How can integer programming improve airline scheduling?

Integer programming helps solve optimization problem involving binary variables. Resource allocation or assignment problem involve assignment decision (0/1, assigned or not assigned) that are optimal i.e. maximize/minimize the objective function. Such problems can be modeled as integer programs and solved to optimality using efficient algorithms/tools that have been developed over the years.

Integer programming is a mathematical optimization technique used in operations research. It tackles optimization problems where some or all variables must be integers. For instance, in airline scheduling, discrete quantities like the number of flights or crews cannot be fractional. Integer programming utilizes binary variables (0 or 1) to represent assignments, such as whether a flight or crew is allocated to a route or time slot. By defining an objective function and constraints reflecting operational requirements, it finds the optimal solution to maximize or minimize the objective while adhering to constraints.

MIP is by far the most used method in airline optimization. Unfortunately, much to the detriment of the industry. See, airlines work off of fantastic plans for crew pairing/crew scheduling, fleet assignment, revenue management, etc. Everything looks amazing. On paper. And then those plans have to be executed and the airlines are losing their shirt on the day of operation. In case you have ever wondered as a passenger: The airlines know that, if today is screwed, the best course of action is to get back into their plan for tomorrow, or else tomorrow is screwed also. That is why they do not care about today. What is needed is robust plans that are optimized against a cloud of futures. That is why we built InsideOpt Seeker.

Airlines need to assign fleet and crew to the flight routes that they decide to service. They can use integer programming approach for fleet (and crew) assignment decisions. These problems can be modeled as an integer programming problem where fleet (or crew) assignment decision can be modeled as 0 or 1 (i.e. assigned or not) for a given route with objective to minimize cost, lost potential revenue, increase utilization etc., and satisfying capacity and operational constraints,

I'm not convinced that the root issue is the use of optimization (MIP, Genetic algorithm); it is the omission of uncertainty or stochastic in models— which means optimization can still be highly effective with a combination of simulation and added uncertainty. This is heavy plugging and reeks of bias (I.e., conflict of interest). Linear Programming and its derivatives are great for maximizing profit, assuming certainty and “everything is known”. However, they work better when stochastic elements like weather and cancellations are considered, too.

Integer programming for airline scheduling involves formulating the problem as a mixed-integer linear program (MILP). Variables representing aspects like flight times, crew rosters, and aircraft assignments are defined as either continuous or integer. The objective function and constraints are expressed linearly, incorporating factors like operating costs, revenue, and regulatory requirements. Specialized algorithms like branch-and-bound or cutting planes are then employed to solve the MILP efficiently. These methods yield optimal or near-optimal solutions within a reasonable timeframe, considering the problem's scale and complexity.

Integer programming techniques can be applied to fleet and crew assignment problems in airline industry. Airline revenue management solutions also model seat allocations as binary variables with integer programming constraints.

Flight Scheduling: Optimizing flight schedules to maximize profitability, minimize costs, and meet demand while adhering to operational constraints. Crew Scheduling: Assigning crews to flights efficiently to minimize costs, ensure regulatory compliance, and optimize crew utilization. Aircraft Scheduling: Allocating aircraft to routes and flights to maximize utilization, minimize costs, and maintain reliability. Fleet Assignment: Determining the optimal assignment of aircraft to routes and flights considering factors such as aircraft type, capacity, and maintenance requirements. Gate Assignment: Optimizing gate assignments at airports to minimize delays, improve turnaround times, and enhance operational efficiency.

Main challenge is the complexity. Decomposition techniques or heuristics should be employed to find near-optimal solutions. For small problems MILP works well and gives the optimal solution.

Data Availability and Quality: Accurate data on demand, capacity, costs, and constraints is crucial for reliable solutions. Model Complexity and Scalability: The large number of variables, constraints, and parameters can lead to complex and difficult-to-solve models, especially as problem size increases. Solution Time and Memory Requirements: As the problem size grows, solution time and memory requirements may increase exponentially, posing computational challenges. Feasibility and Acceptability: The optimal solution provided by integer programming may not always be feasible or acceptable in practice due to operational, regulatory, or customer constraints.