CASE STUDY: BRISBANE AIRPORT
Brisbane, in Australia, decided to redevelop its international airport. This involved,
basically, moving large amounts of sand from various sources to various destinations.
Normally, how the sand is going to be moved is left to the judgement of the building
company, but Brisbane, in order to guide the competitive tender and judge the
submissions from interested companies, employed consultants to model the situation.
This was justified on the grounds that 2 million cubic meters of earth had to be moved,
and moving earth around represented a large portion of the cost of the redevelopment.
This is a two-phase problem formulation. In the first phase the problem is simplified to
produce a tentative solution. The second phase includes further complexity. You are
required to formulate, and solve with LINGO, the problem in its first phase and in its
second phase.
The sand was available at several locations, but these were grouped into five sources,
which very much matched the work to be done by the construction company: Apron
(AP), Terminal (TM), Airline Area (AA), Maintenance Compound (MC), and Access
Road (AR). Similarly, after grouping, there were nine destinations: Localiser North
(LN), Extension (EX), Low Areas (LA), Roads (R), Car Park (CP), Localiser South
(LS), Fire Station (FS), Oil Industry (OI), and Perimeter Road (PR).
The amount of earth available at each source and required in each destination is given in
the table below. The table also gives the distance between sources and destinations.
Due to difficulties in the terrain, the possibility of sending earth from MC and AR to LS
was not contemplated.
LN EX LA R CP LS FS OI PR Avail’e
AP 22 26 12 10 18 18 11 8.5 20 960
TM 20 28 14 12 20 20 13 10 22 201
AA 16 20 26 20 1.5 28 6 22 18 71
MC 20 22 26 22 6 2 21 18 24
AR 22 26 10 4 16 24 14 21 99
Requ’d 60 217 444 315 50 7 20 90 150 1355
Distances are measured in units of 100 metres, earth volumes are measured in cubic
metres.
In the first part of this case study you are required to find the minimum cost schedule
for taking earth (sand) from the source to the destination. The cost is obtained by
multiplying volume by distance. Notice that this is a “balanced problem”, this means
that the total amount available is equal to the total amount required.
Second part of the problem. The above formulation is very tentative and does not
take into account a very important practical issue: there are destinations that cannot be
accessed from the sources until the perimeter road has been built. The table below
gives the accessibility conditions. I have marked with * the destinations that can only
be accessed in a second stage when the road has been built. You can think of this
problem as a two-step one: first you can move earth around while, at the same time, you
build the perimeter road; second, you move earth to the sites that the perimeter road has
made accessible.
