**1. Introduction**

The world population is increasing at an exponential rate and available water resources are reducing due to pollution and the effects of the climate change that increase the severity of droughts and favor other extreme events [1]. This places stress on many public services and dramatically increases the gap between water supply and demand. In many countries, urban growth has exceeded, and continues exceeding, the growth of supply infrastructure [2]. This growth generates the conditions necessary for operators of water supply systems to embrace intermittent water supply (IWS) [3]. Many countries in Africa, Asia, and Latin America have IWS [4].

Reducing poverty and improving public health is an important part of the Millennium Development Goals [5]. Achieving this goal is threatened by water shortages, lack of supply guarantees [6] and poor quality of supplied water. Although it is considered that the drinking water supplied through pipeline systems is safe, many studies show that deficiencies in the network, caused by IWS, can create conditions so that water is not safe and reliable [7–13]. The lack of reliable water supply systems in developing countries can undermine much of the hope for improvements in public health [14], and have negative effects for drinking water system objectives [15].

IWS generally seeks to reduce the per capita water demand based on savings in capital and operating costs. However, instead of being smart, this strategy brings negative consequences that outweigh the positive factors [16,17]. Symptoms of system failure include very low levels of pressure, and insufficient supply in the remotest and highest points. Generally, intermittent supply is adopted by necessity rather than by design and results in serious system impairment [18].

The best way to protect water quality is by maintaining positive and continuous pressures throughout the network [13,19]. Thus, continuous water supply ensures security. The supply change from intermittent to continuous is one of the main challenges concerning water and health in developing countries [20].

The cost of risks to the health of users must also be considered (in terms of their incomes, medical treatments, *etc.*) as it is much greater than the cost of replacing deficient pipes [11] that are detrimental to continuous water supply.

According to several studies [21–23], IWS systems produce insufficient pressure in less favored sectors or areas (nodes located on high points and/or far away). Such conditions may be favorable for reducing water losses. However, they also produce inequity in the supply [18].

Insufficient funding and mismanagement [17] are two of the main causes of the origin of IWS. System improvements in these scenarios do not derive from increasing the water supply sources, but from improving system infrastructure and management. However, a shortage of funding does not allow operators to make large investments, so they should look for profitable long term planning strategies. In this sense, phased or gradual improvements can be a good option.

The growth of cities occurs horizontally and/or vertically, as a result of residential, industrial, and commercial developments, and community facilities, *etc.* [24]. This growth requires expanding the network capacity and the correction of anomalies or reduced system performance [25].

When undertaking the expansion of a water supply network, the goal is to supply a much larger demand. However, when this expansion does not take into account the network capacity and the influence of the new expansion, various scenarios may appear that reduce the capacity of the network and threaten the quantity and quality of the service. Reducing the capacity of the network may lead, for example, to intermittent supply.

Generally, the network of an IWS system has insufficient capacity. However, this situation can be imperceptible because the operators manage to cover the demanded flows through differentiation of supply schedules, sectorization, and use of household tanks. Increasing the network capacity in IWS systems that seek to reach continuous water supply (CWS) is a task that must be carefully analyzed.

In this paper, the *theoretical maximum flow* is proposed as an indicator of network capacity. This element is endowed with its true dimension as a quantitative element that is crucial in decision-making, assessment, management, maintenance, exploitation, and design of drinking water distribution systems.

The theoretical maximum flow is important to evaluate the behavior and evolution of a drinking water system and its relationship with intermittent supply. It also serves as a basis for proposing a greedy algorithm that enables the definition of a schedule for pipe modification stages, and thus efficiently expands network capacity.

The case of study has two parts. In the first part, we evaluate the growth of the southern subsystem of the city of Oruro (Bolivia), which was originally built to offer continuous supply. However, various network modifications imposed an ideal environment for intermittent supply. In the second part, we consider the possibility of increasing the current network capacity, as part of various actions to revert to CWS. Based on the IWS classification given by Totsuka *et al.* [17], the system only suffers economic scarcity and managemen<sup>t</sup> problems, and not physical scarcity. Thus, only the actions related to infrastructure improvement are analyzed.
