# Large Problems

## MOD

Modena Network (MOD) includes three hundred and seventeen pipes, two hundred and sixty-eight demand nodes, and four reservoirs with fixed head within 72.0 m to 74.5 m. The pipe material is the same as PES. A uniform Hazen-Williams roughness coefficient of 130 is applied to all pipes. The minimum pressure head of all the demand nodes is maintained at 20 m. The maximum pressure head of each node of MOD is provided in Table MOD.1 In addition, the flow velocity in each pipe is enforced to be less than or equal to 2 m/s. Table MOD.2 shows commercially available diameters and the corresponding unit costs. Figure MOD.1 depicts the layout of MOD.

 Table MOD.1. Maximum pressure head requirement of each node of MOD ‌‌‌MOD Table 1 Table available in Microsoft Word 2003 format due to its large size
 Table MOD.2. Diameter options and associated unit costs of MOD ‌‌‌
 Figure MOD.1. Layout of Modena Network

## BIN

Balerma Irrigation Network (BIN) includes four hundred and fifty-four relatively small length pipes, four hundred and forty-three demand nodes (hydrants), and four reservoirs with fixed heads within 112 m to 127 m. The material of pipes is polyvinyl chloride (PVC). The Darcy-Weisbach roughness coefficient of 0.0025 mm is applied to all the pipes. The minimum pressure head above ground elevation is 20 m for all the demand nodes. Table BIN.1 shows commercially available diameters and the corresponding unit costs. Figure BIN.1 depicts the layout of BIN.

 Table BIN.1 Diameter options and associated unit costs of BIN ‌
 Figure BIN.1. Layout of Balerma Irrigation Network ‌

## EXN

Exeter network has three thousand and thirty-two pipes including five hundred and sixty-seven considered for duplication, five valves, one thousand eight hundred and ninety-one junction nodes and seven water sources. Two major reservoirs (node 3001 and 3002) supply water to the system at fixed head of 58.4 m and 62.4 m respectively. The system is also fed by its neighbour systems via node 3003 to 3007 at fixed rates. Three non-return valves (also known as check valves) are connected to node 3001 and 3002 to control the flow direction into and outside the system. One pressure reducing valve locates in the downstream of node 3004 to maintain the downstream pressure within 58.4 m. One throttle control valve is also in the link downstream of node 3004 to control the flow and pressure of system.

The minimum pressure requirement of demand nodes is 20.0 m. There are ten available discrete pipe sizes and one extra option as 'do nothing'. The unit cost for duplicating the existing pipe depends on both the diameter selected and the road type. Table EXN.1 shows the pipe diameters, the corresponding Colebrook-White friction factors (following Darcy-Weisbach formula) and unit costs. The location of major roads is specified in Table EXN.2 in terms of pipe ID. Figure EXN.1 depicts the layout of EXN.

 Table EXN.1. Roughness coefficients and unit costs of EXN ‌‌‌‌
 Table EXN.2. Location of major road in terms of pipe ID ‌‌‌‌
 Figure EXN.1. Layout of Exeter Network1

1 This network is a bit different from the one available at EXNET. The modifications are summarised as follows: (1) Node 1610 has been removed to avoid isolated junction; (2) 20 PM in the section of “TIMES” of input file has been changed to 8 PM; (3) Since it is impossible for junction 1107 to meet the minimum pressure requirement, it is ignored in the calculation of constraint violation. Also, it would be too complicated to highlight all the pipes considered for duplication, these pipes are tagged in the input file given.