STEM help / Calculation framework

10.3.4.3 Allocating costs of slack capacity

Some Resource costs, such as Operations Cost, are charged pro-rata to utilisation, and therefore only arise from the used capacity of a Resource. These used costs are always allocated directly to the corresponding Services. Other costs, such as Maintenance Cost, arise from the full installed capacity of a Resource, and therefore contain a slack component when a Resource is not fully utilised.

When a Resource is first installed, the costs of any slack capacity are allocated in the same proportions as the costs of the used capacity, i.e., in proportion to the capacity used by each respective Service. However, in subsequent years the demand for a Service may fall, increasing the proportion of slack costs to allocate.

You can set a flag in stem.ini which causes STEM to generate a run-time warning when slack costs exceed a specified percentage of total costs – see 11.4 STEM.INI. If slack costs do become significant, there are two global inputs you can set to tailor the way this additional slack capacity is allocated to suit the circumstances of your model.

Reallocation of costs

A choice governing the allocation of the costs of slack Resource capacity, between the Services which previously used it.

No: the costs of newly-slack capacity of a Resource are allocated according to each Service’s historical usage of that Resource; but the allocation of the costs of existing slack capacity remains unchanged.

Yes: the costs of all the slack capacity of a Resource are re-allocated each year, according to each Service’s historical usage of that Resource.

Past-usage significance

A discount factor governing the responsibility of Services for the costs of slack Resources, previously used by those Services.

Slack costs are allocated to Services on the basis of their historical usage of a Resource, where usage in previous years is progressively discounted. For example, a factor of 0.5 would mean that only half of last year’s usage, and only one quarter of the preceding year’s usage, would be counted.

Slack costs are allocated on this basis, either when Resource capacity first becomes slack, or every year, depending on the Reallocation of Costs input.

For a given Resource, the proportion of slack costs, ai,n, allocated to a particular Service, i, in year n will be:

where

ui,n = capacity used by Service i in year n

un = total used capacity of this Resource in year n

k = Past-Usage Significance, between 0 and 1.

Under extreme circumstances, such as the demand for a Service falling to zero, the installed capacity of a Resource may become completely slack. If the input Reallocation of Costs = Yes, the costs of such Resources will not be allocated to any Service. Again, you can set a flag in stem.ini which causes STEM to generate a run-time warning when this occurs – see 11.4 STEM.INI.

Example

In one year, a Service, Service 1, requires a Resource to be installed and uses 0.2 of the installed capacity. The remaining 0.8 of the capacity is slack. In the absence of any other Services using this Resource, all costs arising from this Resource are allocated to Service 1.

In the following year, a new Service, Service 2, is introduced, which uses 0.5 of the Resource’s existing capacity, while Service 1 continues to use 0.2, leaving 0.3 slack.

The used portion of any costs arising from the Resource is allocated directly to the two Services in proportion to their individual usages. The Reallocation of Costs input governs how the slack portion of any costs is allocated between these Services:

No: the remaining slack costs are left with the Service that initially caused the slack capacity of the Resource to be installed, so the whole 0.3 of slack is charged to Service 1.

Yes: the slack costs are reallocated every year according to each Service’s historical usage of the Resource. With Past-Usage Significance = 0.0, the costs are re-allocated on the basis of current-year usage, so the 0.3 of slack is distributed in the ratio 2:5 between Service 1 and Service 2. If Past-Usage Significance is increased to 1.0, the slack is distributed in the ratio 4:5.

 

© Implied Logic Limited