# 10.3.18 Locations and deployment

For each Function or Resource you can specify the number of sites over which demand is spread, either directly as a time series or as a reference to a separate Location element. The latter is useful if you have several Functions or Resources with common siting requirements. A Location specifies the number of sites for a class of location, e.g., the number of towns in a region, but not the distribution of Resources across those sites.

#### Distribution

You can choose one of five assumptions about how demand is spread across sites, which affect the basis for calculating the number of Resources required.

One for one: the number of units of Resource must be at least equal to the number of Sites. In this case, the number of Sites represents the minimum number of units of Resource that are required, i.e., one unit of Resource on each site.

Monte Carlo: provides an approximation to the situation where demand is spread across a number of sites according to a normal distribution. The total number of installed units in this case, N, is given by the following equation:

where

Nmin = minimum installation required if demand were concentrated in one single place

s = number of Sites input

MCF = Monte Carlo Factor input.

The number of additional units installed is s/MCF, representing the amount of slack capacity required to allow for the number of Sites.

The Monte Carlo Factor must be positive. A value of 1 represents one spare unit of Resource installed at each site, on top of the minimum Resources required; while a value of 2 means that there is at least half a slack unit at each site on average.

Homogeneous: the number of units of Resource must be a multiple of the number of Sites. This corresponds to the situation where demand is uniformly spread over a number of sites. In other words, this distribution installs the same number of units at each site.

Smoothed Homogeneous: when the number of units required by demand is below the number of Sites, the number of Sites has no effect, but subsequently the number of units must be a multiple of the number of Sites (as with Homogeneous distribution). This distribution might be used where a Service is rolled out gradually over a number of sites. It installs the same number of units at each site, once every site has at least one, assuming from thereon that demand is distributed uniformly across sites.

Extended Monte Carlo: same as Monte Carlo, but at least one unit is provided per site.

#### Deploy any resource

To allow for non-uniform distribution of demand, you can specify a deployment for a Function or for each individual Resource within a Function, or both. Where both a Function and some of the Resources implementing that Function specify a Deployment, the following procedure applies:

1. For each Resource that specifies a Deployment, the constraint is applied, i.e., additional units of Resource are installed to match the Distribution.
2. If a Deployment is specified for the Function and the input Deploy Any Resource = No, then this Deployment is applied to those Resources in the Function that do not specify a Deployment of their own.
3. If a Deployment is specified for the Function, and the input Deploy Any Resource = Yes, then the specified Deployment is applied to the Function as a whole. Additional units of one or more of the Resources are installed to match the Distribution, on the basis of the total number of Resource units installed for the Function. In this case the choice of Resources to provide the additional units required is based on the pattern of the most recent installation of additional units of Resource, as specified by the Resource Requirements of the Services and Transformations using the Function.

Typically, you would use a Deployment for the whole Function if all the Resources that fulfilled that Function were interchangeable; perhaps if one were replacing another over time. Deployment by Resource might be more appropriate if different Services used different Resources exclusively.

The costs of spare capacity within a Resource, installed as a result of Deployment, are fed back to Services just like any other slack costs – 10.3.4 Cost Allocation.

#### Example

The Monte Carlo distribution can be used to model the situation where a number of units is required in addition to those required by demand.

The simplest way to achieve this is to set the number of Sites equal to the number of extra units required (in each year) and the Monte Carlo factor to 1.

The number of Sites can be specified as a simple time series, or as the Output of a Transformation. This facility can be useful where the quantity of a Resource depends on two independent measures such as users and traffic. This could be modelled by the number of users driving the installation of the Resources, together with a number of Sites, which is defined as the Output of a Transformation driven by the quantity of another Resource, driven in turn by traffic.

Note: No costs would be allocated on the basis of traffic in this example.

The following graph shows the number of units of a Resource that would be installed as demand increases across a constant 50 sites, according to each of the five distributions.

Installed Units according to different distributions