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Revenue Management in Air Transport<br />Cost-based Overbooking Model<br />M. S. Awad<br />Abstract: <br />Three factors lead to the best earning of revenue in aviation, they are; right flight scheduling, optimum fare maxing and proper inventory control. while the main principle of airline revenue management is to sell the right services to the right customer at the right time for the right fare, and that can achieved by developed, the optimum overbooking policy that minimize the cost of two main cost elements, i.e No Show cost and Denied Boarding cost, the problem is solved by implementing U curve technique which define the right overbooking policy, so by analysis the historical data of a specified route, defining the existing overbooking policy that also may reflect a denied boarding cases and the corresponding no-shows distribution, the no-shows data firstly fitted to Poisson distribution to reflects the probability of no show in the analysis. A good overbooking strategy will be the one that minimize the expected of denied boarding and opportunity cost of spoilage. this leading to define clearly Overbooking and No-show curves. <br />Keywords: Revenue, Overbooking, No Show, Denied Boarding, Poisson distribution <br />Introduction: <br />Revenue management (RM) is the process of understanding, anticipating and influencing passenger behavior in order to maximize revenue or profits from a fixed, perishable resource as availability of airline seats. The problem is to sell the available seats to the passengers at the right time for the right fare. This may lead to fare discrimination. Revenue management is a large revenue generator for several major industries, such as airline industry. So revenue management is a set of revenue maximization strategies and tactics meant to improve the profitability of certain businesses. It is complex issue because it involves many aspects of management control, including rate management, revenue streams management, and distribution channel management.<br />Revenue Management was introduced by major US carriers as a reaction on new low-cost carriers started up in the late 1970'S after US airline deregulation. The first reaction has been to match the low prices, but this was not successful because of the much higher cost structure of the big carriers. And one of the first Revenue Management instruments were the ‘super saver fares’ of American Airlines which have been the first capacity controlled discounted fares in the Airline market.<br />The principle of placing booking limits on discounted fares allowed the big carriers to protect their high-yield market segments while simultaneously competing with the new low-cost carriers in the low-yield segment.<br />In the meanwhile Revenue Management has become an industry standard with sophisticated tools in place. The revenue gains from applying Revenue Management have been estimated between 10 and 30 per cent and no Airline will survive without some form of Revenue Management. Other industries like Hotels, car rentals, cruise lines and so forth followed and adopted the Revenue Management principles to their needs.<br />Yield management has significantly altered the travel and aviation industry since its inception in the mid 1980s. It requires analysts with detailed market knowledge and advanced computing systems who implement sophisticated mathematical techniques to analyze market behavior and capture revenue opportunities. It has evolved from the system airlines invented as a response to deregulation. Its effectiveness in generating incremental revenues from an existing operation and customer base has made it particularly attractive to business leaders that prefer to generate return from revenue growth and enhanced capability rather than downsizing and cost cutting. In the airline industry, capacity of aircraft is regarded fixed because changing what aircraft flies a certain service based on the demand is the exception rather than the rule. When the aircraft departs, the unsold seats cannot generate any revenue and thus can be said to have perished. <br />Airline Revenue Management:<br />Fig. No. ( 1 ) Revenue Management TheoryBased on the revenue management theory the cross functional of managing revenue is impact by main factors, <br />Flight Scheduling – <br />Developing a tactical flight scheduling based demand forecasting.<br />Pricing - <br />Defining the working environments, airline should set a price strategy, as competitive pricing, proactive pricing, and reactive pricing. <br />Inventory Control<br />Related the utilize the aircraft capacity by defining the over-booking levels, optimum revenue mix, and authorization levels<br />The product of an airline offers is to a great extent defined by Scheduling, Pricing and capacity. Scheduling defines the routing, the frequency, the departure time, whether it is a non-stop or a connection. Pricing defines the price and the conditions. There are other features of the product like service, seat pitch, lounges and so on which are defined by product management and frequent flyer programs.<br />The quality of the product determines the demand for it. There are other external factors like economy, marketing and sales effort and so forth which also have an influence on the demand.<br />The role of Revenue Management is to match the demand with the capacities given by Scheduling. This is done by determining the availability of the capacity aircraft. In order to optimize the availability, Revenue Management has to know how much money the company will get when this product is sold. For this purpose either the fares from pricing can be used or historical average revenues from revenue accounting.<br />Yield Management (YM) involves the tactical control of an airline's seat inventory for each future flight departure. YM is the airline's last chance to maximize revenue. So setting booking limits on the different fare classes offered on a specific flight departure is a dynamic and tactical way for the airline to maximize total flight revenues, given the aircraft capacity, scheduling and pricing decisions. So to maximize overall revenue the decisions within Scheduling, Pricing and Revenue Management should be harmonized. Accordingly the main function of RM Airlines is to maximize the revenue by protect seats for later-booking, high fare business passengers. And it has two main components:<br />Differential pricing: <br />Fig. No. ( 2 ) Differential PricingIn the O-D market, various fare products are offered at different prices with different characteristics for travel. The economic concept of "willingness to pay" (WTP) is defined by the theoretical price demand curve. The price-demand curve can be interrupted as the maximum price that given number of consumers will all pay for a specified product or service. The use of differential pricing principle by airline is an attempt to make those with higher WTP purchases the less restricted, higher–priced fare product options. The successful use of differential pricing principles depends on the airline's ability to identify different demand groups or segments. So the airline needs to keep a specific number of seats in reserve to cater to the probable demand for high-fare seats (P3). The price of each seat varies inversely with the number of seats reserved, that is, the fewer seats that are reserved for a particular category, the higher the price of each seat. This will continue till the price of seat in the premium class equals that of those in the concession class. Depending on this, a floor price (P2) (lower price) for the next seat to be sold is set. So revenue is a function of price * min {demand, capacity}. as shown in figure ( 2 ). <br /> <br />Yield Management (YM): <br />Yield Management and Revenue Management, carry the same meaning, It is a process determines the number of seats to be made available for each fare class by setting booking limits on low fare seat. So most airlines have implemented revenue management systems, that routinely and systematically calculate the booking limits on each fare / booking class for all the future flight departure. Usually YM systems take a set of differentiated prices/products, schedules and the assigned flight capacities. <br />Fig. No. ( 3 ) Normal Booking CurveAssuming the fixed operating cost associated with a committed flight represent a very high proportion of total operating expense in the short term, the objective of revenue maximization is effectively one of the profit maximization for the airline. When airlines realize that the differential pricing method is not enough to maximize the revenue, they look to YM as effective tool to improve the revenue. And based on the type of the consumers i.e leisure and business travelers the pattern of booking is developed, as shown in the figure no.( 3 ) So both leisure and business passengers typically prefer to travel at the same times and compete for seats on the same flights. Without capacity controls on discount fare seats, it is more likely that leisure traveler will displace business passengers on peak demand flights. This is due to fact that the leisure travelers tend to book before business travelers, a phenomenon made worse by advance purchase requirements on discount fares. Therefore the main objective of YM is to protect seats for later booking, high-fare business passengers. This is done by forecasting the expected future booking demand for higher fare classes and performing mathematical optimization to determine the number of seats that should be protected from ( or not sold to ) lower fare classes. In turn, any seats that are not protected for future high-fare demand are made available to lower fare class bookings. <br />Yield Management System <br />The size and complexity of airline seat inventory control problem require the use by airline of computerized RM systems. So airline RM systems have evolved in both computer database and mathematical modeling capabilities over the past 15-20 years. <br />Based on a classical system, the sequence is exploring in four steps, this system is basically developed on historical data of PNR (Passenger Name Record) <br />Data CollectionReservationOptimizationForecastFlowchart No. ( 1 ) Yield Management System<br />Data Collection:<br />The basic collected data of revenue management are:<br />Revenue Data<br />Historical Booking <br />No-Show Data<br />Actual Booking<br />Forecast: <br />Forecasts are the basis for optimization in Revenue Management systems. The most important things to forecast are demand and no-shows or show-up rates. For management reports a forecast of passengers on board is interesting as well.<br />The forecasts are usually based on historical bookings and availabilities which are stored in a data base.<br />Sophisticated Revenue Management systems allow the users to influence the forecasts at various aggregation levels in order to adjust them to changes that are not reflected in the booking history. There might be fare changes, changes in the market structure because an important competitor leaves the market, special events like Olympic Games and many more.<br />Demand forecaster and No-show forecaster are the main modules of a typical leg or segment based Revenue Management system. The forecasts of demand are based on current bookings of the flight and on historical bookings of comparable flights. The no-show forecasts are based on historical bookings and no-show information which usually comes from a check-in system. Both forecasts are used in the optimization. The no-show forecasts are used to calculate overbooking levels and the demand forecasts are used to calculate booking levels by booking or fare class. The resulting control parameters are passed to the Computer Reservation system in order to control availability and booking requests. There is a lot of variability and uncertainty in the demand forecasts, especially at the very detailed level at which Revenue Management forecasts have to be produced. Reasons are seasonality, fare changes, schedule changes, sell-up and diversion effects, spill and recapture, economical factors and so forth. There are two possible consequences of bad demand forecasts: Empty or spoiled seats due to over-forecasting high fare demand and bad fare mix due to under-forecasting high fare demand.<br />As a rule of thumb, improving the forecast accuracy by 10 percentage points translates to a revenue increase of 1 per cent in average, on high demand flights up to 4 per cent. It has been shown in several simulations that a moderate over-forecasting increases revenue especially on high demand flights, since it forces people to sell-up.<br />There are two possible consequences of bad show-up rate forecasts: Empty or spoiled seats due to over-forecasting show-up rates and over sales or denied boarding due to under-forecasting show-up rates.<br />Optimization: <br />Optimization models are done in two steps<br />Booking limits optimization <br />In fare-mix optimization the booking limits are calculated. A popular and robust heuristics for that step is EMSR (expected marginal seat revenue) published by Peter Belobaba in the late eighties. It needs three different forecast values by booking class: mean demand, demand variability, and expected revenue or fare. This model calculated the recommended booking limits for each booking class on the flight departure in question. <br />Overbooking optimization <br />In this step a demand forecasts are fed into overbooking model which also make use of historical information about passengers no-show rates for the same flight leg and day of week to calculate an optimal overbooking level for the future flight departure.<br />Both the booking class limits and overbooking level are calculated by the mathematical models. <br />Reservation:<br />The reservation procedure is related to the airline pattern, is it legacy or low cost carriers, and with the advanced so feeding by the out comes of the optimization models to define the overbooking level, terms as AU (Authorized Capacity), CAP (Physical Capacity), BKD (conformed booking), and NSR ( No-show rate), are interfere in overbooking issue. <br />Overbooking Problem:<br />Fig. No. ( 4 ) Overbooking ProblemThe goal of Overbooking is to minimize the risk of spilled revenue due to passenger cancellations and no-shows, to accomplish this, airlines routinely overbook flights to balance the need of generating additional revenue while minimizing the risk of over sales<br />Cabin Overbooking<br />Passenger no-show and cancellation creates a large risk of spilled revenue<br />The goal of overbooking is to minimize the risk of spilled revenue due to passenger cancellations and no-shows, proactive analysis and consistent monitoring of flight behavior leads to overbooking success.<br />There are three major performance rates that affect overbooking levels:<br />Show-up Rate measures the number of bookings on hand on day of departure versus the number of passengers that actually boarded the aircraft<br /> Cancellation Rate refer to the decline between the peak-level of advance bookings compared to the bookings on hand one day before departure.<br />Board Rate is a combination of the Show-up Rate and the Cancellation Rate, and is calculated as follows - Show-up Rate * (1 – Cancellation Rate).<br />Overbooking helps to minimize the risk of lost revenue due to passenger no shows<br />However overbooking can result in denied boarding.<br />Cost of denied boarding has to be measured against the revenue benefit gained which can evaluated by Cost-based overbooking model.<br />Cost-based Overbooking Model:<br />The objective of Cost-based overbooking model is to find the optimum overbooking policy that minimize the total combined cost of denied boarding and spoilage ( no-show) cost.<br />Optimum Overbooking Policy = MIN[Cost of DB + Cost of SP ] ……1<br />Where <br />DB : Denied Boarding <br />Fig. No. ( 5 ) Cost-based Overbooking ModelSP : Spoilage<br />A simple overbooking algorithm takes the no-show forecast and overbooks to compensate for those no-shows.<br />A more sophisticated overbooking takes the different costs of no-shows and denied boarding into account as well as the uncertainty of the no-show forecasts. It calculates the expected costs of spoiled seats and denied boarding for each possible overbooking level and selects that one with minimum expected costs.<br />Figure ( 5 ) shows the two cost elements.<br />The risk of spoilage, that is empty seats despite high demand, is the greater, the smaller the overbooking limit is. On the other hand the risk of denied boarding increases with increasing overbooking limit. <br />The sum of both costs has a minimum and the corresponding booking limit minimizes the expected total costs. <br />Case Study - Method:<br />Based on actual data of Yemenia for sector SAH-DXB, of 2006-2008 Historical data, 2009 and 2010 not included in the analysis, due to the financial crisis, and the tragedy accident of Yemenia Aircraft in Moroni So 2011 data forecasted and period of July 2010, is considered for no-show data. the data of no-shows fitted to Poisson distribution, by using minimum least square analysis to estimate and define the correct mean factor of the distribution, then by implementing the cost-based overbooking model, cost of no show and the cost of denied boarding with respect to the overbooking policy, the problem is solved and optimum policy is defined by minimizing these costs.<br />Forecasting Demand Distribution<br />Fig. No. ( 6 ) Forecasting SAH-DXBForecasting is a powerful tool for planning and taking right decision to predict and control seasonality of the traffic pattern of a certain sector we study carefully the historical data of carefully; based on the objective study the right forecasting is selected. In our case a three year data based is selected 2006 -2008 and based on these figure, a theoretical model is developed, actual figures of 2009 and 2010 are not include in the data analysis as in 2009, Yemenia lose one of aircraft in a tragedy accident, and in 2010 the region subjected to financial crisis, and recession. This will affect the final results. <br />So the purpose of forecasting is to assigned the right capacity aircraft to operate, and calculates the corresponding frequencies, to act as the physical capacity in RM system. So we will know the peak traffic time and low season time and we will move accordingly. The forecasting fairness of the used model is R2 equal 74% , and it is a suitable goodness of fit. <br />No-Show Passenger Forecasting:<br />Table ( 1 ) Basic Data CollectionsIt is a complex issue to forecast the number of no-show per flight, as mentioned above, demand forecasting can be forecasted. likely wise No-Show passengers can be forecasted in the same manner, to get No-Show passenger per month, assuming the process is follows Poisson sampling, so by considering a historical data of No-Show of one month, and fitted to a Poisson by minimum least square analysis and ch square test based on the number of sampling. <br />Fig. No.( 7 ) Frequency Distribution of No Showa) Data Collection:<br />Based on actual data, period Oct 2010, for No-Show passengers is collected, then represented by histogram, Figure no. ( 7 ) these no-show data are related to the environmental/ operational pattern, that mean we have to restricted to capacity of aircraft, time of departure, route connectivity and other factors.<br />Fig. No.( 8 ) Fitting Poisson Distribution b) Fitting Data to Poisson distribution:<br />Assume that a tentative selected distribution is Poisson, <br />now the issue is how to select the right parameters for this distribution i.e the value lamda, ( ) the rate of no-show,<br />There are many methods to estimate the value of ( ) one of them is MLS, <br />First we have to solve the problem with initial estimation, that the average value ( ) Average Value = 2.143<br />This lead us to (Sum of Squares Errors) = 0.148<br />While by using Solver concept, Targeting, minimize the errors by changing the value of ( ) <br />Optimum value of ( ) = 3.055<br />With min sum of squares errors of = 0.005<br />This effect can be represented by developing actual cumulative distribution and with a theoretical one that represented Poisson distribution with two cases of lamda () <br />Initial Value (Average) <br />Optimum Value <br />Which is fair enough to hold study, but we have to ensure this a fair decision by implementing Kolmogorov Test<br />Kolmogorov Test:<br />When the population is less than 30 reading, the best test is kolmogorov test, we assume that the sample frequency distribution <br />So the test procedure is as follows<br />Step 1. : <br />Step 2. : Select . the level of significance of the test.<br />Step 3. : Specify the rejection region <br /> <br />Where is obtained from appendix (1)<br />Step 4. : calculate the statistic:<br /> .<br />Step 5. : If reject H0 and conclude that F(f) does not describe the data; otherwise, accept H0 and conclude that F(f) describes the data.<br />In our case we are trying to fit the practical data to Poisson distribution<br />As shown in Table ( 2 ).<br />Table ( 2 ) Kolmogorov Test<br />While there are two possible critical values, based on level of frequencies ( 7 s) and number of no shows are 15 at = 0.05 these values are 0.486 , 0.338 Respectively so we will select the lowest value is the more convenient and fair value to consider. <br />………( 0.486 ) ……...( 0.338 )<br /> ……. <br />……….<br />c) Analysis – Cost-based Overbooking Model: <br />This model is defining the optimum overbooking policy based on the following inputs:<br />No-show Passenger Cost:<br />This is an opportunity lose revenue cost due to the no-show of passenger it is the revenue almost in hand, as empty flown seat never get back. So it can be calculated as the fare of SAH-DXB = 270 USD per no-show passenger. <br />Denied Boarding Cost: <br />This is a critical cost, caused by oversells polices of airlines, and its includes a variety of elements, some of them are not quantifiable in monetary terms:<br />Cash compensation paid to involuntary denied boarding.<br />Free travel vouchers as incentive for involuntary denied boarding.<br />Meals and hotel costs for displaced passengers<br />Space on other airlines to accommodate displaced passengers.<br />Cost of lost passengers goodwill. <br />Based on Yemenia compensation program, it cost =150 USD for SAH-DXB sector. <br />So by developing Overbooking lose table, Table ( 4 ), probability of no-show is calculated based on Poisson distribution and accordingly cost <br />Analysis<br />Table ( 3 ) No-shows - Poisson distributionFirst, we have to represent the data by Poisson distribution, and accordingly to utilize the probability function of Poisson distribution in Overbooking Lose Table.<br />Two cost are evaluated<br />No-Show Cost:<br />The lose of opportunity may calculate as the following <br />Fare SAH-DXB = 270 USD <br />So the expected cost of lose opportunity <br />(0*0.047+1*0.134+2*0.219 ......+7*0.024)*270 = 2.958*270 <br />= 798 USD per flight<br />So No Show Cost = (No. of No-show - No. of Overbooking) * Probability of No show * cost of no show cost per seat<br />Provided that No Show is greater than Overbooking<br />Denied Boarding Cost: <br />Airline Estimate the cost incurred per overbooking procedure per reservation is 150 USD per passenger.<br />So Denied Boarding Cost = (No. of Overbooking - No. of No-show) * Probability of No show * cost of denied boarding per passenger<br />Provided that Overbooking is greater than No Show<br />No-show passengers equal Overbooking reservation : <br />Net resulting cost is zero.<br />Table ( 4 ) Overbooking Lose Table That’s lead us to develop an Overbooking Lose Table. This shows clearly the Zero diagonal values across the table<br />It is developed based on no-show Poisson distribution, no-show cost and denied boarding cost<br />Finally these two costs are superimposed to drive the U curve of overbooking policy. <br />The best policy is lowest cost value in the curve<br />While to define the protection level of overbooking, we have to use <br />Where <br />Cu = the $270 seat contribution that is lost in no-show event)<br />( i.e the number of no-shows is underestimated)<br />Co = the $150 opportunity loss associated with not having seat available for overbooked i.e denied boarding cost ( the number of no-shows is overestimated).<br />d = the number of no-shows based on based experience, and <br />x = the number of overbooked seats. <br />By referring to table no. ( 4 ) at 3 overbooking policy (optimum case) the cumulative probability function is 0.632 which is less than 0.643 the condition is fulfilled. <br />Results:<br />Based on Yemenia No-show data of Oct. 2010 for sector SAH-DXB, and a initial costs of no-shows and denied boarding as inputs, two main curves are plotted, no-show cost curve and denied boarding cost, resulting a U shape curve that define the optimum overbooking policy i.e three overbooking reservation. These ascertain by using critical values i.e at optimum level ( 3 Overbooking) as shown in fig. ( ). The analyss based on monthly data, and should be repeated monthly taking in consideration the seasonality's, shocks and trends<br /> <br />Fig. No. ( 9 ). Optimum Overbooking Policy0228600<br /> <br />Table ( ) Basic Data CollectionsSummary: <br />The study shows the importance of no-show rates, and its sampling / art of fit with Poisson distribution. The historical data is collected and demonstrated by frequency distribution it is analyses by two methods, first by minimum least square analysis using cdf data then fitted by kolmogorov test, supported by defining and critical values i.e at optimum level ( 3 Overbooking), while the ratio of Denied Boarding cost to No-Show cost, play a major rules in shaping the U curve approach, this give a clear picture for top management of airlines to select right policy, and the impacts of these costs in overbooking policy. Finally the mathematical model can extend further to use more relevant model Gama distribution to compare the outcomes results.<br />