Discrete Allocation
Discrete allocation is the allocation of resources (f.e. land units) to a set of categories (f.e. land use types) based on the suitability of each resource for each category and restrictions on the number of resources that should be allocated to a category.
In the context of the GeoDMS and its applications, it is defined as finding the Xij > = 0 for each resource i and category j that solves the following semi assignment problem for given suitabilities Sij:
Thus Xij represents whether land unit i is allocated to land use type j and only one single allocation per land unit is allowed.
If there are only two land use types, only the difference between the two suitability maps matters, and one can use the nth element or rth element function for the allocation (or use the weighted variants to implement quantitative allocation).
Discrete allocation can also be used to aggregate a discrete map (aka Downsampling) to larger zones or raster-cells while keeping the total area's constant or within bounds by using the amount of each land use type in or near an aggregate unit as suitability for that type and the total areas as claims (rounded down as minimum claim and rounded up as maximum claim).
When applied iteratively and by incorporation of dynamic neighbourhood enrichment, one can simulate land-use change caused by natural processes while minimum demands and/or maximum land-use restrictions (as specified by the claims) are maintained. When applied iteratively with feedback from future (neighbourhood-dependent) yields on the current suitability, one can model a time-consistent market equilibrium.
In the GeoDms, discrete allocation can be done with the function: discrete alloc.
In Luisa, the suitabilities for discrete allocation are called transition potentials and there are three modeltraits for calculating them:
