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\journalname{Annals of Operations Research}

\begin{document}

\title{On the Combination of Water Emergency Wells and Mobile Treatment Systems: A Case Study of Berlin - Supplementary Material}

\author[*]{Christoph Stallkamp \footnote[1]{The authors contributed equally to this paper.} \footnote[2]{Corresponding Author: \email{christoph.stallkamp@kit.edu}}      \and
        Florian Diehlmann~*               \and
        Markus Lüttenberg           \and
        Marcus Wiens                \and
        Rebekka Volk                \and
        Frank Schultmann
}

\institute{C. Stallkamp
           \and
           F. Diehlmann
            \and
           M. Lüttenberg
            \and
            M. Wiens
            \and
            R. Volk
            \and
            F. Schultmann \at
            Institute for Industrial Production (IIP), Karlsruhe Institute of Technology (KIT)
}

\date{Received: date / Accepted: date}
% The correct dates will be entered by the editor

\maketitle

\renewcommand*{\thefootnote}{\arabic{footnote}}

\begin{abstract}
A shortage of water leads to severe consequences for populations. Recent examples like the ongoing water shortage in Kapstadt or in Gloucestershire in 2007 highlight both the challenges authorities face to restore the water supply and the importance of installing efficient preparedness measures and plans. This study develops a proactive planning approach of emergency measures for possible impairments of water supply systems and validates this with a case study on water contamination in the city of Berlin. We formulate a capacitated maximal covering problem as a mixed-integer optimization model where we combine existing emergency infrastructure with the deployment of mobile water treatment systems. The model selects locations for mobile water treatment systems to maximize the public water supply within defined constraints. With the extension to a multi-objective decision making model, possible trade-offs between the water supply coverage and costs, and between the coverage of differently prioritized demand points are investigated. Therefore, decision makers benefit from a significantly increased transparency regarding potential outcomes of their decisions, leading to improved decisions before and during a crisis.  

\keywords{humanitarian logistics \and water contamination \and emergency wells \and disaster \and GIS \and optimization}

\end{abstract}

\section*{Data Collection and Processing for the Case Study of Berlin}
\label{sec:data}
The introduced model is applied to a case study with the focus on a terrorist attack on the public water supply of Berlin, Germany.

The data collected consists of the demand structure, the available emergency wells, location candidates for available water treatment systems and distances between supply and demand. The following subsections provide an overview of the detailed data collection and processing.

\section{Demand}
\label{sec:data_de}
The First German Water Securing Regulation (1. WasSV) determines the amount of water that must be provided to the public in case of an emergency. It distinguishes between regular residents that should be supplied with 15 liters of water per day and residents of highly vulnerable facilities such as hospitals which must be provided with 75 liters per patient and day. In intensive care facilities, the amount is raised to 150 liters per patient and day \citep{bundesrepublik_deutschland_erste_1970}. 

We used ArcGIS Desktop 10.6 to process the available GIS data. The regular residents are mapped using a discrete representation of the residential buildings provided by the senate of Berlin in its open data portal \citep{geoportal_berlin_geoportal_2019}. The map 'Einwohnerdichte 2018' shows the building blocks of Berlin and provides additional data, including their number of residents \citep{amt_fur_statistik_berlin-brandenburg_einwohnerdichte_2019}. The centers of the mapped polygons are determined to represent the blocks as discrete demand points. The amount of demand per point is calculated by the number of its residents and the established supply standard of 15 liters per person. Regular residents have an summed up emergency water demand of 56,216,805 liters per day.

The water demands of hospitals, nursing homes, and assisted living facilities is caused by the high vulnerability of their residents. Locations are geocoded based on addresses from the registers “Berliner Krankenhausverzeichnis“ and “Deutsches Seniorenportal” \citep{berliner_krankenhausgesellschaft_e.v._berliner_2019, privatinstitut_fur_transparenz_im_gesundheitswesen_gmbh_betreutes_2019}. The number of residents of each facility is established. For some facilities, there is no information accessible regarding residents or beds per building. There we used the average of all available information per facility type to enrich the data. The full utilization of the facilities is assumed.

The water supply standards for high care facilities are used to calculate their demand. Since no consistent information regarding the number of beds within intensive medical care facilities is available, a ratio is calculated based on the statistical report of hospitals in Berlin \citep{amt_fur_statistik_berlin_brandenburg_krankenhauser_2018}. According to the 1. WasSV, intensive medical care facilities include surgical and infection medicine facilities \citep{bundesrepublik_deutschland_erste_1970}. The evaluation of beds within infection medicine facilities is not possible. Therefore, the calculation is limited to beds in surgical facilities. This leads to 24\% of beds that are within intensive medical care facilities \citep{amt_fur_statistik_berlin_brandenburg_krankenhauser_2018}. As a result, we estimate the demand per day and patient for each high care facility with the help of the expected demand (76\% demand of 75 liters and 24\% demand of 150 liters). Therefore, the considered 74,619 beds equal a special demand of 5,996,781 liters per day.

To avoid unnecessary trips, a predefined percentage ensures that, if demand is allocated to a water supplying facility, an adequate amount of water is supplied per person. We assume that a threshold of 20\% of the German standard for water quantity is suitable, resulting in 3 liters per person and day. This is in line with \cite{the_sphere_project_sphere_2018}, who define 3 liters as the absolute minimum in the aftermath of a disaster. 

The analysis of demand is limited to the stated types of facilities. Water supply for food suppliers or industry is not investigated due to the assumption that there is no public life during the response phase.

\section{Emergency Wells} \label{sec:data_ft}
The emergency water supply chain combines existing infrastructure with mobile water treatment units. The existing infrastructure for water emergencies includes emergency wells that are placed throughout Berlin.

The average output of one well is 6$m^3$ per hour, with a maximum operating time of 15 hours per day \citep{langenbach_trinkwasser-_2008}. This leads to an average water supply of 90,000 liters per well and day. The supplied water will be disinfected with chlorine if needed \citep{langenbach_trinkwasser-_2008}. It is assumed that all 1,028 emergency water wells considered are accessible and can be operated.

The daily costs associated with the operation of an emergency water well are separated into personal costs and costs associated with equipment and consumables. Table \ref{tb:costWells} summarizes the estimated expenses that amount to a rounded 10,700 \EUR{}.

It is assumed that infrastructure specialists  of the THW operate the emergency water wells. The emergency water supply is established for two weeks. A loss of earnings for the volunteers is assumed leading to personal expenses of 22\EUR{} per volunteer and hour \citep{bundesrepublik_deutschland_verordnung_2018}.

The required equipment for the operation includes a drinking water laboratory to monitor the water quality and equipment to distribute water to the public. Due to the assumption that the public is requested to bring containers \citep{BundesamtfurBevolkerungsschutzundKatastrophenhilfe.2016b}, only the costs for the drinking water laboratory are considered.

We assume that the capacities of the wells are fully utilized, resulting in an operating time of 15 hours and a water supply of 90,000 liters per day. According to \cite{langenbach_trinkwasser-_2008}, the water is disinfected with chlorine before distributed. For establishing the associated cost, the product Micropur Forte MF 1T by Katadyn was used for reference. It is assumed that quantity discounts and framework agreements reduce the market price by 50\%, leading to costs of 0.75 \EUR{} per 10 liters of water \citep{trager_micropur_2019}.

Based on the assumption that all 1,028 emergency wells are operated, fixed supply costs of 11,308,000 \EUR{} arise that can not be influenced by the model.

\begin{table}[htbp]
\small
\begin{tabularx}{\textwidth} {p{4,5cm} p{1.5cm} p{1.5cm} p{1.5cm} p{2.5cm} p{4.5cm}}
\hline
\textbf{Cost Driver} & \multicolumn{2}{c}{\textbf{Expenses}} & \textbf{Quantity} & \textbf{Sum} & \textbf{Source} \\
\hline
\multicolumn{6}{c}{\textbf{Personal Costs}} \\
\hline
Volunteer THW & 22.00 \EUR{} & per hour & 12 & 3,960,00 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
\hline
\multicolumn{6}{c}{\textbf{Equipment Costs}} \\
\hline
Drinking Water Laboratory & 18.20 \EUR{} & per day & 1 & 18.20 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
\hline
\multicolumn{6}{c}{\textbf{Consumables Costs}} \\
\hline
Disinfectant & 0.075 \EUR{} & per 1 litre & 90,000 & 6,750.00 \EUR{} & \cite{trager_micropur_2019} \\
\hline
Sum & & & & 10,728.20 \EUR{} & \\
\hline
\end{tabularx}
\caption{Operating Costs of an Emergency Water Well.}
\label{tb:costWells}
\end{table}

\section{Mobile Water Treatment Plants} \label{sec:data_wt}
The THW has 14 drinking water specialist groups, each of which has a UF-15 drinking water treatment system.\footnote{Private email exchange with THW.} The UF-15 treats well or surface water using ultrafiltration with a capacity of 15$m^3$ per hour \citep{veolia_water_technologies_mobile_2019}. The operating time of the system is 20 hours per day, which yields to 300,000 liters of water per day \citep{bundesanstalt_technisches_hilfswerk_trinkwasseraufbereitungsanlage_2012}. The treated water fulfills the drinking water quality standards of the drinking water ordinance \citep{bundesrepublik_deutschland_verordnung_2018}.

The water treatment units support the already existing service system of wells. Locations for placing the mobile water treatment units have to be identified, wherefore location criteria are established. Table \ref{tb:locationCriteria} provides an overview of the identified location criteria.

\begin{table}[htbp]
\small
\begin{tabularx}{\textwidth} {p{2.5cm} p{7cm} p{2cm} p{3cm}}
\hline
\textbf{Criterion} & {\textbf{Description}} & \textbf{Value} & \textbf{Source} \\
\hline
Access to water & Ability to feed water treatment systems with water must be ensured. Therefore, it must be possible to bridge the distance between water source and system with a pump. Alternatively, delivery by truck can be ensured by the proximity of the road network. & 1,200 meters & \cite{corsten_produktionswirtschaft:_2016}, \cite{staatliche_feuerwehrschulen_bayern_wasserforderung_2018} \\
Access road network & Transportation of water to the water treatment system must be possible if it can not be supplied water by pump. Therefore, the maximal distance to next road must not exceeded the maximal distance a pump can bridge. & 1,200 meters & \cite{corsten_produktionswirtschaft:_2016}, \cite{staatliche_feuerwehrschulen_bayern_wasserforderung_2018} \\
Distance to demand & Location candidates must be within the maximal allowed supply routes to at least one demand point & 2,000 meters &\cite{epa_planning_2011}, \cite{Fischer.2013} \\
Available area & Operating site must have a minimum size & 60 x 60 metres & \cite{epa_planning_2011} \\
\hline
\end{tabularx}
\caption{Location Criteria for Location of Water Treatment Systems.}
\label{tb:locationCriteria}
\end{table}

Possible sites should have a minimum area of 60 x 60 meters. Since the water treatment system is also used as a distribution station, locations should be close to demand \citep{epa_planning_2011}.

The location should also have access to a raw water source \citep{corsten_produktionswirtschaft:_2016}, which can provide a water feed of $15m^3$ per hour, to exploit the full capacity of the UF-15. According to the school for fire brigades in Bavaria, one pump can cover a distance of around 1,200 meters when providing the necessary water feed \citep{staatliche_feuerwehrschulen_bayern_wasserforderung_2018}. The needed water feed are 250 liters per minute. Assuming the used pumps have 10 bar output pressure, than these pumps can cover a distance of 1,210 meters providing 600 liters per minute. Therefore, we assume that this also applies at 250 liters per minute. The THW has confirmed this assumption in a private email. This criterion separates possible locations into two sets. Both sets are evaluated since locations farther than 1,200 meters from water can be fed by tank trucks. Therefore, the locations must be accessible by road or at least must be close to a road so that a water pump can cover the distance and transportation of water to the site is possible.

These criteria were used to process data provided by Berlin's Geoportal. The map "Reale Nutzung 2015" provides an overview of the land use within the city. The map classifies areas of Berlin into categories like "industrial use", "traffic area", or "brown field" \citep{geoportal_berlin_reale_2019}. Considered locations are restricted to categories like "brown field", "grassland", "green area", "town square" or "farmland", indicating an open operation area.

Remaining sites are evaluated according to their area, and sites that are too small are excluded from the assessment. The distance to the next street and thereby the availability to supply water by truck is examined using the map "Detailnetz Berlin" that displays the road network of the city and is provided by \cite{geoportal_berlin_detailnetz_2019}. Areas are excluded if they are further than 1,200 meters away from the next street. Therefore, one pump can cover the distance between the site and the next road \citep{staatliche_feuerwehrschulen_bayern_wasserforderung_2018}. The distance between demand and locations is analyzed similarly. Areas are eliminated if they are further than 2,000 meters away from the next demand point. This limits the assessment within the range of supply routes established by \cite{langenbach_trinkwasser-_2008}.

The last step is about evaluating the distance between location candidates and possible water sources. A map of Berlin's surface water is used to determine adequate water sources \citep{geoportal_berlin_gewasserkarte_2019}. Surface water classified as "wetland" or "reservoirs" are excluded from consideration. The average water depth of all water bodies recorded in the Berlin Water Atlas is used to determine the volume of each potential water source \citep{stadtverwaltung_berlin_gewasseratlas_2002}. The volume of the water bodies defines the number of water treatment systems that can be operated over a period of 14 days. Operating a fully utilized treatment system requires 300$m^3$ of water per day. Over 14 days, this results in 4,200$m^3$ of water that is required. 695 water sources have at least the capacity to supply one water treatment system. Each location candidate is allocated to the closest water source. 

The location candidates are separated into two sets: the first set is within a distance of 1,200 meters to a water source and can be supplied by a water pump. Locations in the second set need to be supplied by a tank truck. The first set contains 2,403 locations, and the second set contains 157 locations. The areas were aggregated to points.

The cost calculations for the location that require water by truck follows. The average distance of 1,516 meters between the set of water distant location and sufficient water sources is used to calculate the average travel time needed for a truck. \cite{wisetjindawat_planning_2014} conducted a survey among freight forwarders who distributed goods during the aftermath of the Great East Japan earthquake, asking for their average driving speed. They separated between expressways and regular roads. 
If we apply the resulting 16 kph for regular roads to our case study, an average travel time of 5.69 minutes for one way and 11.37 minutes for both ways follows.

Other time factors are the flowrate for filling the trucks and the set-up time. According to the fire brigade of Berlin \footnote{Private email exchange with Fire Brigade of Berlin.}, an appropriate flow rate for filling tanks on vehicles is 850 liters per minute. The set-up time is assumed to be 10 minutes.

The THW drinking water specialist groups have water supplying capacities of 10,000 liters that can be used to supply raw water to mobile water treatment systems.\footnote{Private email exchange with THW.} Therefore, we assume that 14 trucks with a capacity of 10,000 liters each are available. One truck can supply one water treatment system for 40 minutes. Based on the introduced time factors, a truck needs 33 minutes to be refilled. Thus, two trucks are needed to run one water distant treatment system (assuming that no vehicle breaks down, and there is no delay in operations). This limits the operable number of treatment systems that receive their water by truck to seven.

\begin{table}[htbp]
\small
\begin{tabularx}{\textwidth} {p{4,5cm} p{1.5cm} p{1.5cm} p{1.5cm} p{2cm} p{4cm}}
\hline
\textbf{Cost Driver} & \multicolumn{2}{c}{\textbf{Expenses}} & \textbf{Quantity} & \textbf{Sum} & \textbf{Source} \\
\hline
\multicolumn{6}{c}{\textbf{Personal Costs}} \\
\hline
Volunteer THW & 22.00 \EUR{} & per hour & 18 & 7,920,00 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
\hline
\multicolumn{6}{c}{\textbf{Equipment Costs}} \\
\hline
Pumps & 35.00 \EUR{} & per day & 4 & 140.00 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
Power Generator & 4.77 \EUR{} & per hour & 1 & 95.40 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
Water Tanks & 7.70 \EUR{} & per day & 12 & 92.40 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
Drinking Water Laboratory & 18.20 \EUR{} & per day & 1 & 18.20 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
UF-15 & 884.00 \EUR{} & per day & 1 & 884.00 \EUR{} & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
\hline
Sum & & & & 9,150.00 \EUR{} & \\
\hline
\end{tabularx}
\caption{Operating Costs of a Water Treatment System.}
\label{tb:costTWA}
\end{table}

Table \ref{tb:costTWA} provides an overview of expenses considered estimating the daily operating costs of the UF-15 system. This includes personal costs for the drinking water specialist groups, which are 22 \EUR{} per volunteer and hour \citep{bundesanstalt_technisches_hilfswerk_verordnung_2012}. The equipment includes four pumps to provide water for the treatment process. Since the THW has different types of pumps, the average expense of the listed equipment is calculated, resulting in 35 \EUR{} per pump and day \citep{bundesanstalt_technisches_hilfswerk_verordnung_2012}. We followed the same approach to calculate expenses related to emergency power generators, which included their fuel consumption \citep{statistisches_bundesamt_daten_2019, bundesanstalt_technisches_hilfswerk_verordnung_2012}. 

The water tanks required to supply the UF-15 system result in additional expenses. A drinking water laboratory ensures the quality of the processed water. Finally, the deployment of the system also leads to expenses. We assume that that the public is requested to bring containers \citep{BundesamtfurBevolkerungsschutzundKatastrophenhilfe.2016b}. This leads to an estimated total daily operating costs of rounded 9,200 \EUR{} per system.

However, if a treatment system is placed at a location more than 1,200 meters away from a water source, additional costs occur. As described above, two trucks are needed to supply one treatment system. It is assumed that the drivers of the trucks are volunteers of the THW so that the stated personal costs can be applied. Costs for the vehicles include the costs for the trucks and the required fuel. The costs for the trucks are provided by \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} and are 4.50 \EUR{} per hour. The diesel consumption is specified with 28 litres per 100 kilometers. The average distance traveled is 74 kilometers per operating day, and the assumed price per liter diesel is 1.01 \EUR{} \citep{statistisches_bundesamt_daten_2019}. This leads to fuel costs of 20.90 \EUR{} per day and truck. Therefore, the additional daily costs associated with operating the treatment system at a location further away from a water source are rounded to 1.100 \EUR{}.

\section{Distance Between Demand Points and Water Source} \label{sec:data_dis}
We define the distance between supply and demand points as $supply~route$. This supply route represents the service standard and is used to select locations for water treatment systems. Within the case study, supply routes between interacting points are calculated using the Euclidean distance. However, the assumption of direct links is not applicable when considering overland routes. Therefore, a tortuosity factor of$\sqrt{2}$ is introduced to embrace real road conditions \citep{delivand_assessing_2011, diehlmann_techno-economic_2019}.

According to \cite{langenbach_trinkwasser-_2008}, reasonable supply routes in the context of emergency water wells are between 500 and 2,000 meters. We assume this also applies for the supply with water treatment systems. Therefore, the maximum service standard is examined for a supply route of 1,250 meters, evaluating an intermediate scenario. A sensitivity analysis for different supply routes lengths follows in the Section 6 of the manuscript.

Table \ref{tb:dataOverview} provides an overview of the collected data for the case study. It includes the parameter settings for the optimization runs.

\begin{table}[htbp]
\small
\begin{tabularx}{\textwidth} {p{6.5cm} p{3cm} p{5.5cm}}
\hline
\textbf{Parameter}   & \textbf{Value} & \textbf{Source} \\
\hline
\multicolumn{3}{c}{\textbf{Optimization Parameters}} \\
\hline
Distance to water ($dW$) & 1,200 meters & \cite{staatliche_feuerwehrschulen_bayern_wasserforderung_2018} \\
Desired maximum distance between supply and demand ($S$) & 1,250 meters & \cite{Fischer.2013} \\
Number of available water treatment systems (UF-15 units) ($p$) & 14 & Email exchange with THW \\
Maximum number of water treatment systems that can be supplied by trucks ($q$) & 7 & \cite{wisetjindawat_planning_2014}, \newline
Email exchange with fire brigade Berlin and THW \\
Minimum percent of demand supplied per trip ($pd$) & 20\% & \cite{the_sphere_project_sphere_2018} \newline \cite{bundesrepublik_deutschland_erste_1970} \\
Operating Costs Water emergency wells ($costEW$) & 10,700 \EUR{} per day & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012}, \cite{trager_micropur_2019} \\
Operating Costs Water Treatment Systems ($costLW$) & 9,200 \EUR{} per day & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012} \\
Operating Costs Water Treatment Systems further away from water source ($costLC$) & 10,300 \EUR{} per day & \cite{bundesanstalt_technisches_hilfswerk_verordnung_2012}, \cite{statistisches_bundesamt_daten_2019} \\
\hline
\multicolumn{3}{c}{\textbf{Spatial Demand Structure}} \\
\hline
Number of regular demand points & 14,755 &  \cite{amt_fur_statistik_berlin-brandenburg_einwohnerdichte_2019} \\
Number of special demand points \newline (hospitals, nursing homes, sheltered housing) & 529 & \cite{berliner_krankenhausgesellschaft_e.v._berliner_2019},  \cite{privatinstitut_fur_transparenz_im_gesundheitswesen_gmbh_betreutes_2019} \\
\hline
\multicolumn{3}{c}{\textbf{Emergency Wells}} \\
\hline
Number of operated emergency water wells ($FT$) & 1,028 & \cite{geofabrik_gmbh_openstreetmap_2019} \\
Daily drinking water supply ($c_j$) & 90,000 liters per well & \cite{Fischer.2013} \\
\hline
\multicolumn{3}{c}{\textbf{Mobile Water Treatment Systems}} \\
\hline
Location candidates next to surface water ($WT$) & 2,403 & \cite{epa_planning_2011}, \cite{corsten_produktionswirtschaft:_2016}, \cite{Fischer.2013}, \cite{staatliche_feuerwehrschulen_bayern_wasserforderung_2018}, \cite{geoportal_berlin_reale_2019} \\
Location candidates that must be supplied by trucks ($DWT$) & 157 & \cite{wisetjindawat_planning_2014}, email exchange fire brigade Berlin, email exchange THW \\
Daily drinking water supply ($c_j$)& 300,000 liters per system & \cite{bundesanstalt_technisches_hilfswerk_trinkwasseraufbereitungsanlage_2012} \\
\hline
\multicolumn{3}{c}{\textbf{Distance}} \\
\hline
Distance Calculation & Euclidean Distance & \cite{mwemezi_optimal_2011} \\
Tortuosity factor & $sqrt(2)$ & \cite{diehlmann_techno-economic_2019} \\
\hline
\end{tabularx}
\caption{Overview of Relevant Input Data for the Optimization Model.}
\label{tb:dataOverview}
\end{table}

\begin{acknowledgements}
\label{acknowledge}
This research was supported by the German Federal Ministry of Education and Research (BMBF) in the NOLAN project (grant number: 13N14457). Furthermore, we want to thank the employees at diverse disaster management authorities for their support during the data collection and validation process. 
\end{acknowledgements}

\section*{Conflict of interest}
\label{conflictOfInterest}

The authors declare that they have no conflict of interest.

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\end{document}
