Column Generation Algorithms for Machine Scheduling and Integrated Airport Planning

Abstract

In this thesis we consider both scheduling problems from a theoretical point of view, as well as from a practical point of view. With respect to the theoretical point of view, we consider two machine scheduling problems. The first problem is minimizing the sum of weighted tardiness when all jobs have a corresponding release date, due date, weight, and a processing time that is equal for all jobs. We show for what kind of instances this problem is solvable in polynomial time and we provide a branching strategy that can be used in a branch-and-bound method to use as much structure of the problem to solve the problem efficiently. The second machine scheduling problem we consider is minimizing the maximum lateness of the jobs when all jobs have a release date, due date, and deadline. We do this by first formulating the problem a integer linear programming problem with the time-indexed formulation. We then determine a lower bound for the minimum value of the maximum lateness by means of a column generation approach. After this we use this lower bound to speed up the solving of the integer linear programming problem. With respect to the scheduling problems from a practical point of view, we consider two real-life problems that occur at an airport. The two problems we consider are the gate assignment problem (i.e. determine which flight will be assigned to which gate when it arrives at the airport) and the bus planning problem (i.e. determine which bus is used to transport passengers to or from a flight that is assigned to a gate that is not connected to the terminal building via a air-bridge). For both problems we provide a model and a solution method based on column generation. We did not only consider these two problems as separate problems, but we also integrate them into one large model. This integration allows for using information from the bus planning problem while solving the gate assignment problem which results in better overall solutions. We have implemented the models and solution methods for both the separate problems as well as the integrated problem and then used data provided by Schiphol to test these implementations. The experiments show that we can solve not only the separate problems in a matter of minutes, but also the integrated model for a complete day of data can be solved in about 15 minutes.