Allocation Models

Another simple generic model supported in OPUS is the Allocation Model, which does not require estimating model parameters. This model proportionately allocates some aggregate quantity to a smaller unit of analysis using a weight. This model could be configured, for example, to allocate visitor population estimates, military population, nursing home population, and other quantities to traffic analysis zones for use in the travel model system. Or it could be used to build up a simplistic incremental land use allocation model (though this would not contain much behavioral content).

The algorithm for this type of model is quite simple. To create an Allocation Model, we need to specify six arguments:

$\bullet$

Dataset to contain the new computed variable

$\bullet$

Name of the new computed variable $Y$ , which will be indexed by the ids of the dataset it is being allocated to, $Y_i$ .

$\bullet$

Dataset containing the total quantity to be allocated (this can contain a geographic identifier, and will include a year column).

$\bullet$

Variable containing the control total to be allocated, $T$

$\bullet$

Variable containing the (optional) capacity value $C$ , indexed as $C_i$

$\bullet$

Variable containing the weight to use in the allocation $w$ , indexed as $w_i$ , with a sum across all $i$ as $W$

The algorithm is then just:

$$Y_i = min(round(T\frac{w_i}{W}),C_i)$$ (3)

If a capacity variable is specified, we add an iterative loop, from $m$ to $M$ , to allocate any excess above the capacity to other destinations that still have remaining capacity:

$$T^m = sum(round(T\frac{w_i}{W}) - C_i)$$ (4)

In each iteration, we exclude alternatives where $Y>=C$ , and repeat the allocation with the remaining unallocated total:

$$Y^m_i = Y^{m-1}_i + (T_m\frac{w_i}{W})$$ (5)

We then iterate over $m$ until $T^m = 0$

This simple algorithm is fairly versatile, and can be used in two modes: as incremental growth or as total values. If used in incremental mode, it adds the allocated quantity to the existing quantities. The alternative, total, mode for this model replaces the quantities with the new predicted values.