Optimization model for the family house allocation problem in a
mining camp
Jorge Amaya ([email protected])
Eduardo Zapata ([email protected])
Centro de Modelamiento Matemático, Universidad de Chile, Chile
Abstract
Our problem can be explained as follow: a mining camp is a small urban system, where all
the management is done by the company (the employer). The main problem is how to
allocate the existing infrastructure (offers) to the workers (demands). Precisely, the
company gives a number of houses to be allocated to them, following some general criteria,
according to the state laws and the institutional arrangement, particularly the labor contracts
and the general agreements with the unions of workers.
The model is constrained by the following conditions: each worker (including his family)
must be allocated to a house; the number and characteristics of the houses are given; the
houses must be allocated from the center (where all main services are installed) to the
border; the camp must be connected, which means that no “island” is permitted. In the
same manner, we cannot accept empty sectors inside the city borders. We also consider the
camp is composed by concentric circles and we impose on the constraint that each circle
has to be completely allocated.
The objective function is the total cost of the solution, given by several items: annual cost
of the houses (it depends on the age of the property, the neighborhood in which it is
located, the expected use of water and energy by the type and size family, among others).
The corresponding model is a 0-1 linear programming problem. In the case we applied the
model, the size of the problem looks moderate, but in general this could be a very large
decision instance, depending on the detail of the representation of the mining camp.
Specifically, we divide the camp in blocks, which have known capacities (number of
houses and its characteristics): Each block is interpreted as a node in a graph, where the
arcs are given by certain precedence relations, representing the fact that the city must be
occupied from the center to the border (this extends upwards a modified version of the
maximal closure problem).
In this talk we explain the model construction and the corresponding software developed
for this application.