A.50.3 Solving LPs with special structure

The following predicates allow you to solve specific kinds of LPs more efficiently:

transportation(+Supplies, +Demands, +Costs, -Transport)

Solves a transportation problem. Supplies and Demands must be lists of non-negative integers. Their respective sums must be equal. Costs is a list of lists representing the cost matrix, where an entry (i,j) denotes the integer cost of transporting one unit from i to j. A transportation plan having minimum cost is computed and unified with Transport in the form of a list of lists that represents the transportation matrix, where element (i,j) denotes how many units to ship from i to j.

assignment(+Cost, -Assignment)

Solves a linear assignment problem. Cost is a list of lists representing the quadratic cost matrix, where element (i,j) denotes the integer cost of assigning entity $i$ to entity $j$. An assignment with minimal cost is computed and unified with Assignment as a list of lists, representing an adjacency matrix.