IEOR E4405.001 Airline Crew Scheduling Presented by: Fatima Khalid

1. IEOR E4405.001 Airline Crew Scheduling Presented by: Fatima Khalid

2. Scope • Goal of airline industry: Maximization of Profits. • Requirement for reaching the goal: Planning at strategic, tactical and operational levels. • Airline planning involves processes such as timetable, fleet assignment, crew pairing and crew assignment. • Note: Focus of presentation: Crew pairing and Crew assignment.

3. Research based on following papers • A Stochastic Programming Approach to the Airline Crew Scheduling Problem Joyce W.Yen • An Optimization Approach to Solving the Airline Crew Pairing Problem Amy Cohn and Shervin AhmadBeygi

4. Characteristics of Crew Scheduling Problem • Comprises of two components • Crew-Pairing Problem: Assigning crew pairings (crew comprising: pilot, co-pilot and flight attendants) to flights such that all flights are covered. • Crew Assignment: Crews are assigned to given pairings. Most airlines use a kind of bidding system to assign pairings to crews.

5. Two costs components: Background on Aircraft Economics

6. IP Formulation – Crew Pairing: • Min Σp cp xp • st Σp δfp xp = 1 for all f • xp E {0, 1} for all p Terminology: Xp -> is the binary variable taking the value 1 if pairing p is included in the solution else the solution is 0. δfp -> is a binary variable with value 1 if flight is included in the pairing else 0. Cp -> cost of pairing p.

7. Solution to the problem formulated • First Approach: Branch and Bound (as explained in class) • The Algorithm tries to find the optimal solution of the problem, that is root problem. • In case the optimal solution could not be found, the feasible region is then subdivided into sub regions and the algorithm is then applied to each respective sub-region, resulting in sub problems. • If an optimum solution is found to a sub problem it is feasible solution to the root problem but not necessarily globally optimal. • The optimal solution to the sub problem can be used to prune the tree.

8. Solution to the problem formulated • Second Approach: Carmin Algorithm • This algorithm uses reduced costs and dual values to find the integer solutions. • The IP is formulated as unconstrained non-linear problem • The reduced cost is found by finding solutions to the equation ri= c i + yi where yi = (ri- + ri+) / 2

9. Analysis • The advantage of using branch and bound over Carmin’s method is the confirmation of optimality that branch and bound solution has. • In addition, model doesn’t change with duals • However, drawback is the lack in efficiency in finding the solution.