Large-scale Integer Programming Research Articles

The fleet assignment problem: Solving a large-scale integer program

Given a flight schedule and set of aircraft, the fleet assignment problem is to determine which type of aircraft should fly each flight segment. This paper describes a basic daily, domestic fleet assignment problem and then presents chronologically the steps taken to solve it efficiently. Our model of the fleet assignment problem is a large multi-commodity flow problem with side constraints defined on a time-expanded network. These problems are often severely degenerate, which leads to poor performance of standard linear programming techniques. Also, the large number of integer variables can make finding optimal integer solutions difficult and time-consuming. The methods used to attack this problem include an interior-point algorithm, dual steepest edge simplex, cost perturbation, model aggregation, branching on set-partitioning constraints and prioritizing the order of branching. The computational results show that the algorithm finds solutions with a maximum optimality gap of 0.02% and is more than two orders of magnitude faster than using default options of a standard LP-based branch-and-bound code.

The relocation of ambulance stations: A successful case study

Urban ambulance stations represent substantial investments in physical facilities and hence relocation decisions are long term strategic in nature and occur very infrequently. The problem of finding locations for facilities typically leads to a large scale integer programming problem. If there is also a choice as to the staging of these over time the problem becomes even larger. However, in this work it was found that by frequently discussing the problem with management and adapting the problem formulation to their needs it decomposed naturally into a number of sub-problems which were much easier to solve, and which were much more intelligible to management. As a result the recommendations of the study were accepted and are in the process of being implemented.