Nonlinear Optimization in Airlines - Literature review Example

Nonlinear Optimization in Airlines

Introduction

Airlines are among the companies that measure their products by their accuracy, quality, functionality, timeliness and price. For their customers, these factors are translated to safety, flexibility of flights, service satisfaction, efficient ticket purchase and reasonable prices. To provide the best quality of services and service, airlines depend on optimization based support systems to make their decisions (Gabrel, et al. 2013). These optimization systems provide profitable and tight schedules, set plans, cost-effective fare classes, crew pairings, gate assignments, aircraft routes, maintenance schedules, training programs, food service plans and baggage handling procedures.

The airline business is a field that that provide the basis of interplay for the use of optimization theories and practice that will lead to results. The nature of the airline business and transactions provides the nest Avenue where optimization practices and procedures can be effected. Some factors such as strict and severe competitions between airlines, large-scale operations, and resources that are tightly coupled such as aircraft, airports and maintenance facilities, provide the background for efficient optimization theories in whichever field in the airlines (Yang, et al. 2016). Also, the dynamic environment that is characterized by the dynamic customer behavior encourages the use of principles that will project how to handle the customers regarding pricing their services and other operations that will affect the customers directly. Airlines have complex operational plans that cannot be planned abruptly without analyzing them through optimization producers by using the optimization systems that will provide the real-time nature of the business and help in crucial decision making.

In the last several decades’ airlines have been unprecedentedly impacted by optimization due to the evolvement and improvement of technology which has led to designing of complex systems that have computing technology and optimization of methodologies. Competition and high demand from customers have also changed the way airlines incorporate nonlinear optimization in their business operations.

This paper shall look at the several areas in the airline industry that nonlinear optimization procedures are being applied to make the business more efficient and reliable. Such areas include flight planning, crew scheduling, traffic control, yield management and Network design.

Network designs

Network designs use the nonlinear optimization theories to come up with optimal routes in the network structure that will ferry particularly targeted passengers with the least transportation cost as possible. The routing system that is used to map out such network routes has been found to have an impact on airfares, yield management and services offered. The network design is the crucial element that affects the operations of the airlines as well as its market share. The right optimization theories have to be put in place to ensure that the best network design is chosen for the airline.

The hub-spoke network system

It is a system being implemented by many airlines. Airlines have marked centrally located airports as their hubs such that they can transport passengers between these hubs and their points of destination (Lernbeiss, 2016). A plane arrives at a hub as an intermediate link where passengers change planes to continue with their flight to their destinations. This was a strategy developed to link passengers whose numbers do not qualify for a direct flight to their destinations. For instance in America. The airline hub system is located at Dallas/Fort Worth, where passengers can disembark and board over thirty more airlines. Such centralization makes traveling easier and costs effective for the airlines. It has been attributed to the use of nonlinear optimization procedures. Airlines are now using this method which was derived from the use of the following optimization formulae which is efficient and reliable (Lernbeiss, 2016). With the primary objective of cutting down on transport costs, they come up with this theory to minimize on hub locations.

Yield management

Due to the unusual use of nonlinear methods to formulate strategies, competition has increased tremendously, and now airlines have to put more effort in yield management. Yield management is also known as revenue management. With the intense competition globally, returns management has to be put in consideration. Optimization of yield management is a priority to many airlines. They do so by having a variety of fairs and flights that charge a lot differently from other flights so that it can accommodate all types of travelers. They offer deeply discounted fares which are attractive to customers. However, to be able to achieve such milestones and make decisions on discounting fairs, it is paramount that the airline uses non-linear optimization methods to improve their accuracy and make wise decisions. Discounting the fares means that it will attract a huge customer pool who will occupy seats which would have been sold for higher prices. Such complications in decision making and the implications of increasing and reducing the fair prices are well sort and solved by non-liner methods.

The problem that most researchers face is the seat allocation, a mechanism to optimize on revenue on every passenger plane. Using the hub and spoke operations a plane can carry passengers of different destinations on every set and when they alight on a central hub, they all embark on different planes. The plane has optimized its seat capacity instead of carrying a single destination with a fixed price. Also, the desirability of the airline, as well as its comfort levels, will also bring about the various variations in prices (Pardlo’s, et al., 2012). Models have to be developed that optimize the seating capacity of all destinations to maximize revenue and cut down on costs. Belobaba came up with a linear optimization model which comes up with a seat allocation algorithm for two fare classes where the demand for each seat by a passenger is taken to be an independent random variable (Azadeh, et al. 2013). Fi is revenue generated per passenger on a plane in class i and bi(si) Is the number of passengers expected in flight. The cabin capacity id represented by

C = S1 + S2 that maximizes the total revenue of the plane. Hence the overall solution for the expected revenue

R = R1 (S1) + R2(C S1) = f1b1(S1) + f2b2 (C S1)

Which solves the equation

@R=@S1 = @R=@S2:

Thus the optimal allocation of S1; S2 satisfying

f1P1(S1) = f2P2(S2);

Where Pi(x) is the profitability index, X represents the seats. In this non-linear optimization method, seats are allocated between the fair classes so that the expected total revenue increases. The Pi(Si) is from the historical records of the airlines. Little Wood suggested that passengers paying f2 should be accepted into the airlines as long as

f2 P1(S1) f1;

where P1(S1) is represented by the profitability of selling the remaining seats, S1.

Flight management

In the airline process management, flight planning is very critical. Whenever a flight is allocated, a major proportion of both costs and revenues are fixed. The airline has to make sure that within the fixed schedule, to optimize all the opportunities that are available (Li, et al. 2014). So optimization of flight schedules via nonlinear optimization is essential to the company. In most airlines, a flight schedule Is made many months before it is executed giving it more time for the various departments involved to scrutinize it and make necessary changes. In the process of review, the flight economics and the drafts feasibility are evacuated and then sent back to the planning department for them to make the final copy. Nonlinear optimization comes in when the draft is being evaluated (Cedars. Et al. 2016). Optimization theories and formulas have to be put in place so that all the schedules and other activities pertaining the flight is put in place in the order of sequence. Before the timetable reaches its final state, it has to go through such iterative procedures and evaluations since in flight planning there is no room for mistakes. The demand revenues and the destination of each flight are put into consideration when planning a flight plan. Features such as distances, routes, fuels and speed are put into consideration. These are the factors or elements that are used I the calculation of nonlinear optimization formulae’s which gives the planning team the right information for planning. To capture all the elements of an airline's operations in the flight plan is a complicated task which requires optimal planning and use of nonlinear methods to facilitate the amplifying of elements like operation costs, route characteristic and passenger demand (Lernbeiss, 2016). In a most airline, the methods used first consider the frequency of each route, determine its departure time based on the demand and variability of variables affecting it.

Krcmar-Nozick proposed a multi-criteria model that incorporates major models in determining an efficient flight schedule in a tight, competitive environment (Balakrishnan, 2016). The model aims to maximize the profits P's of the company by subtracting the cost of each route from the revenues. The cost of the flights is directly proportional to the frequency of each flight. Passengers p captured by an airline on the route (Jamil, et al. 2013). The other element captured by the formulae is the level of the passenger’s satisfaction. They have to consider the desired passenger departure time and the airlines departure time. The model takes assumptions of the departure times by considering the delay of each flight due to discrepancies of passengers desired needs. Recently, an algorithm designed by Talluri uses assignment swaps to improve on daily fleet management. It finds swap opportunities that satisfy the requirement of aircraft count and flow balance. It employs the methodology of using a small number of calls to identify the swiftest algorithm which exists and is efficient to the airline. Delta Airlines were the first airline to use the algorithm, and it has been a great success (Azadeh, et al. 2013). The flight planning schedules have become more accurate and reliable. It translates to a flow of customer and time saving which in turn brings in more revenues. Nonlinear algorithms and formulas are a great success and have contributed immensely to the accuracy of light planning and management.

Crew scheduling

In most airlines across the globe, crew management takes the biggest chunk of expenses after fuel expenses. The number of flights for the biggest airlines in America is in thousands hence saving time by the airline crew could result in saving millions which can be channeled into other sectors of the airlines. It has made researchers and academia to put more efforts in researching this area. Every time, algorithms are being developed to help the airlines in reducing the cost of crew, management. Nonlinear optimization models have been in use ad mathematicians are doing their best to improve on the models based on the current challenges that the airlines are facing (Aktürk, et al. 2014). Improvement of the formulae’s and change in the structure of algorithms will depend on the nature of flight, distance and destination, Also, the number of crew member’s is determined, and they are all incorporated into the algorithm.

Airlines now designing the crew assignments immediately after the current crew assignment is out and running. It starts immediately because it I a complex process that has to consider many factors surrounding a flight (Balakrishnan, 2016). When ploughing pilots and flight attendants to flights, they must conform to the rules that have been set by the airline administrators like the union contracts. There is a maximum amount of work that can be assigned to a crew depending on the flight. Besides, each of the crews has their base where they have to rest before embarking on the next flight. When they are resting, the plane cannot take off with its crew hence another crew is assigned the job according to the schedules. The planning has to ensure that each flight has been served accordingly. Scheduling all flights in an airline and ensuring that at any given time the flight has a crew attendant who will have several flights and later goes to their base for rest is managed by the nonlinear algorithms and systems that have been put in place. When crew pairing, the management has to look at the costs involved such as hotels costs and per Diem. The principal pay for the attendants is the guaranteed hours of flight minus the actual hours that have been flown. The algorithms that are used in crew management have been integrating into to the nonlinear systems where data is fed and the system systematically generates the desired data according to the variables and details fed to it.

Many attempts are being and to solve the crew management challenges especially the set positioning and set covering items. The theoretical works that have been used over time are effective but only works for the limited size of data hence making them insufficient. For an optimal solution, these methods could not be used because they could not be applied in real world situations (Li, et al. 2014). However, the methods being used provided useful insights in designing a solution to the problems. The kind of problems that airlines face are thousands of flights and billions of crew pairings. Before the optimization process, the columns are generated to provide the actual data. The optimization methods and procedures used have to pair the billions of pairs available each flight and ensure that the timetable is reliable.

Air traffic flows control

Airlines face the problem of flight delays which increase the costs of operation. It also affects other downstream flights hence inconveniencing passengers. Such problems can occur when flight delays and when its ready to take off another flight plane is landing If the flights are not managed appropriately, it can lead to collusion in midair. A reduction in flight capacity by any airport will affect thousands of flights (Gandomi, 2013). However, such cases caused by weather changes is beyond human control. Delays are categories into two, the less costly ground delays that are beyond the set take off and the airborne delay that is beyond the fixed landing time. .When these scenarios happen, the data is immediately captured by the optimization systems which is analyzed and fed into the systems; it is this data that flight managers use to manage the planes in flight and those on the ground. A delayed landing of an aircraft can course millions of dollars in forms fuel and expense. The nonlinear algorithm is used to solve such problems because standard formulas cannot (Azadeh, et al. 2013). The evolvement of the algorithms has helped in the flight management because they can be able to formulate how the flights will take off and land. Something that distinct systems cannot., The flight management system is complicated for a lot of data and other events that affect it are used to generate the accuracy of the landing and takeoff times for each flight.