A Primal-Dual Approach for Large Scale Integer Problems

This paper presents a refined approach to using column generation to solve specific type of large integer problems. A primal-dual approach is presented to solve the Restricted Master problem belonging to the original optimization task. Firstly, this approach allows a faster convergence to the optimum of the LP relaxation of the problem. Secondly, the existence of both an upper and lower bound of the LP optimum at each iteration allows a faster searching of the Branch-and-Bound tree. To achieve this an early termination approach is presented. The technique is demonstrated on the Generalized Assignment problem and Parallel Machine Scheduling problem as two reference applications

A parallel genetic algorithm for the set partitioning problem

This paper describes a parallel genetic algorithm developed for the solution of the set partitioning problem- a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high- quality integer feasible solutions were found for problems with 36, 699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints

Pairing Generation for Airline Crew Scheduling

Airline planning is a complex and difficult process. The biggest airlines in the world plan for and operate fleets of over 700 aircraft using tens of thousands of crew members. As such, small percentages in savings translate to millions of dollars. In this thesis, we study the pairing and duty generation problem in the context of airline crew scheduling, and propose approaches to improve the computational speed and the solution quality. We propose several enumeration algorithms to generate all possible duty periods of a given schedule to improve on the time required to generate duty periods; and present a set of column generation models to improve on the solution quality. When tested on a real test case study, the proposed approaches are found to improve the computational times from 142 seconds down to less than one second, and the cost savings of 13.7%

Robust crew pairing for managing extra flights /

The airline industry encounters many optimization problems such as scheduling flights, assigning the fleet, scheduling the crew. Among them, the crew scheduling problem is the most studied one. The main reason is that the crew cost is one of the largest components of the operational cost for an airline company. Therefore, there are many models proposed in the literature to find a cost efficient crew schedule. Most of those models divide the crew scheduling problem into two separate problems, namely the crew pairing and the crew assignment problems. The crew pairing problem that we study here aims at finding the least costly subset of pairings, which cover the scheduled flights. Although there are many approaches to solve the crew pairing problem, most of them assume no disruptions during the operation. However disruptions due to weather conditions, maintenance problems, and so on are common problems leading to higher operational crew cost in practice. These kinds of disruptions result in delaying or canceling some scheduled flights. Another disruption that local airline companies face is adding an extra flight to predetermined (regular) flight schedule. In this study, we propose a model that provides robust crew pairing schedule in the case of adding an extra flight to the regular flight schedule. Two solution approaches are along with the mathematical model are proposed. The objective of the proposed model is to maximize the total number of solutions, while maintaining the increase in the crew cost at an acceptable level. A crew pairing problem is then solved by both the proposed model and the conventional model. Finally, computational experiments are conducted to demonstrate the benefits of the proposed model

Analisis kriteria dan pemilihan basis tempat tinggal pilot dengan menggunakan fuzzy analytic hierarchy proces (studi kasus di PT.X)

Salah satu masalah yang sering dihadapi perusahaan penerbangan adalah penugasan pilot atau penjadwalan pilot. Penjadwalan pilot berhubungan erat dengan penempatan crew base, karena setiap pilot memulai duty period (masa kerja) dari crewbase. Karena hal inilah penempatan crewbase menjadi hal yang penting. Pemilihan penempatan crewbase juga menjadi salah satu permasalahan di PT. X, salah satu perusahaan yang bergerak pada bidang penyedia jasa transportasi udara. Perhitungan secara matematis dapat berperan dalam menentukan pemilihan penempatan crewbase. Untuk menyelesaikan permasalahan ini akan dilakukan analisis mengenai pengaruh masing-masing kriteria dalam penempatan crewbase. Setelah itu akan dilanjutkan dengan pemilihan penempatan crewbase dengan menggunakan metode fuzzy AHP. Metode AHP digunakan untuk pembobotan kriteria dan alternatif. Penggunaan fuzzy berguna untuk merepresentasikan kesamaran penilaian expert yang menjadi input utama dalam metode FAHP. Pada Tugas Akhir ini, terpilih kriteria yang paling berpengaruh adalah kriteria rute yang dapat terlayani tanpa istirahat, dan alternatif yang memiliki bobot tertinggi yaitu CGK (Cengkareng) memiliki bobot 0.2849. =============================================================================================== One of the problems often faced by the airline company is pilot assignment or pilot scheduling. Pilot scheduling is closely related to crewbase selection, because pilot starts their duty period from crewbase. Because of this, crewbase becomes important. Crewbase selection is one of the problem in PT. X, one of the airline company in Indonesia. Mathematical calculations can play a role in determining crewbase selection. To resolve this issue we will do an analysis of the effect of each criterion in the crewbase selection, after that it will proceed with crewbase selection using fuzzy AHP method. AHP method is used for weighting of criteria and alternatives. Fuzzy used to represent the vagueness of expert judgment, which is the main input of FAHP. In this final project, we obtained that the most influential criteria is route could be served without the rest, and alternative which has the highest weight is CGK (Cengkareng)with 0.2849

Minimizing airline passenger delay through integrated flight scheduling and aircraft routing

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering; and, (S.M.)--Massachusetts Institute of Technology. Operations Research Center, 2004.Includes bibliographical references (p. 83-86).Statistics show that airline flight delays and cancellations have increased continuously over the period from 1995 to 2000. During the same period, customer dissatisfaction and complaints have followed a similar, even more dramatic trend. In 2001, as a consequence of the September 1 th terrorist attacks and the resulting airline schedule reductions, delay levels decreased, but only temporarily. With growing passenger demands and stagnant capacity passenger delays and disruptions are again on the rise. Approaches to mitigate schedule disruptions include: 1) re-optimizing the schedule during operations after a disruption occurs. For example, an airline operations controller might decide to cancel or postpone some flight legs or to re-route some aircraft to recover the rest of the schedule; and 2) building robustness into the schedule in the planning stage. By robustness we mean the ability to absorb flight delays so these effects are minimized on passengers and crews. In many cases, trying to reduce delays in the planning stage can be less costly for the airlines, especially if the actions suggested to modify the schedule are not expensive. Pushing back a flight's departure time only ten minutes might cost the airline little but can potentially reduce the number of passenger misconnections given the stochastic nature of airline operations. Canceling a flight during operations for example, can be however very costly. The primary goal of this research is to propose planning models to re-route aircraft and re-time flight departures, either separately or simultaneously, in order to distribute slack time in the network optimally and reduce passenger delays. Using data from a major U.S. airline we observe that with our model, we can reduce flight and passenger delay levels.by Sepehr Sarmadi.S.M

Integrated fleet assignment with cargo routing

Master'sMASTER OF ENGINEERIN