Airport Gate Assignment Considering Ground Movement - Computational Logistics - page 189

between allocations and the robustness of solutions was discussed by Bolat [2]
and Diepen et al. [5]. This is also included in our objective function. We aim to
avoid small gaps by maximizing the time gaps within a defined time window.
Dorndorf et al. [8,9] and Kumar et al. [12] included towing in their mod-
els. They modelled the towing using three flights: (arrival)+(tow away); (tow
away)+(tow back); and (tow back)+(departure). In this paper we assume that
there are always enough remote stands for towed aircraft and model it using two
flights: arrival+tow away and tow back+departure. This reduces the number of
variables used by the model and eliminates the associated constraints. In both
the current and the previous models, the decision about an exact towing time has
been left in controllers' hands: they can pick the most appropriate time within
an established time period.
Cheng [4] analysed the push-back conflicts that can be observed between
adjacent gates. He analysed flights which can be in conflict due to scheduled
departing/arriving times and did not allow these to be allocated to neighbouring
gates. His idea of detecting conflicts and resolving them by introducing hard
constraints into his model is similar to the idea used in our model. Our extension
allows a gate to be a member of one of the arbitrarily defined groups of gates
which are considered, rather than only considering neighbouring gates. Kim et
al. [11] introduced probable conflicts into the model as a soft constraint and
minimised them. That approach introduces many new variables into the model,
which makes it harder to solve. Moreover, it is dedicated to a specific architecture
of an airport, where gates are grouped on ramps and two non-crossing taxiways
which lead to them are present. However, at many airports the taxiways cross
and there are often bottlenecks which make access to gates harder.

4Mod lFormu on

A mixed integer programming model has been used here to model the problem.

4.1 Notation and Definitions

- F - the set of all flights
- n - the total number of flights
- f -aflight

- e f - the on-gate time of flight f , a constant for each flight f
- l f - the off-gate time of flight f , a constant for each flight f
- G - the set of all gates
- m - the total number of gates available
- g

∈ F := { 1 , ..., n }

- a gate
- F ( g ) - the subset of flights that can use gate g
- Sh - the set of pairs of gates that cannot be used simultaneously due to
shadow restriction
- GR

∈ G := { 1 , ..., m }

- a subset of gates (group of gates)
- M - the number of conflicting flights allowed to be allocated to one GR

∈{ GR 1 , ...., GR 5 }