1. IEOR E4405.001 Airline Crew Airline Crew Scheduling Scheduling Presented by: Presented by: Fatima Khalid 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. Background on Aircraft Economics Two costs components: Cost Components Aircraft Variable Costs (Operating costs, i.e fuel) Fixed Costs (Monthly Payments)

6. IP Formulation – Crew Pairing: Min Σ p c p x p st Σ p δ fp x p = 1for all f x p 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. δ fp -> 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 r i = c i + y i 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.