Technological and industrial advances have resulted in the growth of large enterprises.Optimization models have been developed to increase the efficiency of partsof these systems, but models that optimize entire enterprises are frequently immenseand very complex to solve. Sequential solution techniques have resulted, which leadto useful, but not globally optimal, solutions. For example, airlines develop flightschedules based on strategic business objectives, and sequentially plan operationalprocesses to execute the schedule. Proven models that exist for the operationalsubproblems are solved sequentially, begin with a flight schedule, and allow limitedfeedback in the planning process. Since small changes to the individual parts haveproduced millions of dollars in improvement, an overall optimal solution could yielda significant increase in the airline's profit.We consider a modelling paradigm that moves toward integrated methods for theairline schedule planning phase using surrogate representations of the operationalproblems. In this context, surrogate models are relatively easy to solve, yet suffi-ciently representative of the operational problem to reflect its impact on schedulechoices. To illustrate, we develop surrogate models of maintenance scheduling, crewscheduling, and revenue generation. We solve the master schedule problem with eachsurrogate model using well-known decomposition techniques, and then combine thesurrogates into a single model that is readily decomposed into multiple subproblemsand solved.The model developments include additional considerations in constructing surrogatemodels. For example, to demonstrate validation of a surrogate's utility, wecompared the feasibility indications from the maintenance subproblem surrogate tothose from a larger, exact model of maintenance feasibility. The crew scheduling surrogatemodel development incorporates disruptions in the master schedule, drivingthe schedule to account for both crew costs and the impact of random disruptions.Finally, in the revenue management subproblem, we consider random demand thatimpacts a schedule's profitability.While surrogate solutions are inherently of little utility operationally, the resultsare useful for shaping the master schedule towards a global optimum. The paradigmallows for consideration of the subproblems in initial planning, so that solutionsobtained from the full models are based on a schedule that may lead to a betteroverall bottom line.

In airline scheduling a variety of planning and operational decision problems have to be solved. In this thesis we consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights of a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved subsequently. Also, in minimal cost solutions, aircraft and crew are highly utilised and short turn around times are usually used for aircraft and crew. If such a solution is used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day due to the lack of buffer times. We formulate an integrated aircraft routing and crew pairing model that can generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic approach that is capable of generating good quality solutions quickly, the second approach can solve the integrated model to optimality. In an extension of the integrated model we allow the departure times of some flights in the schedule to vary in some time window. This creates additional flexibility that leads to aircraft routing and crew pairing solutions with improved cost and robustness compared to the integrated model without time windows. Using data from domestic Air New Zealand schedules, we evaluate the benefits of the approaches on real world problem instances. Our solutions satisfy all rules imposed for these problems and are ready to be implemented in practice. We generate solutions that dramatically improve the cost and robustness of solutions obtained by existing methods.

In airline scheduling a variety of planning and operational decision problems have to be solved. In this thesis we consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights of a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved subsequently. Also, in minimal cost solutions, aircraft and crew are highly utilised and short turn around times are usually used for aircraft and crew. If such a solution is used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day due to the lack of buffer times. We formulate an integrated aircraft routing and crew pairing model that can generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic approach that is capable of generating good quality solutions quickly, the second approach can solve the integrated model to optimality. In an extension of the integrated model we allow the departure times of some flights in the schedule to vary in some time window. This creates additional flexibility that leads to aircraft routing and crew pairing solutions with improved cost and robustness compared to the integrated model without time windows. Using data from domestic Air New Zealand schedules, we evaluate the benefits of the approaches on real world problem instances. Our solutions satisfy all rules imposed for these problems and are ready to be implemented in practice. We generate solutions that dramatically improve the cost and robustness of solutions obtained by existing methods.

In airline scheduling a variety of planning and operational decision problems have to be solved. In this thesis we consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights of a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved subsequently. Also, in minimal cost solutions, aircraft and crew are highly utilised and short turn around times are usually used for aircraft and crew. If such a solution is used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day due to the lack of buffer times. We formulate an integrated aircraft routing and crew pairing model that can generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic approach that is capable of generating good quality solutions quickly, the second approach can solve the integrated model to optimality. In an extension of the integrated model we allow the departure times of some flights in the schedule to vary in some time window. This creates additional flexibility that leads to aircraft routing and crew pairing solutions with improved cost and robustness compared to the integrated model without time windows. Using data from domestic Air New Zealand schedules, we evaluate the benefits of the approaches on real world problem instances. Our solutions satisfy all rules imposed for these problems and are ready to be implemented in practice. We generate solutions that dramatically improve the cost and robustness of solutions obtained by existing methods.

In airline scheduling a variety of planning and operational decision problems have to be solved. In this thesis we consider the problems aircraft routing and crew pairing: aircraft and crew must be allocated to flights of a schedule in a minimal cost way. Although these problems are not independent, they are usually formulated as independent mathematical optimisation models and solved sequentially. This approach might lead to a suboptimal allocation of aircraft and crew, since a solution of one of the problems may restrict the set of feasible solutions of the problem solved subsequently. Also, in minimal cost solutions, aircraft and crew are highly utilised and short turn around times are usually used for aircraft and crew. If such a solution is used in operations, a short delay of one flight can cause very severe disruptions of the schedule later in the day due to the lack of buffer times. We formulate an integrated aircraft routing and crew pairing model that can generate solutions that incur small costs and are also robust to typical stochastic variability in airline operations. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic approach that is capable of generating good quality solutions quickly, the second approach can solve the integrated model to optimality. In an extension of the integrated model we allow the departure times of some flights in the schedule to vary in some time window. This creates additional flexibility that leads to aircraft routing and crew pairing solutions with improved cost and robustness compared to the integrated model without time windows. Using data from domestic Air New Zealand schedules, we evaluate the benefits of the approaches on real world problem instances. Our solutions satisfy all rules imposed for these problems and are ready to be implemented in practice. We generate solutions that dramatically improve the cost and robustness of solutions obtained by existing methods.

We develop a detailed, large-scale, airspace planning and collaborative decision-making model (APCDM), that is part of an $11.5B, 10-year, Federal Aviation Administration (FAA)-sponsored effort to increase U.S. National Airspace (NAS) capacity by 30 percent. Given a set of flights that must be scheduled during some planning horizon, we use a mixed-integer programming formulation to select a set of flight plans from among alternatives subject to flight safety, air traffic control workload, and airline equity constraints. Novel contributions of this research include three-dimensional probabilistic conflict analyses, the derivation of valid inequalities to tighten the conflict safety representation constraints, the development of workload metrics based on average (and its variance from) peak load measures, and the consideration of equity among airline carriers in absorbing the costs related to re-routing, delays, and cancellations. We also propose an improved set of flight plan cost factors for representing system costs and investigating fairness issues by addressing flight dependencies occurring in hubbed operations, as well as market factors such as schedule convenience, reliability, and the timeliness of connections. The APCDM model has potential use for both tactical and strategic applications, such as air traffic control in response to severe weather phenomenon or spacecraft launches, FAA policy evaluation, Homeland Defense contingency planning, and military air campaign planning. The model is tested to consider various airspace restriction scenarios imposed by dynamic severe weather systems and space launch Special Use Airspace (SUA) impositions. The results from this model can also serve to augment the FAA's National Playbook of standardized flight profiles in different disruption-prone regions of the National Airspace. / Ph. D.

The air transportation market has been growing steadily for the past three decades since the airline deregulation in 1978. With competition also becoming more intense, airline companies have been trying to enhance their market shares and profit margins by composing favorable flight schedules and by efficiently allocating their resources of aircraft and crews so as to reduce operational costs. In practice, this is achieved based on demand forecasts and resource availabilities through a structured airline scheduling process that is comprised of four decision stages: schedule planning, fleet assignment, aircraft routing, and crew scheduling. The outputs of this process are flight schedules along with associated assignments of aircraft and crews that maximize the total expected profit. Traditionally, airlines deal with these four operational scheduling stages in a sequential manner. However, there exist obvious interdependencies among these stages so that restrictive solutions from preceding stages are likely to limit the scope of decisions for succeeding stages, thus leading to suboptimal results and even infeasibilities. To overcome this drawback, we first study the aircraft routing problem, and develop some novel modeling foundations based on which we construct and analyze an integrated model that incorporates fleet assignment, aircraft routing, and crew pairing within a single framework. Given a set of flights to be covered by a specific fleet type, the aircraft routing problem (ARP) determines a flight sequence for each individual aircraft in this fleet, while incorporating specific considerations of minimum turn-time and maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenance operations. This stage is significant to airline companies as it directly assigns routes and maintenance breaks for each aircraft in service. Most approaches for solving this problem adopt set partitioning formulations that include exponentially many variables, thus requiring the design of specialized column generation or branch-and-price algorithms. In this dissertation, however, we present a novel compact polynomially sized representation for the ARP, which is then linearized and lifted using the Reformulation-Linearization Technique (RLT). The resulting formulation remains polynomial in size, and we show that it can be solved very efficiently by commercial software without complicated algorithmic implementations. Our numerical experiments using real data obtained from United Airlines demonstrate significant savings in computational effort; for example, for a daily network involving 344 flights, our approach required only about 10 CPU seconds for deriving an optimal solution. We next extend Model ARP to incorporate its preceding and succeeding decision stages, i.e., fleet assignment and crew pairing, within an integrated framework. We formulate a suitable representation for the integrated fleeting, routing, and crew pairing problem (FRC), which accommodates a set of fleet types in a compact manner similar to that used for constructing the aforementioned aircraft routing model, and we generate eligible crew pairings on-the-fly within a set partitioning framework. Furthermore, to better represent industrial practice, we incorporate itinerary-based passenger demands for different fare-classes. The large size of the resulting model obviates a direct solution using off-the-shelf software; hence, we design a solution approach based on Benders decomposition and column generation using several acceleration techniques along with a branch-and-price heuristic for effectively deriving a solution to this model. In order to demonstrate the efficacy of the proposed model and solution approach and to provide insights for the airline industry, we generated several test instances using historical data obtained from United Airlines. Computational results reveal that the massively-sized integrated model can be effectively solved in reasonable times ranging from several minutes to about ten hours, depending on the size and structure of the instance. Moreover, our benchmark results demonstrate an average of 2.73% improvement in total profit (which translates to about 43 million dollars per year) over a partially integrated approach that combines the fleeting and routing decisions, but solves the crew pairing problem sequentially. This improvement is observed to accrue due to the fact that the fully integrated model effectively explores alternative fleet assignment decisions that better utilize available resources and yield significantly lower crew costs. / Ph. D.