A Genetic Simulator For Airline Yield Management - IJERT
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013A Genetic Simulator for Airline Yield ManagementPardeep Kumar MittalAssistant ProfessorDept. of Computer Science& ApplicationsK.U.KurukshetraDr. Rakesh KumarProfessorDept. of Computer Science& ApplicationsK.U.KurukshetraAbstract1. IntroductionYield management is the concept of identifying variousstrategies for optimizing yield (revenue) in variouscapacity-constrained services. The core concept of yieldmanagement is to provide the right service to the rightcustomer at the right time for the right price.A popular definition of yield management is given byNetessine as “Yield management is the process ofunderstanding, anticipating and reacting to consumerbehaviour in order to maximize revenue or profits.”[1]The big question is when yield management should beapplied. Are there any conditions under which it can beapplied? The answer lies in the following three basicconditions: There is a fixed amount of resources available for sale. The resources sold are perishable. Different customers are willing to pay a different pricefor using the same amount of resources.Yield management can be applied in a number ofindustries, although it is more popular in airlines industryand hotel industry.Although there are no specific guidelines for a yieldmanagement process, it may contain data collection,IJERTV2IS90734segmentation, forecasting, optimization, and dynamic reevaluationIn mathematics, computer science, or management science,optimization is the selection of a best element (with regardto some criteria) from some set of available alternatives. Inthe simplest case, an optimization problem consists ofmaximizing orminimizing a real function bysystematically choosing input values from within anallowed set and computing the value of the function.Generally, optimization includes finding "best available"values of some objective function given a defined domain,including a variety of different types of objective functionsand different types of domains.To solve various optimization problems, one may usealgorithms that terminate in a finite number of steps, oriterative methods that converge to a solution (on somespecified class of problems), or heuristics that may provideapproximate solutions to some problems.IJERTAirline yield management now-a-days has become a veryimportant research area. As more and more companies arecoming in the field of airlines, it has become very difficultto sustain for a company without incorporating yieldmanagement. Therefore most of the companies are tryingto incorporate the yield management in their system. Thebasic purpose of the yield management is to maximizerevenue within the specified constraints. This paper is anattempt to design a basic decision-support tool for airlineyield management using genetic algorithm. The geneticsimulator has been designed using Matlab.Dr. P.K.SuriDean (R&D)Chairman & Professor(CSE/IT/MCA)H.C.T.M., Kaithal1. Literature ReviewFrom a historical perspective, the interest in Yield(Revenue) Management practices started with thepioneering research of Rothstein [2] and Littlewood [3] onairline yield management. However, it was probably afterthe work of Belobaba ([4], [5] and [6]) and the AmericanAirlines success [7] that the field really took off. Theairline industry provided researchers with a concreteexample of the tremendous impact that RevenueManagement tools can have on the operations of acompany (e.g. [7]). At this stage, however, much of thework was done on capacity management and overbookingwith little discussion of dynamic pricing policies. Inessence, prices (fares) in these original models wereassumed to be fixed and managers were in charge ofopening and closing different fare classes as demandevolved. During the 90’s, the increasing interest inRevenue Management become evident in the differentapplications that were considered. Models became industrywww.ijert.org2379
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013used as a technique to solve this problem. The decisionsupport tool considers the effect of time-dependentdemand, ticket cancellations and overbooking policies.2. Problem Definition and FormulationIn this problem an assumption regarding a flight operatingbetween a specified origin and destination has been made.The reservation for the flight starts form the first date ofexpected reservation up to the date of departure. The periodof reservation may be divided in a single or more than onetime slices. Another assumption is to fix the fare of eachclass during each time slice and also assumed as known.Following notations has been assumed for this problem:Ct Total capacity of a flightNα, β Number of customers belonging to class β duringtime slice α.Fβ Fare for class β.Uα, β Upper limit of demand for class β during time sliceα.Lα, β Upper limit of demand for class β during time sliceα.For finding the objective function, the purpose of whichobviously is to maximize the revenue, one have to assumesome constraints, which can be:First assumption is that there will be no cancellations andno-shows. The total number of passenger travelling shouldbe less than or equal to the capacity of the flight.The number of customers travelling in each class should begreater than or equal to lower bound and less than or equalto the upper bound.On the basis of above assumptions, the objective functioncan be written as:Max. Σβ Σα Nα, β Fβ . (1)Subject to the constraintsΣβ Σα Nα, β Ct & Lα, β Nα, β Uα, β for all α and β,Nα, β 0, which indicates that number of customers ineach time slice can be positive onlyIJERTspecific (e.g. airlines, hotels, or retail stores) with a higherdegree of complexity (e.g. multi-class and multiperiodstochastic formulations). Furthermore, it was in the lastdecade that pricing policies really became an activecomponent of the Revenue Management literature (e.g.[8],[9], [10] and [11]).Several authors report “success stories” on how effectiveRevenue Management has been done in practice ([12] and[13]). An example of successful Revenue Managementsystem can be found in British Airways. Among thereported in 1992 reasons of company success were costcutting and sophisticated Yield Management. The companyattributed its success to being “a low-cost and high-revenuecarrier” [12]. The next successful Revenue Managementimplementation example can be found within the AustrianAirlines company that has been one of the mostconsistently profitable airlines in Europe in the pastdecades. During the Gulf War that has caused profits of themost airlines to decline, the Austrian Airlines hasexperienced its “twenty-first consecutive year of profits”[13]. This has proven the company capability to performeffectively during extremely cyclical periods. The companyowes its success to smart investment choice into a RevenueManagement and decision-support computer system. Thissystem has helped to monitor all historical data on thecompany flights as well as has made it possible to performflights forecasts up to a one year period with highprecision. Moreover, the new Revenue Managementsystem has allowed the company management to look forfuture business opportunities by supplying it with decisionmaking tools to forecast future flights demand. In addition,the implementation of this system has enabled the companyto keep her prices at stable level while other companieswere trying to survive by lowering their flight prices [13].Bitran and Caldentay in their paper examined the researchand results of dynamic pricing policies and their relation toRevenue Management[14]. The survey is based on ageneric Revenue Management problem in which aperishable and non-renewable set of resources satisfystochastic price-sensitive demand processes over a finiteperiod of time.Genetic algorithm in yield managementIn a system proposed by Aloysius George et.al. , in order tomaximize the revenue of airline, an optimized flightbooking and transportation terminal open/close decisionsystem has been presented using Genetic Algorithm[15]. Inthis system, the particular booking terminal’s historicalbooking data is observed. Consequently, its frequency isgenerated with linguistic variable and deviation of bookingis interpreted. Using the observed data and geneticalgorithm, the terminal open/close decision system isoptimized.In an article presented by Srinivas and Shashi [16], thefocus is on developing a decision-support tool to estimatethe number of seats to each fare class. Genetic algorithm isIJERTV2IS907343. Implementation using Genetic AlgorithmThe formulation specified in above section is basically aLinear Programming Problem with the variables beingassumed as integers. Therefore the problem actuallybecomes an integer programming problem. This problemcan easily be solved using any standard method to solveLPP. But the traditional LPP methods becomes complexwhen there is a presence of discrete integer variables. Alsothere is large amount of input information is required suchas constraints, therefore necessitating complex modellingand simulation. Therefore instead of using the basictechniques, an attempt has been made to solve the problemusing genetic algorithm.The basic advantage of using GA lies in the fact that itstarts searching for optimal solution from multiple points,while most of the other methods start from a single point insearch space. Thus there is less chance of sticking at localmaxima when GA is being used. Further, if someonewww.ijert.org2380
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013Initial PopulationOnce the representation is fixed, the first issue indeveloping the algorithm is that of the initial population.This is typically performed by randomly generatingindividuals so that the population can cover wider areas ofthe search space. Nonetheless, there are other morespecialized methods. A very common approach is togenerate the individuals in a greedy manner, which meansthat every individual is constructed in a way such that atevery time, the next gene is given the value that optimizesthe evaluation function for that individual. Occasionally,the solutions may be somehow seeded in areas wheresolutions are likely to be found. In proposed simulator thebasic method of randomly generating individuals has beenused.GA parameters such as total number of generations, crossover probability, mutation probability, population size,total number of iterations are fed as input in this step. Hereassumption is that the typical range for population is 50500. The random numbers are generated assumingpopulation is normally distributed.Parent SelectionSelection is the method through which certain elements inthe population are chosen to be combined. This selectionmechanism tries, in general, to choose parents that arelikely to produce a high-quality descendant. Typically, twoindividuals are chosen to reproduce and yield descendants.Different kinds of selection mechanism are RouletteWheel, Ranking, Tournament, Multiparent, etc. Inproposed simulator, researchers have used two selectionmechanisms: (i) Roulette-Wheel and (ii) Tournamentselection and are explained below:Roulette-Wheel Selection: In this method, a certainprobability is to be chosen for every individual in thepopulation. This probability depends directly on theabsolute fitness of the individual [18]. The main drawbackof this mechanism is that the best candidates are very likelyto take over the whole population very quickly which mayresult in the loss of diversity sometimes. Diversity is one ofthe main causes for the genetic algorithm being used sowidely. To maintain diversity a combination of roulettewheel selection with some other selection mechanism canbe used.Tournament Selection: This is one of the simplestmechanisms, and also the least time-consuming. It consistsof choosing k individuals completely at random, and thenselecting the two individuals with highest fitness function.Obviously, the complexity of this method depends on thevalue of k. The probability for tournament selection isfixed as 0.75 in proposed simulator.ReproductionFor the purpose of reproduction, the parents(individuals)are combined in such a way that a high quality individual(descendant) will be obtained. This mechanism is alsoknown as crossover. In some GAs, this operator is able togenerate more than one descendant (usually two), but oneIJERTwishes to modify the model for the whole airlines, it can beeasily implemented using GA. Additionally GA does notrequire gradient and derivative information and thus can beused to solve even complex real world problems withdiscontinuous functions. [17].For solving the above formulated problem, a geneticsimulator has been implemented using Matlab and isexplained below:RepresentationTo solve any problem using Genetic Algorithm, the veryfirst issue is the selection of encoding scheme to representthe chromosomes. There are a number of encodingschemes available in literature such as binary, octal,hexadecimal, permutation and tree etc. Encoding schemeselected will further dictate what will be the crossover andmutation operators. There are two basic principles to selectan encoding scheme: (i) Principle of minimal alphabet and(ii) Principle of meaningful building blocks [17]. It hasbeen observed that in the said problem, binary encodingscheme is the base option that also satisfies both criteria.While this technique is very commonly used, in presentcase the first thing is to decide the length of the binarystring. The number of genes in the binary string in presentcase is based on number of classes and number of timeslices that are considered in an airplane. The number ofgenes will be evaluated asNumberofgenes numberoftimeslices * numberofclasses *numberofbits . (2)For example, if it is assumed that number of time slices are1, number of classes are 4 and number of bits are 8, thenthe number of genes will be 32 and these genes will berepresented with a binary sequence generated randomly.Evaluation FunctionClosely related to the representation, the issue of theevaluation function arises. This function associates a valueto every individual in the population, and corresponds tothe quality of that individual. Thus, differentrepresentations of the same problem may have differentevaluation functions, since this is typically calculated fromthe values of the genes of each individual and through thegenotype-to-phenotype mapping. The evaluation functionis often referred to as fitness function in the EvolutionaryComputation field. In proposed simulator, an evaluationfunction in Matlab has been designed to evaluate thechromosomes. The fitness value of each string(Chromosomes) is calculated by decoding the binarystrings which represents the information about the numberof passengers belonging to each fare class. However, thefitness value is bounded by the expected demand range foreach fare class. The final parameter value λ for the numberof customers belonging to a particular class can beevaluated as:λ Lb ((Ub – Lb) *d)/(2l – 1),where d is the decoded value and l is the length of thechromosome.IJERTV2IS90734www.ijert.org2381
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013the next generation. A technique associated with thisoperator (independent of the mechanism type) is to alwaysmaintain the highest quality individual in the population.This technique is usually referred to as elitism.TerminationThe termination condition indicates when it is time for thealgorithm to stop. At this point, the algorithm will usuallyreturn the best individual according to its fitness function.One can distinguish two kinds of termination condition:Objective reached: when a GA is implemented to reach acertain goal (i.e., a solution of a certain quality), reachingthat goal should be the indication for the algorithm to stop.External conditions: However, the previous case is veryrarely achieved, due to the stochastic nature of thesealgorithms. Therefore, different criteria must be used.Different conditions include fixed number of generationsreached, maximum time allowed reached, fitnessimprovement does not occur for a certain period oftime/generations, manual inspection, a combination of theabove. In proposed simulator, researchers have maintaineda fixed number of ightYield Init pop Randomly Generated population.//Initialize Population with size n curr pop Init pop. While ( !stop criterion)// Condition to stop with maximumiteration being fixed as max Evaluate Fitness of curr pop. Create mating pool according to Roulette-wheelSelection OR Tournament Selection.// Selection Apply Crossover like One-point, Two-point &Uniform Crossovers on mating pool withprobability 0.80. Apply Mutation on mating pool with probability0.03.// Mutation Replace generation with (λ μ)-update ascurr pop.// Replacement End While EndIJERTwill assume from now on that only one descendant is goingto be generated. Thus, different crossover operators are onepoint, multiple point, uniform, arithmetic, etc. In presentcase, one point, two point and uniform crossover has beenused, and are explained as follows:One point crossover: This is the most popular method. Itconsists of choosing a point randomly, and copying thegenes of a parent, from the beginning until this point, to thedescendant, and the genes of the other parent from thatpoint till the end.As an example, imagine two parents of the form:First ( 0 1 0 0 1 1 1 1 0 ), Second ( 0 0 0 1 1 0 1 0 0 )and k 5 is the crossover point, the descendant wouldeither be( 0 1 0 0 1 / 0 1 0 0 ) or ( 0 0 0 1 1 / 1 1 1 0 )Two point crossover: It is similar to the previous crossover,and the only difference is that instead of 1 point, two pointsare chosen randomly. Then, to generate a descendant itwould copy the genes of each parent in turns after eachcrossover point.Uniform crossover: It is slightly different than the previousone. It treats each gene independently and decides fromwhich parent it is going to be inherited (typically with thesame probability).MutationThis operator is the source of great diversity. It is based inthe biological fact that some genes can mutate for differentreasons, and thus, the descendant can acquire genes that arefrom neither of its parents. The most common ones arerandom bit modification, swap mutation, insert mutation,scramble mutation, etc. In this particular case, the randombit modification has been used which is explained below:Random bit modification: Consists on changing the valueof some bits with a given probability. The operator changesthe value of every bit in the sequence with a certainprobability. If the representation is binary as in our case,the effect is that of flipping a bit, either from 0 to 1 or from1 to 0.Selection of the New GenerationThis is the mechanism that replaces the last population by anew one. In order to do so, some algorithms completelyreplace the previous population for the new set ofdescendants or offspring. However, this is usually not avery effective technique, and GAs normally implementsmechanism to generate the new population from both, theprevious one and the offspring. Some of these mechanismsare fitness based, generation based, replace worst, etc.Derived forms of generational update are used like (λ μ)-update and (λ, μ)-update. This time from a parentpopulation of size μ, a little of children is produced of sizeλ μ. Then the μ best individuals from either the offspringpopulation or the combined parent and offspringpopulations (for (λ, μ)- and (λ μ)-update respectively),form the next generation[19]. In proposed simulator thefitness based replacement has been used i.e. selectionfocuses on keeping the individuals with higher fitness forIJERTV2IS907344. ResultsGenetic algorithm is used as a solution technique for thesingle-leg airlines problem using various combinations ofdifferent operators.In this case, a single flight is considered to operate betweengiven origin and destination. The capacity of the flight isassumed to be 100. The following GA parameters are takeninto considerations:Population size 75Maximum number of iterations 50www.ijert.org2382
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013Cross-over probability 0.80Mutation probability 0.03Tournament Selection parameter 0.75Number of simulations 30Using the above parameters and various combinations onecan get the tables 1 and 2, which are shown at the end ofthe paper.Results obtained for each combination of operators areshown below: Using combination of Roulette Wheel selection andthe three types of cross-overs i.e. one-point, two-pointand uniform, the following results were obtained:Fig.4 : Lower Bound, Upper Bound, and Estimated FitnessFig.5: Average FitnessIJERTFig.1 : Lower Bound, Upper Bound, and EstimatedFitnessFig 6: Maximum FitnessFig.2: Average Fitness Using combination of Roulette Wheel andTournament selection along with one-point crossover,following results have been obtained:Fig 3: Maximum Fitness Using combination of Tournament selection and thethree types of cross-overs i.e. one-point, two-pointand uniform, following results have been observed:IJERTV2IS90734www.ijert.orgFig.7 : Lower Bound, Upper Bound, and EstimatedFitness2383
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013Fig.8 : Maximum and Average Fitness Fig.11 : Lower Bound, Upper Bound, and EstimatedFitnessUsing combination of Roulette Wheel andTournament selection along with two-point crossover,following results have been observed:IJERTFig.12 : Maximum and Average FitnessFig.9 : Lower Bound, Upper Bound, and EstimatedFitnessFig.10 : Maximum and Average Fitness Using combination of Roulette Wheel andTournament selection along with uniform crossover,following results have been observed:IJERTV2IS907345. InterpretationUpon comparing the above results with [16], it has beenobserved that the solution found using GA is optimal andthe results obtained are at par with [16]. Looking at thetables and graphs obtained by different combinations ofvarious selection and cross-over methods the followingfindings has also been observed:1.The best estimation is obtained in most of thecases when tournament selection is used irrespective of thecross-over operators, while when roulette wheel selectionis used the best estimation is generally obtained in case ofone-point cross-over.2.There are three different combinations which canbe considered as better combinations as compared toothers. These are tournament selection along with uniformcross-over or one-point cross-over and roulette wheelselection with one-point cross-over.3.The combinations which should be discardedcompletely are roulette wheel selection and two-pointcross-over, roulette wheel selection and uniform cross-overas the results produced by these combinations are notfound to be very useful.4.Looking at various graphs for the average fitnessof the population, it is clearly visible that one-point crossover always yields not a very good average fitness, whilewhen two-point or uniform cross-over is used the averagefitness is quite good and almost same in each case.www.ijert.org2384
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013[6]6. ConclusionIn this paper, an attempt has been made to solve theproblem of yield management using Genetic Algorithm,GA has been used in the said experiment with a number ofvariants in selection and crossover. It is inferred that GAcan be successfully used in the problem of yieldmanagement. Yield management is a problem ofoptimization and GA has been used in past in a number ofother problems of optimization. GA being an evolutionaryalgorithm is a good option for such type of problems wherethe result should evolve with passage of time. Theparticular case study which has been picked is airlines yieldmanagement. The various combinations of differentoperators were tried in an attempt to find the best possiblecombination for maximizing the profit for airlines. Thecombinations which proved to be best were tournamentselection along with either uniform cross-over or one-pointcross-over. However, if one takes into account theimprovement in the total population, then the one-pointcross-over fails. In that case the only combination found tobe very good is tournament selection along with 15]Future ScopeIJERTIn this paper a basic case of yield management in airlineshas been taken into consideration with only a singledecision period. The results obtained although can prove tobe useful for airlines industry; still there are a number ofthings that can be considered for practical implementation.Some of them can be consideration of more than onedecision period, overbooking and cancellation, arrivalpattern of customers, etc. The concept of genetic algorithmcan also be applied to other industry such as hotel industry,sea-cargo industry, essine, S. and R. Shumsky (2002), Introduction tothe Theory and Practice of YieldManagement,INFORMS Transactions on Education, Vol. 3, No. 1Rothstein, M. 1971. An Airline Overbooking Model.Trans. Sci. 5, 180-192.Littlewood, K. 1972. Forecasting and Control ofPassenger Bookings. AGIFORS 12th AnnualSymposium Proceedings, 95-128, Nathanya, IsraelBelobaba, P. (1987). Air Travel Demand and AirlineSeat Inventory Management. Ph.D. Dissertation, MIT.Belobaba,P. 1989. Application of a ProbabilisticDecision Model to Airline Seat Inventory Control. Ops.Res. 37, 183-197.IJERTV2IS90734www.ijert.orgBelobaba, P. (1987), Airline Yield Management: AnOverview of Seat Inventory Control, TransportationScience, 21, 63-73.Smith, B., J. Leimkuhler, R. Darrow, J. Samuels. 1992.Yield Management at American Airlines. Interfaces, 22,8-31.Gallego, G., G. van Ryzin G. 1994. Optimal DynamicPricing of inventories with Stochastic Demand overFinite Horizons. Mgmnt. Sci. 40, 999-1020.Bitran, G., S. Monschein. 1997. Periodic Pricing ofSeasonal Product in Retailing. Mgmnt. Sci. 43, 427443.Feng, Y., G. Gallego. 1995. Optimal Starting Times forEnd-of-Season Sales and Optimal Stopping Times forPromotional Fares. Mgmnt. Sci. 41, 1371-1391.Feng, Y., G. Gallego. 2000. Perishable Asset RevenueManagement with Markovian Time Dependent DemandIntensities. Mgmnt. Sci. 46, 941956.Unternehmen und Markte (1992) Unternehmen undMarkte in Handelsblatt, 12 April 1992, p. 13.Robert G Cross, Revenue Management: Hard-CoreTactics for Market Domination ,1997, BroadwayBooks, New YorkGabriel Bitran and Rene Caldentey, An Overview ofPricing Models for Revenue Management, December,2002Aloysius George, B.R.Rajakumar, D. Binu, GeneticAlgorithm Based Airlines Booking Terminal Open/Close Decision System, ICACCI’12, August 3-5, 2012,Chennai, T Nadu, India.Srinivas S. Pulugurtha & Shashi S. Nambisan, ADecision-Support Tool for Airline Yield ManagementUsing Genetic Algorithm, Computer Aided Civil andInfrastructure Engineering, 2003, 214-233.Goldberg, D.E.(1989), Genetic Algorithms in SearchOptimization and Machine Learning, Addison-Wesley,New York.J.H. Holland, Adaption in Natural and ArtificialSystems, MIT Press, 1975.S.N.Sivanandam, S.N.Deepa, Introduction to GeneticAlgorithm, Springer-Verlag Berlin Heidelberg 20082385
International Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 2 Issue 9, September - 2013TABLE1: LOWER, UPPER AND BEST ESTIMATED DEMANDS IN EACH ASSUMED FARE CLASSDemandFare Class1234Fare100250500800Lower Limit030132Upper Limit6345205Best Estimation3045205TABLE 2: NUMBER OF ITERATIONS FOR THE BEST ESTIMATES IN VARIOUS COMBINATIONS OFSELECTION AND CROSS-OVER rationsAvg. of all simulation except when max isnot achieved192732192317No. of simulation whenmax. is not achieved inspecified iterations92524662IJERTRoulette WheelRoulette WheelRoulette WheelTournamentTournamentTournamentMin. in all simulationsIJERTV2IS90734www.ijert.org2386
Airline yield management now-a-days has become a very important research area. As more and more companies are coming in the field of airlines, it has become very difficult to sustain for a company without incorporating yield management. Therefore most of the companies are trying to incorporate the yield management in their system. The
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