IEx86-HW1-corr

Q2)(Airline Crew Scheduling) Recall the airline crew scheduling prob- lem introduced in class. The objective of the crew scheduling problem is to find a minimum cost assignment of flight crews to a given schedule. We consider a simplified version of the problem where • A flight leg is a single nonstop flight. • A pairing is a sequence of flight legs starting from a base and ending at the same base. There should be exactly one crew for each flight leg. Our goal is to find best combination of pairings to cover the whole flight schedule with minimum cost. The list of flights, their schedule and associated costs are given below. From To Dep Time Arr Time Cost of Flight ( $ ) Istanbul Wien 08:00 10:25 223000 Istanbul Paris 08:00 11:19 236000 Istanbul Thessaloniki 08:00 08:57 120000 Thessaloniki Paris 09:30 12:15 238000 Wien Barcelona 11:50 14:01 195000 Paris Amsterdam 12:40 13:42 115000 Paris Rome 13:00 14:53 142000 Amsterdam Istanbul 15:00 18:15 183000 Barcelona Munich 15:00 16:49 244000 Rome Istanbul 16:00 18:13 245000 Munich Istanbul 17:30 19:58 124000 Two types of costs are incurred: flight costs and resting costs . Flight cost for each flight leg is given in the table. As for the resting cost, there is a unit resting cost of (220$ per min). Meaning, for every minute elapsed between the end of a previous flight and the start of the next flight, 220$ is incurred. Assume that all crews are based in Istanbul. You are asked to find the min- imum cost scheduling of the airline crews that covers all the scheduled flights. a) Propose a formulation for this problem that is amenable to column gen- eration. Now consider the LP relaxation of this formulation. Explicitly indicate the master problem, dual of the master problem, and the pricing problem. b) Give your hand-written solution to the LP relaxation of the formulation proposed above. Include all details in each iteration of the column generation process. c) Write a Python/Gurobi code implementing the column generation from start to the end. 2