of scientific articles dedicated to the study of the humanitarian supply chain (HSC), either general or focussed on a specific issue, was remarkably low 5 years ago. This has changed recently with the publication of a substantial number of papers related to disaster management. There were 120 publications registered in 2009 on this topic in the Science Direct database compared to only 20 publications in 1997.

According to [START_REF] Denizel | Drift or shift? Continuity, change, and international variation in knowledge production in OR/MS[END_REF], three types of research are classically used in OR/MS: management sciences, management consulting and management engineering. In management sciences, the goal is to develop new results to contribute to the body of knowledge in the discipline. As for management consulting, the goal is to solve practical problems using existing, standard methods. Management engineering is between the two, as its goal is to solve those practical problems for which it is necessary to adapt existing tools in fundamentally novel ways. Management engineering is by far the most widely used in the humanitarian context. This may be due to the relative youth of this area of research. If the articles are sorted by disaster contributions, more than half of the research published is on the development of analytical models followed by case studies and theory (one-fourth) [START_REF] Altay | OR MS research in disaster operations management[END_REF]. As for research methodologies, mathematical programming is the most frequently utilised method.

But few or no humanitarian organisations go as far as using optimisation-based decision-support systems. This goes against traditional recommendations found in the academic and business world. According to [START_REF] Simchi-Levi | Designing and managing the supply chain[END_REF], a thorough logistics network analysis, for example, should consider complex transportation cost structures, warehouse sizes, manufacturing limitations, inventory turnover ratios, inventory costs and service levels. These issues typical in humanitarian world could benefit from the use of optimisation-based decision-support systems that can solve large-scale problems efficiently.

OR/MS researchers are no doubt aware that the main criteria of the success of optimisation-based approaches consists in producing a complete and representative mathematical model of the studied system. But considered an art by many and weird science by some, mathematical modelling is not as simple as it seems. This is particularly true in the humanitarian context, as in all new research areas, where researchers have difficulty identifying the right decision variables and parameters to be able to develop accurate and relevant analytical models. This paper tackles the issue by focussing on modelling techniques rather than solution algorithms.

Based on enterprise modelling (EM) methodologies, the present article proposes a conceptual modelling approach that aids in understanding, analysing, evaluating and then developing the formal expression of an HSC. Such a model, therefore, clearly has an added value for practitioners and should allow reliable quantitative models to be produced. From an academic point of view, we are not implementing a typical OR/MS method for developing analytical models, but instead, we are proposing a complementary approach, or to be more specific, one that should precede it. EM enables researchers to keep a business view of operations. With their needed cuts, OR/MS analytical models may move away from such a view. We agree with Barr on the fact that the disciplines of computer science and operations research have been linked since their origins, with decision support modelling being one of the connections between these two areas [START_REF] Barr | Interfaces in computer science and operations research[END_REF]. Thus, we are referring to logical models as found in computer science [START_REF] Gruninger | The logic of enterprise modelling[END_REF] to facilitate mathematical modelling expression.

Our findings will be presented in three parts. First, we will provide the reader with a brief overview of what a relief operation is and how it evolves over time. Knowing that disaster relief is approximately 80% logistics (Van Wassenhove 2006), we will also present a global model of an HSC, briefly underlying the differences with common commercial supply chains. We will provide a brief analysis of the literature on the key elements that constitute a successful humanitarian operation. This literature highlights the need for improvement in terms of coordination capabilities, which drives our future application case.

Second, a specific business process modelling approach to formalise humanitarian operations will be described. This approach originates from the usual process improvement strategy proposed in enterprise modelling (EM) standard ISO19439 [START_REF] Afnor | Enterprise integration-framework for enterprise modelling[END_REF], but some complementary developments have been included to take into account humanitarian specificities. Based on these logical models, a step to support identification of relevant decision variables and parameters is useful for the development of relevant and reliable quantitative models in a humanitarian context.

Finally, we will portray an application case elating to the sudden-onset International Federation of Red Cross (IFRC) business processes.

Basics of relief chains

Salient features of humanitarian supply chains

Various approaches and definitions [START_REF] Kilger | Supply chain management and advanced planning: concepts, models, software and case studies[END_REF][START_REF] Mentzer | Defining supply chain management[END_REF][START_REF] Arnold | Cordination in humanitarian relief chains: practices, challenges and opportunities[END_REF] consider supply chain management (SCM) as coordinated systems that manage flows. [START_REF] Cooper | Characteristics of supply chain management and the implications for purchasing and logistics strategy[END_REF], for example, define SCM as an integrative philosophy for managing the total flow of a distribution channel from the supplier to the ultimate user. [START_REF] Simchi-Levi | Designing and managing the supply chain[END_REF] specify that SCM is a set of approaches utilised to efficiently integrate suppliers, warehouses and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimise system-wide costs while satisfying service level requirements. If we exclude some unsuitable terms such as "user", "store" or "service level", the concept of SCM explains what humanitarian organisations, suppliers and donors must do to minimise the impact of a crisis: this is the humanitarian supply chain (HSC).

According to Van Wassenhove (2006), HSCs are about 15 years behind their privatesector counterparts who realised long ago the importance of using efficient supply chains. He also explains that humanitarian logisticians have been struggling for recognition and that humanitarian organisations are just beginning to wake up to the fact that logistics are crucial. Indeed, the effectiveness of the supply chain is a critical factor in the performance of humanitarian relief organisations, yet this sector has been slow to make much-needed investments in logistics (W.E.F. The Synergos Institute 2005).

Although the humanitarian world has become aware of logistics, work in the context of natural or man-made disasters is very different from logistics in the business context. Several authors (Van Wassenhove 2006;[START_REF] Beamon | Humanitarian relief chains: issues and challenges[END_REF]Stephenson 2005;[START_REF] Oloruntoba | Customer service in emergency relief chains[END_REF]Kovcs and Spens 2007) have tried to identify the characteristics of the former's particular context. We have retained six different categories: -the Stakeholders, -the Categories of Flows Managed, -the Funding Process, -the Dynamics and the Complexity of the Environment, -the Humanitarian Operation Life Cycle, and -the Humanitarian Space.

The Stakeholders The humanitarian distribution channel goes through many different stakeholders, that we call Strategic Humanitarian Units (SHU) starting from suppliers and going to beneficiaries (but not to consumers or users). These SHUs are of a different nature: they are international agencies such as the World Food Programme (WFP), international non-governmental organisations (INGOs) such as Care International, non-governmental organisations (NGOs), implementing partners, the military, donors, private companies and governmental agencies. All these SHUs have, to some extent, the following proprieties: -They are under resourced, with limited skills availability and high employee turnover that limits institutional memory and efficiency. -Ineffective leverage of technology (i.e. non-robust equipment) and in particular, information systems that are relatively basic. Many relief logistics departments rely on manual systems without any Information Technology. -Command / control systems are lacking.

-Several operations need to be done at the same time.

In addition, not all of these stakeholders have the same incentives.

The Categories of Flows Managed The humanitarian distribution channels manage the traditional categories of flows, but these present some specificities:

-Physical flows are material (food, relief items, etc.) and human (organisational skills). -Informational flows (order transmission, tracking and coordination of physical flows) that are poorly structured and managed. -Financial flows that are unilateral (from donors).

Moreover, because the media places such high pressure on agencies to compete for visibility, organisations have to consider the media flow, to better control what is within their sphere of influence. For instance, Van Wassenhove (2006) explains that ineffective use of the media by humanitarian organisations can lead to inundations of unsolicited donations to the supply chain, with resulting bottlenecks, instead of the much-needed resources.

The Funding Process HSC are financed by donors, like governments, private companies, or individuals, through a funding process. The funding process is a channel for donations from individual people or donor organisations to the beneficiaries (through several SHUs). Thus, contrary to Commercial Supply Chains, the financial flows are not parallel with the material flows.

The Dynamics and the Complexity of the Environment The dynamics of HSCs are very specific because they endeavor to respond to certain vital needs due to sudden or long-term crises. An HSC does not start with a customers expression of needs and does not want to make a profit. Under these conditions, it is quite difficult to apply best practices in terms of planning and scheduling. There is evidence of a frequent lack of planning in relief supply chains, resulting in inefficiencies. For example, the overuse of expensive and unsafe air charters, failure to pre-plan stocks, congestion at ports caused by unplanned deliveries, delivery of useless or unwanted items to disaster victims and a lack of inter-organisational collaboration for information systems [START_REF] Oloruntoba | Customer service in emergency relief chains[END_REF]. Generally, an SHU has to -assess needs; -consider unforeseeable conditions and very short time frames; -work under emergency conditions and to be agile; and -manage despite a lack of transparency. The environment of HSCs includes several specific characteristics that intensify its complexity: -A politically volatile climate in which humanitarian organisations have to operate; -Apolitical missions; -A high level of uncertainty in terms of demand, supply and environment.

Other constraints on managing an HSC come from unforeseeable, complex, particular and unstable external actors such as local governments (where the crisis takes place), donor governments, the military (third-party service providers), or privatesector logistics providers (i.e. transportation, warehousing).

The Humanitarian Operation Lifecycle If we consider a project to be a temporary endeavour undertaken to achieve a particular aim, then HSC operations can be defined as a project. In fact, humanitarian organisations are responsible for producing relevant outputs and hence they must be constantly aware of the project goal (minimising the impact of a crisis), project purpose, and of course, the internal measurements of project management efficiency. Concretely, there are two kinds of project environments for implementing humanitarian logistics operations: -Slow-onset disasters: Droughts, epidemics, famine/food insecurity, population movements, and man-made disasters.

In this case, the focus is on capacity building, using national staff, cost savings, low budgets, planning and scheduling and long time frames. -Sudden-onset disasters: Hurricanes, cyclones and typhoons, earthquakes, floods, volcanic eruptions, technological and man-made disasters.

In this case, the focus is on providing medical assistance, providing food and nonfood items, launching appeals, globally assessing needs, using international staff, high budgets and very short time frames. Figure 1 distinguishes the four different phases in the life cycle of a humanitarian operation directly inspired from Van Wassenhove (2006) (2005): Preparedness, Immediate Response (Ramp Up), Support (Maturity) and Dismantling (Ramp Down). The duration of the operations varies according to the function of the project's characteristics (sudden-or slow-onset). Nevertheless, the duration is much less important than it would be for any comparable industrial project. This linear life-cycle may also be represented as a learning loop, where dismantling is followed by preparedness [START_REF] Safran | A strategic approach for disaster and emergency assistance[END_REF].

The Humanitarian Space Humanitarian organisations live by their principles of humanity, neutrality and impartiality. In other words, they will help everyone in need wherever found; they will not influence the outcome of a conflict with their intervention; and they will not favour one group of beneficiaries over another. These principles define the 'space', both physically and virtually, in which they need to be able to operate to do their job effectively (Tomasini and Wassenhove 2009). A set universal minimum standards in core areas has been defined by The Sphere Project (2004).

Figure 2 summarises how an HSC operates.

2.2 Key elements for a successful humanitarian operation "A successful humanitarian operation mitigates the urgent needs of a population with a sustainable reduction of their vulnerability in the shortest amount of time and with the least amount of resources" (Tomasini and Van Wassenhove 2005). Consequently, a successful response to a disaster is not improvised and must be prepared to be effective. 2009) have demonstrated how crucial this problem is. The shortage of qualified staff and the excessive turnover often have harmful consequences on the management of crises. However, methods exist in business management that should be adapted to design relevant skills management systems for the humanitarian sector. 4. The community: Finding effective ways of collaborating with other key players such as governments, the military, business and other humanitarian organisations. See Stephenson (2005), [START_REF] Benini | Network without centre? A case study of an organizational network responding to an earthquake[END_REF] for an application of "organisational design" best practices to humanitarian relief efforts. [START_REF] Pettit | Emergency relief logistics: an evaluation of military, non-military and composite response models[END_REF] have detailed the relations between military and humanitarian organisations. See also Refugee Studies Centre ( 2007) and Van Wassenhove and Samii (2003) for details of centralised coordination regarding a UN agency.

Operations and process management:

Recognising logistics as a central role in preparedness. Then setting up goods, agreements and means needed to move the resources quickly. Several papers discuss operations and process management in HSCs. They study mainly the improvement of unitary operations or business processes in a humanitarian context. Examples include transportation and inventory management (Stapleton et al. 2009b;[START_REF] Whybark | Issues in managing disaster relief inventories[END_REF]Akkihal and Blanco 2006 among others); the development of flexible technology and software for supporting humanitarian operations [START_REF] Blecken | Supply chain management software for humanitarian operations: review and assessment of current tools[END_REF]; metrics and performance measurement in a humanitarian context [START_REF] Davidson | Key performance indicators in humanitarian logistics[END_REF]Beamon and Balcik 2008 among others).

Most of the research that we have referred to earlier is quantitative and has been implemented with optimisation methods. On the contrary, the "community" key element seems to have been studied only in a qualitative manner mainly through case studies (Tomasini andWassenhove 2003, 2009;Van Wassenhove and Samii 2003;[START_REF] Chandes | Investigating humanitarian logistics issues: from operations management to strategic action[END_REF]. The trouble is that the coordination processes are very complex to understand, and consequently very difficult to translate into a mathematical formula. In fact, stakeholders operate at different levels of an HSC and have to guarantee the coherence of their actions, especially when several members of the network operate at the same time in the same place. In addition, practitioners and researchers have a great amount of difficulty designing quantitative models that allow them to coordinate all operations in a consistent way and in general, to improve the performance of an HSC. The purpose of this paper was to explore this problem of developing quantitative models in a relief chain context with a particular focus on coordination aspects that will 1. counteract the fact that "effective coordination of humanitarian assistance activities remains elusive" (Stephenson 2005). 2. Facilitate the implementation of optimisation techniques on HSCs in order to optimise their performances.

The following paragraphs aim to clarify the various facets of coordination in humanitarian operations.

Coordination: a current problem

Lack of coordination has often been listed as a major weakness of humanitarian operations (Stephenson 2005;Kovcs and Spens 2007;Refugee Studies Centre 2007;[START_REF] Arnold | Cordination in humanitarian relief chains: practices, challenges and opportunities[END_REF]Van Wassenhove and Samii 2003). Classically, the problem of humanitarian operations is that at any one time, there can be as many as several hundred humanitarian organisations at the scene of a disaster, not always acting in a coordinated fashion (Van Wassenhove 2006). Consequently, there can be too many participants in the field without a clear division of work (Van Wassenhove 2006). In addition, the communication between stakeholders can be far from optimal. It is easy to understand that two stakeholders having different incentives will have difficulties sharing information. On the other hand, two stakeholders having the same principal activities should be able to align their operations in order to ensure a proper distribution of aid. And yet, a survey of logisticians that participated in the tsunami relief operations showed that just over half the logisticians (56%) reported working with other agencies in setting up their supply chains (Thomas and Kopczak 2005). All these factors contribute to complexity in the delivery of relief.

To summarise, the bigger the disaster, the greater the number of humanitarian organisations that will have sufficient funding to participate in the humanitarian response and the more difficult coordination will be. Many coordination modes exist as selforganising systems or centralised systems [START_REF] Charles | Improving the design and management of agile supply chains: feedback and application in the context of humanitarian aid[END_REF]. The diversity of stakeholders and the variability of their presence and strength from one disaster to another sometimes makes it very difficult to find and implement the appropriate coordination mode. In the following section, we propose a framework that identifies the main determinants of humanitarian coordination.

Key determinants of humanitarian coordination

Malone and Crowsten have illustrated the difficulty of defining coordination and also the variety of possible starting points for studying the concept [START_REF] Malone | The interdisciplinary study of coordination[END_REF]. This section summarizes the key determinants of coordination in the context of humanitarian aid.

Mobilisation and allocation

Humanitarian organisations have to globally manage and control many different solicitations and operations at the same time. Because they are under resourced, they have to define priorities in order to properly dispatch the funds and, of course, the personnel. This is not always easy. According to Thomas and Kopzac, "in order to effectively respond to the Tsunami, 88% of large aid agencies surveyed had to pull their most qualified staff from the ongoing humanitarian operations in Darfur" (Thomas and Kopczak 2005). Globally, this is a problem of balancing available means.

Coherence and efficiency

The majority of humanitarian organisations fulfil various SHUs in the HSC. A typical example is the International Federation of Red Cross (IFRC) that have headquarters in Geneva, three Relief Logistics Units (in Panama, Dubai and Kuala Lumpur) and more than 180 National Societies around the world. Consequently, when a crisis occurs, headquarters has to guarantee the coherence and above all the efficiency of the global action of the network on this crisis. SHUs must synchronise their actions in order to be increasingly effective and responsive. Globally, this is a problem of synchronisation.

Empowerment and best practices

The two precedent components of coordination needs relate to phases 1, 2 and 3 of the life cycle (Fig. 1). But phase 0 could also be included in the coordination. Indeed, during the preparedness phase, a humanitarian organisation should capitalise on its past experiences in order to define best practices in terms of supplier selection, business processes, skill management, etc. This is one of the gap addressed by the humanitarian reform, which is about "making the international humanitarian community more structured, accountable and professional" (IASC 2007). A survey on the value added of the reform indicates that "while many have not yet seen added value, relatively few believe that clusters are useless or going in the wrong direction" (IASC 2007). However, according to many humanitarian workers, "the success or failure of humanitarian response and coordination is too often dependent or personalities". The independent 2007 Cluster Approach Evaluation Report noted that "…attributing everything to personality underplays the degree to which institutions can and do shape the behaviour, practices, and skills of individuals. Yet the humanitarian community has many serious weaknesses in managing human resources: from recruitment to training to appraisal" (The International Council of Voluntary Agencies 2008). The aim of this coordination should be to ensure the use of these best practices during future operations. Moreover, the personnel clearly have to learn from each other in order to be more efficient in the future. Of course, the objective is not standardisation because each crisis is unique. Globally, this is a problem of training.

To summarise, coordination seems to include three key determinants:

1. Balancing: To mobilise and properly allocate funds and skills for different crises at a given time. 2. Synchronisation: To guarantee the coherence and efficiency of a relief operation. 3. Training: To facilitate the empowerment amongst the network members and the implementation of best practices.

To achieve en effective coordination, this framework suggests that relevant operation reports, formalised strategies, responsive business processes, formal procedures, interoperable Information Systems and a responsive and efficient logistical network should be required.

3 An enterprise modelling approach to support optimisation modelling

Principles

Our proposition consists in establishing a conceptual model of an existing HSC in order to be able to extract a quantitative model to optimise parts of an HSC through OR techniques. The proposed methodology can be broken down into two phases:

1. The first phase corresponds to the implementation of an EM modelling approach in the particular context of humanitarian relief operations. To reach this goal, we propose to develop a dedicated humanitarian EM framework and its related Business Process Modelling techniques. 2. The second phase is the mining of previous conceptual models to extract the main components of future quantitative models that could be used to improve the performance of an HSC. The quantitative models considered address different key elements for a successful humanitarian operation described in the previous section. In this paper we will illustrate our proposition by studying several aspects of coordination problems in the case of a sudden-onset disaster.

3.2

Step 1: Enterprise modelling approach EM could be defined as the art of externalising knowledge which adds value to an organisation or needs to be shared (i.e. to describe elements of the organisation). In other worlds, the use of EM enable to build comprehensive figures, which can explain it far better than any kind of long complicated explanation could. It also enables to graphically formalise a given knowledge, and therefore optimises its usage. The major advantage of EM is that it fosters building a common consensus on how operations work or should work. The EM approach brings a number of methods and tools for representing the structure, behaviour, components and operations of a business entity in order to understand, (re)engineer, evaluate and even control business operations and performance. Other characteristics include the fact that we can implement this approach within a single organisation as well as within a distributed organisation.

According to Vernadat (1996), there are five major motivations for EM: management of system complexity, better management of all types of processes, capitalisation of enterprise knowledge and know-how, Business Process Reengineering and enterprise integration. These motivations have already been described by several humanitarian workers. They all agree that "there is a need to build capacity in preparedness to work hard during disasters but to work even harder between disasters" (Van Wassenhove and Samii 2003). Thus, as humanitarian workers have formulated, "by starting with the overall picture of needs, we might be able to better agree on where the priorities lie and how we can better respond to gaps" (The International Council of Voluntary Agencies 2008).

A typical framework for enterprise modelling Since 2001, a shared framework for EM has been available. In this norm (AFNOR 2001), and in its successor [START_REF] Afnor | Enterprise integration-framework for enterprise modelling[END_REF], three axes are given to drive the analysis:

-The Genericity, which defines the level of detail associated with the model.

-The Model Life Cycle, which is "the set of distinguishable phases and steps an entity may go through from its creation until it ceases to exist". -The View, "a structured representation which is a selective perception of an enterprise model." Model views are used to emphasise the aspects that are relevant to the modeller and the model user's particular interests and context, i.e. function, information/decision, resource or organisation (Fig. 3).

Adaptation of the framework to fit humanitarians specificities As seen earlier, HSCs are project oriented. The response varies according to the typology of crises, the nature and number of the stakeholders, the complexity of the environment, and so on.

A brief overview of the various HSCs that can be implemented is necessary prior to implementing the Enterprise EM approach in order to define the scope of the study. As discussed earlier, there are two kinds of project environments for implementing humanitarian logistics operations: slow-onset disasters and sudden-onset disasters. For each of these types of disasters, the supply chain and the amount of resources needed will also differ depending on the phase of the operation (see Fig. 1). Moreover, the humanitarian distribution channels go through many stakeholders. These stakeholders To summarise, we can say that the framework proposed in the norm ISO 19439 (AFNOR 2006) can be applied, but with minor modifications. The first concerns the life cycle stages. Instead of the seven stages recommended by the norm, humanitarians will focus on the four phases of their supply chain management, i.e. preparedness, immediate response, support and dismantling. This is a limitation of the study. Yet it enables humanitarians to focus on the most important phases of the operations, to limit the number of models and to reduce the time and resources needed to undertake such demanding work. The second modification lies in the genericity. According to the norm, the study should start with generic concepts, then specialise to a specific enterprise. In our case, no shared generic way of managing the supply chain exists. Moreover, the idea is to focus either on specific best practices and generalise them, or on specific gaps and bridge them. Consequently, instead of going from the generic level to the specific, we recommend going the other way around, namely from the specific level to the generic. As for the view axis, the classification given by the norm is valid for humanitarians. The only difference we would recommend concerns the exhaustiveness of the study. According to the norm, all points of view for all phases of the operation life cycle should be studied. Yet again, as this is a time-and resourceconsuming process, and knowing how crucial these two elements are for humanitarian organisations, we suggest restricting the studies to the most pertinent models, depending on the needs identified (Table 1).

The response process can differ depending on the situation (the nature of the crisis, ability of the affected country to face the disaster, volatility of the environment, etc.). And from one organisation to another, it can also vary tremendously. Because of these variations, a clear specification of the scope, coverage and level of detail (crisis typology, targeted stakeholders, etc.) of the EM approach has to come with the model. Indeed, for example, working on a global model is only relevant for a high level of analysis and has a limited interest for a deeper analysis.

Business Process Modelling Notation (BPMN) to model the functional view

Many methods and tools have been developed for modelling organisations. The choice of the most appropriate depends mostly on the modeller's viewpoint(s) and the aim of the study.

Even though different Business Process Modelling techniques could be envisaged, it is not the purpose of the present study to discuss such a choice. We have chosen to work with the Business Process Modelling Notation (BPMN) standard (Object Management Group 2004). This standard pays particular attention to both the sequencing of operations and the flows. It also gives the opportunity to study the interfaces, which facilitates the discussion of coordination and synchronisation problems. The four basic categories of BPMN elements are flow objects, connectors, artifacts and swimlanes (Object Management Group 2004).

According to White and Miers ( 2008), an event is something that "happens" during the course of a business process. An activity is a generic term for work that the company performs. A gateway is used to control the divergence and convergence of the sequence flow. Thus, it will determine traditional decisions, as well as the forking, merging and joining of paths. A sequence flow is used to show the order (the sequence) that activities will be performed in a process. A message flow is used to show the flow of messages between two separate process participants (business entities or business roles) that send and receive them. In BPMN, two separate pools in the diagram represent the two participants. An association is used to associate data, text and other artifacts with flow objects. Associations are used to show the inputs and outputs of activities. A pool represents a participant in a process. A lane is a sub-category within a pool and is used to organise and categorise activities.

Step 2: Optimisation modelling approach

Optimisation-based decision-support systems are concerned with developing and applying models and concepts that may prove useful in helping to illuminate management issues as well as designing and developing new and better systems (The Institute for Operations Research and the Management Sciences 2011). This kind of decision support system is based on a mathematical model. Mathematical modelling problems are often classified as black-box or white-box models, according to how much a priori information is available on the system [START_REF] Bender | An introduction to mathematical modeling[END_REF]. A black-box model is a system for which there is no a priori information available. A white-box model is a system where all the necessary information is available.

Virtually all the quantitative models are located somewhere between these two kinds of models. Usually, it is preferable to use as much a priori information as possible to make the mathematical model more accurate. Indeed, the white-box models are usually considered to be easier to work with and generally to have better behaviour. Often the a priori information comes in the form of knowing the type of functions relating different variables and parameters [START_REF] Hangos | Empirical model building[END_REF].

In the black-box model, both the functional form of the relations between variables and the numerical parameters in these functions are estimated. Using a priori information could result in, for example, a set of functions that probably describe the system adequately. But most of the time, there is no a priori information available. In that case the challenge consists in using the most general variables and parameters possible to cover all the different options. Consequently, there is a serious risk to the relevance of the mathematical model and to its behaviour [START_REF] Hangos | Empirical model building[END_REF][START_REF] Gershenfeld | The nature of mathematical modeling[END_REF] Obviously, optimising an HSC assumes a black-box model due to the youth and the low quantity of the existing explicit knowledge. Our proposition consists in using previous conceptual models (see Step 1) in order to target important elements in the humanitarian system under consideration. These elements should be the variables and the parameters of the mathematical model.

In practical terms, the BPMN notation selected in the previous step to represent the functional view is a perfect means for showing the material and informational flows in the supply chains. The methodology that we propose to implement is the following: 1. Selecting an activity that contributes directly to the added value of the business process (i.e. that contributes directly to the relief of the beneficiaries).

2. Identifying input/output flows of each activity in order to extract the input/output variables. 3. Extracting from each activity the different parameters (costs, cycle time, etc.). The next part proposes an implementation of our proposition on the IFRC case.

The selection of activities with a direct contribution to operations facilitates the distinction between decision variables, which are linked with value-added activities, and input data, linked with other activities.

Application to the IFRC emergency response

There are two options for studying the answer to a given humanitarian crisis: either we study the overall response linking all stakeholders' activities, or we focus on one stakeholder and map only its activities. The present article will present one application of our approach: the supply chain implemented by one stakeholder, the International Federation of the Red Cross and Red Crescent Societies (IFRC), during a suddenonset disaster. Both a particular operation, the 2006 Yogyakarta earthquake, as well as a more general analysis of IFRC procedures have been studied in order to formalise their business processes in case of emergency.

Our aim is to use a BPMN diagram to better understand the situation and facilitate the construction of an OR model to solve some of the coordination issues faced by the IFRC.

The first step consists in building a business model of relief operations. This model is presented by Fig. 5. The few historical elements on the situation at the IFRC are summarised in the following section.

Overview of the situation

The year 2006 marked a further step in the revitalisation of the IFRC. Its disaster management process had been entirely revised to provide a quicker and better response to disasters. The necessity of improvement in this area had, unfortunately, already been clearly demonstrated for many years. After many adjustments, a radical change had been launched in November 2005: the federation had centralised its policy-making efforts in Geneva and had decentralised its operational capacity by creating three Regional Logistics Units (RLUs) with capacities in terms of mobilisation, procurement, stock and warehousing and fleet support in Dubai, Panama and Kuala Lumpur. [START_REF] Gatignon | The Yogyakarta earthquake: humanitarian relief through a decentralized supply chain[END_REF] To attain the potential benefits of this strategy, efficient coordination was of course required. Indeed, the higher the level of decentralisation, the more critical the effectiveness in coordination. For this application, we studied the first major disaster that the IFRC responded to under this new organisation.

The earthquake happened on the 27th of May, 2006. More than 70% of the houses and buildings were damaged. Thousands people were injured by in this disaster. The earthquake caused an electrical blackout and, in several areas, the telephone lines were downed, causing severe communications problems. Moreover, all the gas stations were reported to be out of order and some roads and bridges were damaged. In Yogyakarta, the international airport was unable to operate and flights to and from the city had to be redirected to Surakarta (60 km from Yogyakarta) or Semarang (120 km from Yogyakarta). The figures totalled 6,000 dead and 1.5 million people affected by the disaster.

During the response phase, the Indonesian Red Cross worked together with the regional logistics unit in Kuala Lumpur and the head quarters in Geneva. Other national societies also participated by sending resources. The British, American, Spanish and Danish Red Crosses sent trained people to give a hand in relief operations. The Japanese, Belgian, Spanish Red Crosses sent goods. In May 2006, Kuala Lumpur RLU had been finalising its implementation. Consequently, during the first days after the earthquake, the global coordination was ensured by Geneva, as it had been done before the decentralisation process. In the beginning of June, however, Kuala Lumpur took the lead in the coordination of the logistics services response, as stipulated by the new organisation.

The IFRCs response process commenced well. Indeed, logisticians were present from the beginning and some stock was also available. In fact, the local delegation was able to benefit from the post-tsunami work in progress at the time and from the fact that Mont Merapi, a volcano 70 km from Yogyakarta, had become active two months earlier. For these reasons, even though the Kuala Lumpur RLU had not yet been fully operational (no central warehouse with available stock; human resources still lacking), the situation in Yogyakarta (stock and technical staff available) justifies the hypothesis that the actual response to the crisis in Yogyakarta is close to what it would have been had the RLU been 100% operational [START_REF] Jahre | Does the current constraints in funding promote failure in humanitarian supply chains?[END_REF][START_REF] Charles | The Yogyakarta earthquake: IFRCs rst experiences with the decentralized supply chain[END_REF]).

Business process modelling

Construction of the BPMN

We discuss in this paper only one model: the functional view through a BPMN. This representation allows the relationships between the HSCs entities to be modelled and the activities that are fulfilled and their sequencing to be described. The scope of our study is represented by Fig. 4.

The model presented in Fig. 5 represents the main business processes run by the Red Cross stakeholders from the end of the response phase and the beginning of the support phase (according to the lifecycle described in Fig. 1) to the end of the relief response. The level of detail used here corresponds to the partial level (see Fig. 4). It is indeed sufficiently general to correspond to other operations than the response of the IFRC to the Yogyakarta earthquake, although it would not correspond to other organisations' operations.

The following were the main entities in operation during the crisis:

-IFRC head quarters (Geneva), which ensure the strategic coordination for this operation but potentially also for other operations in other places. -TheRegionalLogisticsUnit(RLU),whichcoordinatedoperationsregionally.Concretely, it consolidated the needs and controlled the pipeline for field distributions ). An RLU is also used to coordinate shipments, track what has been done and potentially do the same for other operations in other places. -The Logistics Emergency Response Unit (ERUlog), composed of members of the British Red Cross in the case of Yogyakarta. They were responsible for reception at the airport, for storage and for execution of shipments in the field. -The Relief Emergency Response Unit (ERUrelief), composed of members of the American and Spanish Red Cross for this crisis. They helped with the field distribution organisation. -The local National Society (NS), was responsible for operations, requesting assistance from others where skilled resources were lacking yet acting independently whenever possible. Regarding its role in logistics operations, it procured locally and executed the relief distribution.

Analysis of the BPMN

The model presented in Fig. 5 enables to analyse operations. A first positive element is the clear definition of nearly everyone's role. The coordination and responsibilities in each level is well identified and hierarchically structured: global coordination in Geneva, regional coordination in RLUs and local coordination at field level. Coming back to our definition of coordination, in Sect. 2.4, we can assert that their synchronization was quite good.

The model nevertheless illustrates that the main issue faced by the IFRC, that is to say the difficulty to gather timely and accurate data from the field, comes from an organizational gap. Indeed, the activity "to collect information" in the BPMN diagram is connected to other activities by messages. It is not linked in a sequence of operations, and is therefore often neglected. The business process shows that the feedback loop to IFRC in Geneva should be structured more formally. Frequent updates on operations are collected and published on IFRC website by the media centre and a specific logistics software has been designed to increase both traceability and accountability. Despite this, information with regard to the nature, number and status of entities transiting the Regarding the analysis in terms of "balancing" capability, a direct consequence of the previous point is that it is difficult for Geneva to properly allocate funds and skills for field operations. The model underlines a lack of macro-vision and control on the operation. No systematic information loop exists to keep Geneva up to date on a daily basis.

As for the "training" component, a positive element is the presence of pre-defined documents and standards, which allows to clarify and speed up communication processes. On the other hand, the functional model puts forward the role of the ERU relief and the fact that, there again, its activities are not linked with others in a sequence of activities. This garbled situation may be related to the fact that "logistics and resource mobilization" and "disaster management" are two separated department at the IFRC. Relief teams often work as partners with logisticians, but with their own hierarchic systems. This may induce a deficit of training of some logisticians in disaster management.

Of course, this analysis is partial. To be complete, the analysis must consider the remaining modelling views, organisation, and decision and all the life-cycle phases.

Quantitative modelling

In Sect. 2.4, we referred to the three key determinants of coordination; here, we will focus on the synchronisation of activities. To guarantee the coherence and efficiency of relief operations, a mixed integer linear program (MIP) has been built to minimise the costs linked to disaster response. Coming back to the humanitarian operations lifecycle presented in Fig. 1, the model developed optimises the synchronization of actors by improving the design of the supply chain and therefore relates to the preparedness phase. This focus on preparedness aims to improve the efficiency of disaster response while taking into account humanitarians constrains detailed in the first three sections of this paper.

Identification of variables and parameters

As shown in the model presented in Fig. 5, our second step is to extract the main components of a MIP to analyse the costs of disaster response.

Following the methodology described in Sect. 3.3, we have selected all the core activities, i.e. those that are directly necessary for sending aid to beneficiaries. They are represented by the darker cells of the business model (Fig. 7).

The next step consists in identifying input/output variables and parameters. They result from each activity which actively provides relief to beneficiaries. As for input data, this comes from the remaining activities. This process can be illustrated by two examples.

Let us first consider the activity "to manage regional warehouse". As you can see in Fig. 7 and its excerpt, Fig. 6, three flows are merged before this activity. They represent the reception of products supplied from global and regional suppliers as well as in-kind donations. Input parameters linked with these flows will therefore be delivery time and costs between global suppliers or donors and regional suppliers. As for output parameters, they are directly linked with the accomplishment of the activity. Managing flows has a cost. Fixed and variable costs linked to the management of this regional warehouse are thus listed as parameters here. The costs associated with the management of the flows depend on the quantity of products arriving as well as on the quantity of products already in stock. The variable associated with this activity is thus the quantity of products in stock in the warehouse. The quantities of products arriving in the warehouses are given by each of the preceding activities.

Let us now consider the identification of input data. It comes from activities which participate only indirectly in the actual shipment of relief aid. For example, the assessment of needs is necessary to ensure that what is sent to the field matches the needs of the affected population. Yet its completion or its lack of completion does not affect the flow of products. The variables and parameters can be visualised in Fig. 7. The list of variables is written in bold, underneath the activities. As for the parameters, they are written in italic and on the right side of the corresponding activities. Table 2 provides an overview of all the notations we have used. The use of these parameters and variables in an optimisation model is thus facilitated. Our approach enabled us to better understand the situation and focus on core activities.

Let us now look at the quantitative model built using the enterprise modelling approach. As we have seen in the first section of this paper, the more efficient the response, the better the coordination will be. The model we have built therefore minimises the costs associated with the response. In our specific context, the effectiveness of operations is also vital. Need assessment provides the nature and quantities of products necessary and the targeted delivery times. The satisfaction of this demand is taken into consideration as a constraint of the model. double Demand of each product to rescue the affected region c at time t DCUG psd double Delivery cost to deliver product p from global supplier s to regional warehouse d (Upstream potential regional warehouse) DTUG sd double Delivery time to deliver a product from donor or global supplier s to regional warehouse d (Upstream regional warehouse) DCUR psd double Delivery cost to deliver product p from regional supplier s to regional warehouse d (Upstream regional warehouse) DTUR sd double Delivery time to deliver a product from regional supplier s to regional warehouse d (Upstream regional warehouse to local warehouses; -Line 3 represents transportation costs from local warehouses to beneficiaries; -Line 4 represents the fixed costs of maintaining functioning warehouses; -Line 5 represents the variable costs incurred in running the warehouses. It is proportional to the quantity of products: the greater the number of products handled by the warehouse, the greater the number of employees required; -Line 6 represents the penalty costs incurred if products are not delivered on time.

Objective Function

Min

Constraints We then wrote a facility location model, similar to classical facility location models, with one transportation mode and three stages. The constraints of our model impose 1. Either the satisfaction of the demand or the addition of a stock-out cost. 2. The presence of products in a potential warehouse if and only if it is opened. 3. The balance of inventory. 4. The rebuilding of contingency stocks. 5. The fact that existing warehouses are already open. 6. The fact that humanitarian organisations may not have the funding to open too many warehouses at the same time. 7. The fact that regional and local warehouses have limited capacity.

We did not detail the model here, as the originality of this paper lies in the building of the model rather than in the model itself. For further detail on the model itself, on managerial recommendations resulting from this MIP as well as on the sensitivity analysis, the reader is encouraged to have a look at [START_REF] Charles | Improving the design and management of agile supply chains: feedback and application in the context of humanitarian aid[END_REF]. Thanks to the business model, we quickly built a relevant model, which can then be used to analyse and compare various supply chain configurations. An improvement in the efficiency of the logistics network can then be made using this model. This is not the purpose of this article, however.

Comparison with other facility location models proposed in the literature

Available facility location models dedicated to the not-for-profit sector mostly focus either on the response phase, like [START_REF] Ozdamar | Emergency logistics planning in natural disasters[END_REF] or on the setting up of prepositioned system locally, like [START_REF] Salmeron | Stochastic optimization for natural disaster asset prepositioning[END_REF].

Out of all the articles published on facility location dedicated to disaster relief, only three articles take a preparedness point of view and work on the global supply network [START_REF] Akkihal | Inventory pre-positioning for humanitarian operations[END_REF][START_REF] Balik | Facility location in humanitarian relief[END_REF][START_REF] Lodree | An insurance risk management framework for disaster relief and supply chain disruption inventory planning[END_REF]. Those three papers focus on effectiveness maximisation. None of the facility location model applied to disaster relief deals with efficiency.

This choice between maximizing effectiveness and efficiency is made obvious by Fig. 7. Indeed, Delivery times and delivery costs are the two main parameters underlined by our BPMN. Our approach enabled us to better visualise this possibility to maximise efficiency rather than effectiveness. The focus on efficiency is also in line with the conclusions of the first part of this paper: one of the main issues with regard to the coordination of humanitarian operations arises from their lack of synchronisation. Synchronisation being closely linked with efficiency, or proposed model better answers the needs of humanitarian organisations. This focus on efficiency has also been made explicit by humanitarians. Interviewees, especially at IFRC, insisted that the problem is not to maximise the coverage because plane deliveries allow them to cover wide distances quickly. According to them, the idea is more about how to achieve a given level of effectiveness in the most efficient way. In other words, they would prefer to minimise the costs to meet the demand in specific time-frames, which is the element we retained thanks to our approach.

The usual method of dealing with demand uncertainty is to use a stochastic or robust optimisation model. Yet, if we refer to [START_REF] Shapiro | Lectures on stochastic programming[END_REF], the stochastic optimisation model optimises the random outcome on average. "This is justified when the Law of Large Numbers can be invoked and we are interested in the long-term performance, irrespective of the fluctuations of specific outcome realizations". In our case, the impact of those "fluctuations" are on human lives and can be devastating. We therefore aligned with the recommendation provided by [START_REF] Shapiro | Modeling the supply chain, 1st edn[END_REF], which is to construct multiple scenarios of an uncertain future and optimise a linear programming model for each scenario. Indeed, according to Shapiro, deterministic optimization of a model of a supply chain planning problem is often the most practical approach. In most planning situations, the development of points (that is, single) estimates of key parameters is difficult enough. For such problems, it is not realistic to attempt to develop extensive descriptions of how the parameters might vary in the future. Although the modeller may sometimes be forced to acknowledge that a deterministic model is imperfect in its description of the future, the benefits of using such a model are still substantial. This choice was also driven by the analysis of our specific application case, disaster relief. Nevertheless, a comparison with other ways to take uncertainty into account should definitively be considered as a topic for future research [START_REF] Shapiro | Modeling the supply chain, 1st edn[END_REF].

A third element that our methodology underlined is the presence of donated products, which also have a cost for humanitarian organisations. Products have to be stored, handled, transported and distributed to the beneficiaries. Those costs are not taken into account in other models dealing with facility locations.

Relevance of the model for humanitarian organisations

Most of the information we used derives from interviews with practitioners and public databases. Transportation costs and times have been based on quotes provided by a major U.S. transportation company, independently validated by discussions with practitioners from MSF and two private companies. Fixed and Variable costs have been calculated on the basis of regional average salaries and GNI/GDP. Information regarding purchase costs and the locations of suppliers has come from our interviews and the IFRC website. Initial values of parameters, such as the required level of service and the size of the contingency stock, also derive from discussions with IFRC (see Charles 2010 for more details).

Our application has therefore been built with and for humanitarians. This model can be readily applied to other agencies with different data and parameters than the one we used for IFRC. Applications for the UNHRD or world vision have already been developed, though without validation by those organisations.

Our aim was not to find a fundamentally novel way to deal with facility location, but rather to solve humanitarians' practical problems. We used algorithms close to existing ones, but made sure that they take humanitarians' specifications into account.

Here again, the reader is encouraged to have a look at Charles (2010) for additional details.

Conclusion

As we have shown in this paper, practitioners and researchers who want to optimise an HSC are often faced with the problem of establishing an accurate and confident quantitative model. This article tackles the problem by developing a dedicated conceptual enterprise modelling approach.

We started by describing HSC salient features in order to underline the interest of optimisation techniques for this new research area. In particular, the problem of coordination in an HSC has been developed. But the recentness of this topic associated with the low quantity of information available constitute a major difficulty in identifying variables, data and parameters that could be necessary for potential mathematical optimisation.

Inspired by the Enterprise Modelling ISO 19439 standard (AFNOR 2006), we formulated a business process modelling approach that assists in understanding, analysing, evaluating and then developing a formal expression of a HSC. A three-step methodology has been developed to convert conceptual information included in a BPMN model into quantitative information, essential for following optimisation steps. In practical terms the paper illustrated our proposition with the emergency response processes of the IFRC. This application case allowed us to formulate an accurate and confident quantitative model that should help to optimise the coordination capabilities of the IFRC by improving the efficiency of its network.

Though our proposition constitutes a significant first step towards supporting the optimisation modelling problems encountered in HSC works, many other issues were not addressed and this leaves room for further research. These issues are 1. Our approach should be improved by receiving complementary practitioners insights. In particular, on-going research work consists in implementing our proposition from the modelling step developed in this paper to the optimisation step [START_REF] Charles | Improving the design and management of agile supply chains: feedback and application in the context of humanitarian aid[END_REF]. This research work should validate the confidence that humanitarian decision-makers could have in our proposition. 2. We formulated a generic methodology that is able to analyse several points of view of ISO 19439 (AFNOR 2006) standards. In the current paper, however, we develop only the functional view towards some BPMN representations. Consequently, one perspective might be other kinds of business process modelling applications. 3. The problem of black-box optimisation models is not specific to the humanitarian context. Thus, it might be interesting to develop our proposition in other research areas that have a similar difficulty in formalising their quantitative optimisation models: sustainable supply chains or service supply chains, for example.

Fig. 3

 3 Fig.3Overview of the framework for enterprise modelling[START_REF] Afnor | Enterprise integration-framework for enterprise modelling[END_REF]

Fig. 4

 4 Fig. 4 Overview of the view, phase and level of the business model used in this application

Fig. 5

 5 Fig. 5 BPMN of the material flows during IFRC's disaster response process

Fig. 6 Fig. 7

 67 Fig. 6 Details of the second step of our approach

Disaster / Crisis... Sudden Onset Slow Onset

  and Pettit and Beresford

	To design the HSC
			To manage the HSC
	Phase 0: Phase 0: :	Phase 1: Phase 1: :	Phase 2: Phase 2: :	Phase 3: Phase 3: :
	Preparedness Preparedness	Immediate Immediate	Support Support	Dismantling Dismantling
		Response Response
	Several months	Disaster / Crisis... 1 to 5 days	3 months to 1 year	Some weeks	time
	Several months	2 to 6 months	1 year to several years	Some months
	Fig. 1 The humanitarian operation life cycle (inspired from Van Wassenhove 2006; Pettit and Beresford
	2005)

resources: Selecting and training people who are capable of planning, coor- dinating, acting and intervening

			Benificiaries	Donors
			Implementing Partners
		International NGO's	Local NGO's
			Hum. Organisations
	Legend:		National Aid Agencies
	Strategic Humanitarian Units
	Product/People flows	1st Tier Suppliers	1st Tier Suppliers
	Information flows
	Financial flows
	Media flows	2nd Tier Suppliers	2nd Tier Suppliers	2nd Tier Suppliers
	Local Environment
	(Local Legislation, Conflict, Health…)
	Fig. 2 Global model of a humanitarian supply chain (inspired from Oloruntoba and Gray 2009; Handfield
	and Nichols 2002)
	of five key elements that have to be in place to produce effective results. These in turn
	lead to effective disaster management. They are as follows:
	1. Knowledge management: Learning from previous disasters by capturing, codify-
	ing and transferring knowledge about logistics operations. See Tomasini and Van
	Wassenhove (2005), Bui and Sankaran (2001), Kaiser et al. (2003) and Benini
	et al. (2003).
	2. Financial resources: Preparing sufficient funds to prepare and initiate operations
	and ensure that they run as smoothly as possible. See Jahre and Heigh (2008) and
	Stapleton et al. (2009a) for details.
	3. Human
	Humanitarians have begun to heed the lessons learnt from previous disasters and realise
	that they have to work hard not only during disasters but also between them (Tomasini
	and Wassenhove 2009). According to Van Wassenhove (2006), preparedness consists

where necessary. The problem of human resources in humanitarian operations is probably the most neglected one in terms of academic research. Nevertheless, many authors (Van Wassenhove 2006; W.E.F. The Synergos Institute 2005; Beamon 2004; Stephenson 2005; Oloruntoba and Gray

Table 1

 1 Adaptation of the methodological framework to take into account humanitarian specificities

		ISO 19439	Adaptation to the modelling of
			humanitarian operations
	Modelling levels	"For different life cycle stages (from	For different life cycle stages (from
		requirements definition to design	immediate response to dismantling)
		specification to implementation
		description)"
	Genericity	Specialisation, i.e. "providing generic	Generalisation, i.e. "the progression
		concepts which are then specialised	from one or more particular concepts
		to a particular industry sector and	to a more general concept which
		finally to a specific enterprise"	represents [the modeller and
		(from generic to partial, then	the model user] shared characteristics
		particular level)	or essential qualities"
	Views	"Classifying concepts by four areas of
		concern or modeller viewpoints
		(function, information, resource and
		organisation)"

Table 2

 2 Notations

	Notation	Definition
	Indices
	p	Product
	s	Supplier
	d	Regional warehouse
	w	Local warehouse
	b	Beneficiaries, i.e. affected region
	t	Time
	Parameters
	D pct

  ) DCUL psw double Delivery cost to deliver product p from local supplier s to local warehouse w (Upstream local warehouse) DTUL sw double Delivery time to deliver a product from local supplier s to local warehouse w (Upstream local warehouse) DCI pdw double Delivery cost to deliver product p from regional warehouse d to local warehouse w (Upstream local warehouse) DTI dw double Delivery time to deliver a product from regional warehouse d to local warehouse w (Upstream local warehouse) Variables QG psdt double Quantity of products p delivered from global supplier s to regional warehouse d at time t QR psdt double Quantity of products p delivered from regional supplier s to regional warehouse d at time t QL pswt double Quantity of products p delivered from local supplier s to local warehouse w at time t QI pswt double Quantity of products p delivered from regional warehouse d to local warehouse w at time t QF pwct double Quantity of products p delivered from warehouse w to the affected region b at time t QW ptw double Quantity in stock of products p in local warehouse w at time t QD ptw double Quantity in stock of products p in regional warehouse d at time t QS pd double Contingency stocks. Corresponds to a quantity of products p to keep in stock at warehouse d prior to disasters in order to facilitate an immediate response (5 days) Stockout pct double Quantity of products p which were not delivered to beneficiary b at time t (QG psdt + QR psdt + QDon psdt ) +

	+	p w b	DCF pwb ×	t		QF pwbt		(2)
	+							w	(CostF w × WCh w )	(3)
	+	t	d	CostV d ×	p	s					w	QI pdwt
		+	t	w	CostV w ×	p		s	QL pswt +	d	QI pdwt +	b	QF pwbt	(4)
	+	p w b	t	(Stockout pbt × S)		(5)
	where
	-Line1representstransportationcostsfromglobalandregionalsupplierstoregional
	warehouses;
	-Line2representstransportationcostsfromregionalwarehousesandlocalsuppliers
	CostF d		double Fixed costs to run the regional warehouse
	CostV d		double Variable costs to run the regional warehouse
	CostF w		double Fixed costs to run the local warehouse
	CostV w		double Variable costs to run the local warehouse
	QDon psdt double Quantity of products p delivered from donor s to
					regional warehouse d at time t
	nbAff		integer Total number of affected
	nbT		integer Duration of operations
	S		d o u b l e P e n a l t yc o s t s ,p e rd a ya n dp e rp r o d u c tn o td e l i v e r e do nt i m e
	MD		double Maximum capacity of the regional warehouse
	ML		double Maximum capacity of the local warehouse
	WCh w		boolean WChw=1 if warehouse w should be opened; WChw=0 otherwise
	WCh d		boolean WChd=1 if warehouse d should be opened; WChd=0 otherwise

d (CostF d × WCh d ) +