Air Cargo Revenue Management

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(1)Air Cargo Revenue Management introducing Unified Density 0|1 Scaled Density o|∞.

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(3) Air Cargo Revenue Management Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Tilburg, op gezag van de rector magnificus, Prof. dr. F.A. van der Duyn Schouten, in het openbaar te verdedigen ten overstaan van een door het college voor promoties aangewezen commissie in de aula van de Universiteit op vrijdag 24 november 2006 om 10:15 uur door Johannes Blomeyer geboren op 3 mei 1961 te Frankfurt/Main, Duitsland..

(4) Promotores: Professor Dr. ir. Hein Fleuren Professor Dr. Jan Bisschop. Printed in Germany. First edition. Proofreading: Giles Stacey (Englishworks) © 2006 Johannes Blomeyer. All rights reserved. No part of this book may be reproduced without the written permission of the author. Unauthorised duplication is a violation of applicable laws. While every precaution has been taken in the preparation of this book, the author assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. In no event shall the author be liable for any loss of profit or any other commercial damage, including but not limited to special, incidental, consequential, or other damages..

(5) Air Cargo Revenue Management Johannes Blomeyer.

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(7) Dedication To the country and the people I love most—Colombia..

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(9) Acknowledgements I would like to thank Professor Dr. Hein Fleuren, who supported me from day one and has not stopped since. Many thanks, too, to Professor Dr. Jan Bisschop without whom there would not have even been a day one—and to Ms. Selvy Suwanto from Paragon Decision Technology B.V. for programming several versions of the Segment Optimiser in the mathematical programming language AIMMS. On a more personal level, I would also like to thank my colleagues at Lufthansa. Preface Goethe in his ‘Farbenlehre’ associated blue with infinity and saw it as the color of transcendence. Jung associated blue with the vertical, the blue sky above and the blue ocean below; he saw a correspondence with the unconscious. Yves Klein postulated Monochrome IKB (International Klein Blue) as the color of the universe and hoped to use it to sensitize the whole planet. At about the same time Yuri Gagarin, the first cosmonaut, looked at us from outer space and reported: “The earth is blue.” This text by Siegfried Loch, printed on the cover of Jasper van’t Hof ’s musical recording “Blue Corner” (ACT 1996, Hamburg), encouraged me to write about Cargo Revenue Management from many different viewpoints —just as Siegfried Loch wrote about blue. April, 2006 Johannes Blomeyer.

(10) Table of Contents Air Cargo Revenue Management+..................................................................... 1 Part I: Introduction 1 Revenue Management in Air Cargo+.............................................................. 3 1.1 Introduction+.................................................................................................. 3 1.2 Literature+...................................................................................................... 8 2 Preliminary Notes+......................................................................................... 15 2.1 Notation+...................................................................................................... 15 2.2 Primary and Secondary Units+.................................................................... 15 Part II: Air Cargo Properties 3 Initial and Derived Properties in Air Cargo+............................................... 19 3.1 Weight, Volume, and Revenue+...................................................................19 3.2 Density, Standard Density, and Chargeable Weight+................................19 3.3 Weight Coefficients, Volume Coefficients, and the Rate per Chargeable Weight+...................................................... 30 3.4 Numerical Examples of Initial and Derived Properties+......................... 32 3.5 Simple Set of Derived Air Cargo Properties+........................................... 34 3.6 Extended Set of Derived Air Cargo Properties+...................................... 36 3.7 Contribution+.............................................................................................. 39 Part III: Overview of Revenue Management in Air Cargo 4 Basics of a Cargo Revenue Management System+...................................... 41 4.1 Flight, Segment, and Leg+........................................................................... 41 4.2 Flight Revenue, Segment Demand, and Leg Capacity+........................... 43 4.3 Booking Process, Booking, and Booking Request+................................. 46 4.4 Instruments in Cargo Revenue Management+......................................... 51 4.5 Contribution+.............................................................................................. 56 Part IV: Nonlinear Density Scaling 5 Various Densities in Air Cargo+.................................................................... 59 5.1 Linear Density+............................................................................................ 59 5.2 Unified Density and Scaled Density+........................................................ 61 5.3 Contribution+.............................................................................................. 70 Part V: Forecasting, Optimisation, and Control 6 Segment Demand (Forecast)+....................................................................... 73 6.1 Segment Demand and Demand Distribution+......................................... 73 6.2 Rate-Density Domains+............................................................................. 78 6.3 Demand Aggregation+.................................................................................83.

(11) 6.4 Rate-Density Grids+................................................................................... 89 6.5 Contribution+.............................................................................................. 91 7 Flight Revenue Optimisation+...................................................................... 93 7.1 Primal Model to Calculate the Revenue of a Flight+................................94 7.2 Dual Model to Calculate the Revenue of a Flight+.................................. 99 7.3 Kuhn-Tucker Conditions and the Optimal Flight Revenue+................ 104 7.4 Rate-Density Grids and the Optimal Flight Revenue+......................... 107 7.5 Contribution+............................................................................................ 109 8 Booking Request Control+........................................................................... 111 8.1 Marginal Bid Price Control+...................................................................... 111 8.2 Lumpy Bid Price Control+........................................................................ 114 8.3 Booking Request Control Overview+....................................................... 115 8.4 Contribution+............................................................................................ 124 9 Booking Request Control with Stowage Loss+.......................................... 125 9.1 Volume Stowage Loss+............................................................................... 125 9.2 Stowage Loss and Optimal Flight Revenue+........................................... 131 9.3 Maximal Acceptable Stowage Loss+......................................................... 133 9.4 Stowage Loss and the Primal-Dual Graph+............................................ 136 9.5 Contribution+............................................................................................. 141 Summary and Conclusions+............................................................................142 Appendix List of Symbols+.............................................................................................. 144 List of Mathematical Programs, Figures, and Tables+................................. 148 Bibliography+................................................................................................... 150 Index+.............................................................................................................. 160 Abstract+.......................................................................................................... 166 Samenvatting+.................................................................................................. 167 About the Author+.......................................................................................... 169.

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(13) Air Cargo Revenue Management This dissertation is about Air Cargo Revenue Management: the Revenue Management of the air cargo industry. One of the most basic definitions of Revenue Management is from Kimes (2001, page 3): “Yield Management [or Revenue Management, for that matter] is a method which can help a firm to sell the right inventory unit to the right type of customer, at the right time and for the right price. Yield Management guides the decision of how to allocate undifferentiated units of capacity to available demand in such a way as to maximize profit or revenue. The problem then becomes one of determining how much to sell at what price and to which market segment.” Another definition, and one which is more suited to the airline industry, is by Garvett and Hilton (1999, page 181): “Good revenue maximizers seek to obtain the best possible yields and load factors given the circumstances. Yet it is easy to get high yields by excessively raising fares and limiting the availability of discounts—and in the process ensuring nearly empty flights. Similarly, it is easy to maximize load factors by giving the product away. Neither strategy will lead to profitability […]. The art is to obtain both high load factors and high yields at the same time” (as quoted in O’Connor 2001, page 133)—or, more precisely, to obtain the highest possible revenue. This dissertation has nine chapters which are clustered into five parts. Part I is the introduction, Part II is about air cargo properties, Part III is an overview of Revenue Management in air cargo, Part IV concerns nonlinear density scaling, and Part V is about forecasting, optimisation, and control. More specifically, the dissertation is organised as follows: the first chapter introduces Air Cargo Revenue Management in general and gives an overview of the existing literature on the subject. The second chapter contains some preliminary notes about notation and quantity units, while the third chapter presents the initial and derived properties of items related to air cargo. The elements and instruments of a Cargo Revenue Management System are introduced in the fourth chapter, and the fifth chapter presents the concept of unified density. Segment demand and flight revenue are discussed in the sixth and the seventh chapters. The subject of Chapter 8 is the control of booking requests in air cargo, and booking request control linked to stowage loss is the focus of the ninth chapter. The dissertation ends with a summary and conclusions.. 1.

(14) PART I: INTRODUCTION.

(15) 1 Revenue Management in Air Cargo The idea of managing revenues in the airline industry originated in the passenger sector and was first applied in the 1980s. Since then, there have been many attempts to transfer these techniques to other industries, including but not limited to air cargo, rail cargo, ocean cargo, and tour operators. Even though the management of cargo revenue is considered to be a discipline in its own right, it belongs to the class of Network Revenue Management problems because Cargo Revenue Management Systems typically involve the quantity-based management of multiple resources. In further specifying the subject, Talluri and van Ryzin writing about Network Revenue Management stated: “When products are sold as bundles [as is the case in air cargo, because a cargo booking consumes weight and volume], the lack of availability of any one resource in the bundle limits sales. This creates interdependence among the resources, and hence, to maximize total revenues, it becomes necessary to jointly manage (co-ordinate) the capacity controls on all resources” (Talluri and van Ryzin 2004, page 81). It should be noted that a Revenue Management problem does not need to have an explicit network structure to be considered as a Network Revenue Management problem (ibid., page 81). Furthermore, there is an important difference between Revenue Management and Pricing: applying quantity-based Revenue Management techniques and the act of setting prices are two different things because a quantity-based Cargo Revenue Management System does not perform freight pricing. Quantity-based Cargo Revenue Management Systems assume that the products have fixed prices and that booking control manages only the allocation of the resources to the different products (as is, incidentally, the assumption with all quantity-based Revenue Management Systems; Talluri and van Ryzin 2004, page 81). Starting with an introduction, this chapter is divided into two sections. The first section introduces Cargo Revenue Management in general, and the second gives an overview of the existing literature insofar as it is relevant to the subject matter.. 1.1 Introduction Since many of the concepts in Cargo Revenue Management originated from Passenger Revenue Management, it is helpful to look at the differences and commonalities between passengers and cargo. Before this, however, the demand for air cargo and the specifics of transporting air cargo are discussed. 3.

(16) PART I: INTRODUCTION. The Demand for Air Cargo To start with a definition, O’Connor defines air cargo as follows: “The term air cargo is generally used in the broad sense, to include airfreight […], mail, and the several types of expedited small package services to which the term air express is now rather loosely applied” (O’Connor 2001, page 153). Passenger baggage on passenger flights is, however, not considered as air cargo. The demand for air cargo has grown steadily over the past 20 years, and this growth is expected to continue into the future. The goods which are transported by air are as diverse as car parts, live animals, and human remains, and most of the cargo traffic is between Europe, Asia, and the United States of America. Air cargo is, of course, not the only means of transporting freight from A to B, so there is competition. O’Connor (2001, page 180) wrote about the competitors: “Competition with other modes means, as a practical matter, with ocean vessels and with trucks. While railroads carry more in sheer ton-miles of cargo than trucks, nowadays it is of a sort that is not divertible to air: low-value-per-ton commodities such as coal, ores, and grain. The truck, being substantially more expensive than the train yet offering what is usually a much faster service, is the carrier of the high-value-per-ton traffic, mostly merchandise and other manufactured or partly processed goods, from which air diverts.” Further, about the competition between vessels and airplanes, he wrote (ibid., page 182): “Various estimates indicate that transportation of the high-value goods for which air and ocean compete, carried on fast modern container vessels, may cost the shipper anywhere between one-tenth and one-third of what it would cost if shipped by air (see Air Cargo World 1996, page 20).” However, “the gap between the two modes with respect to time is far greater. Ship transport may take 10 or 20 days to move cargo where air would take only a day or two. The time advantage by air is so great—so much greater than air’s time advantage over truck on domestic hauls—that international air cargo has shown impressive development despite the cheaper rates by sea” (O’Connor 2001, page 182f.). Turning to the supply side, an odd feature of the air cargo market is that approximately 50% of the offered cargo capacity is on passenger planes: thus, a large part of the cargo offer derives from passengers travelling on passenger planes since each passenger plane offers a certain amount of cargo capacity (see Holloway 2003, pages 179 and 400). The Transportation of Air Cargo A brief overview of the physical transportation of air cargo is given in Figure 1 on Page 5. It shows the process of transporting freight over one or more flight legs. The figure also helps explain some of the business terms used in air cargo. 4.

(17) The Transportation of Air Cargo A brief overview of the physical transportation of air cargo is given in Figure 1 below, which shows the process of transporting freight over one or more flight legs. The figure also helps explain some of the business terms used in REVENUE MANAGEMENT IN AIR CARGO air 1cargo.. Forwarder Air Cargo Carrier. Involved Parties. Consignor. Storage. Consignee. Ground Transportation. Ground Transportation. Storage. Export Handling. Air Transportation (first flight). Import Handling. Transit Handling. Air Transportation (additional flight). Transit Handling. –> Freight Transport Figure 1: Air transportation involving one (or several) flight(s). As As cancan be be seen in in thethe figure, thethe main customers of the cargo carriers areare seen figure, main customers of the cargo carriers thethe forwarders. However, it is not unusual for a carrier to also have some forwarders. However, it is not unusual for a carrier to also have some large consignors asas direct clients. Examples areare thethe automotive industry large consignors direct clients. Examples automotive industry and pharmaceutical industry,with with manylarge largecompanies companiesfrom fromthese these inand thethe pharmaceutical industry, many dustries dealing with their preferred air cargo carriers directly. industries dealing with their preferred air cargo carriers directly. The Differences Passengers and Cargo The Differencesbetween between Passengers and Cargo. Passengersand andcargo cargoare, are,of of course, quite different. However, Passengers course, quite different. However, it is it stillis still worthwhile to compare them, as in this quotation by O’Connor in his book worthwhile to compare them, as in this quote by O’Connor in his book about airline economics: about airline economics: “Air cargo is nearly always one-way; by contrast, passengers are usually round trip. Cargo generally prefers to travel by night, passengers by day. Cargo is passive—that is, it must be physically moved, loaded, and unloaded, while the passengers walk about the airport, as well as on and off the aircraft, under their own power. Passengers do not like indirect routings or plane changes (although […] they often have to put up with these today), !"#$%&'()*(+,%-&.,%#/,(01"(2%3'&$%4 of cargo are not concerned with plane changes Junebut 13,shippers 2006 and recipients and indirect routings as long as the cargo arrives when expected. There are large differences in the weight and volume of cargo shipments, whereas in this respect passengers come close to homogeneous. Passengers prefer newer (or at least new-looking) aircraft and are concerned with the decor and the cleanliness of the cabin, while cargo can travel on older aircraft with no regard for the aesthetics of the cabin” (O’Connor 2001, page 162). With booking periods of typically four weeks ahead, the booking periods of air cargo carriers are significantly shorter than the one-year booking period of a passenger airline. Furthermore, about 80% of air cargo bookings are made during the last three days of the booking period, whereas passenger airlines usually sell a significant number of seats many months ahead. 5. 10.

(18) PART I: INTRODUCTION. It is also important to note that the ten largest forwarders often generate 70% or more of an air cargo carrier’s business, meaning that an air cargo carrier usually has fewer customers than a passenger airline. Further, the applicable freight rates for the large customers are usually negotiated in advance. The rate between Origin A and Destination B, for example, may be agreed upon at 1.– euro per chargeable kilogram for all bookings by a particular forwarder made within the following three months. In addition to the above aspects, Holloway noted some further differences between passengers and cargo. According to Holloway (2003, pages 572f.), cargo space is not as ‘fungible’ as a passenger seat (as can be illustrated by heavy shipments that need a specific location within the plane); the carriage of certain goods is highly regulated (e.g., dangerous goods); and the cargo capacity of a passenger flight (the ‘belly space’) might not be known until very close to departure due to uncertain passenger numbers (‘noshows’) and unknown baggage figures. Another difference between passengers and cargo is, according to Herrmann et al., that low-yield passengers tend to book well in advance, whereas the “excess output of cargo space on many medium- and long-haul routes […] has contributed to the reverse situation where ad hoc late sales are often made at lower-than-contract rates” (see Herrmann et al. 1998; the citation is from Holloway 2003, page 573). However, passengers and cargo are not completely different, since both have a certain weight and volume, and both can be booked on the same flight (if it is a passenger flight). Both passengers and cargo can be booked in advance, both can be cancelled or might not show up at all, and sometimes they share their final destination—as is the case with orchestras and ensembles visiting other countries, since their excess baggage (such as instruments and sound equipment) is commonly declared and transported not as baggage but as cargo. The Specifics of Cargo Revenue Management While Passenger Revenue Management and Cargo Revenue Management share many concepts and ideas (they even share a basic terminology), they are not the same. The major differences are the lumpiness of the cargo demand, the shorter booking period for cargo, the fact that the capacities and the booking requests in air cargo have two dimensions, and the fact that cargo booking requests can cause a substantial amount of stowage loss. However, since the situation with cargo fulfils the general requirements for applying Revenue Management techniques (see Kimes 2001, pages 4ff., for an outline of these requirements, and Hendricks and Elliott (2003) for a discussion on how Cargo Revenue Management is different), an investment in a Cargo Revenue Management System may be sensible—provided that it meets some critical success factors. 6.

(19) 1 REVENUE MANAGEMENT IN AIR CARGO. The Critical Success Factors One of the most critical success factors is a carrier’s ability to segment the demand according to the customers’ willingness to pay. In cargo, this is remarkably more difficult than on the passenger side because the usual restrictions used to separate high-yield customers from the low-yield customers do not hold. There is, for example, no freight ‘under the age of 27’, a ‘Saturday night stay’ does not cause the high-yield freight considerably more discomfort than the low-yield freight, and restrictions requiring the purchase of a return ticket, to give another example, simply do not make sense with cargo. Hence, segmentation is not easy, and the assumption “that demand for a given [fare] class does not depend on the capacity controls; in particular, [that] it does not depend on the availability of other [fare] classes”, as Talluri and van Ryzin put it, is not automatically met. “Its only justification”, they continue, “is if the multiple restrictions associated with each class are so well designed that customers in an upper class will not buy down to a lower class and if the prices are so well separated that customers in a lower class will not buy up to a higher class if the lower class is closed” (Talluri and van Ryzin 2004, page 34). However, if this assumption is not met, the result is a less than perfect demand segmentation (see Talluri and van Ryzin 2004, page 34); and a less than perfect demand segmentation has, of course, an adverse effect on demand forecasting because buying up—as well as buying down—will result in a different demand than was anticipated in the respective rate classes. Further, even if a carrier has been successful in segmenting the demand, the demand forecast can still be wrong and, hence, the quality of the demand forecast is critical for the success of any Revenue Management System. This is true for any Revenue Management System, and especially for a Cargo Revenue Management System. The perceived fairness of a Cargo Revenue Management System is also of great importance since most cargo carriers usually deal with just a few major customers, and they do so on a regular basis. For a further discussion on the subject of perceived fairness in Revenue Management, see Kimes (1994). Other critical success factors are listed in Hendricks and Elliott (2003) under the heading “Challenge Checklists” and in Elliott (2002, pages 11ff.) under the heading “Tactics for Success”.. 7.

(20) PART I: INTRODUCTION. 1.2 Literature An extensive discussion on Revenue Management in general is provided in the book by Talluri and van Ryzin (2004) entitled “The Theory and Practice of Revenue Management”. It does have a section on Cargo Revenue Management but, in comparison with Passenger Revenue Management, this section is small (pages 563-564). Another influential text on Revenue Management is the Ph.D. thesis by Williamson (1992). This thesis, entitled “Airline Network Seat Inventory Control”, discusses various aspects of managing passenger revenues and is a good introduction to the subject. The article “Revenue Management and e-Commerce” by Boyd and Bilegan (2003) traces the history of Revenue Management and gives a good overview of earlier literature on forecasting, optimisation, and control. The Literature on Cargo Revenue Management A broad search has revealed that there is little literature specifically on Cargo Revenue Management. The revenue research overview by McGill and van Ryzin (1999), for example, has a bibliography of over 190 references, but almost all of them refer to Passenger Revenue Management. It is only in the past two or three years that interest in Cargo Revenue Management has risen substantially. Generally speaking, there are four types of literature on Cargo Revenue Management in the public domain: scientific papers from academia, papers by the vendors of Cargo Revenue Management Systems, reports from practitioners, and published patent applications. In addition to this cargospecific literature, a number of publications claim that their results can also be applied to cargo. The major literature that relates to the subject of this dissertation is outlined below in chronological order. The article “Air Cargo Revenue Management: Characteristics and Complexities” by Raja G. Kasilingam (1996) focuses on the differences between Passenger Revenue Management and Cargo Revenue Management, and discusses “some of the complexities involved in developing and implementing [Cargo Revenue Management]” (page 37). Kasilingam also presents a one-dimensional model for overbooking and a one-dimensional model for bucket allocation (a form of booking request control) (pages 41-43). In his book “Logistics and Transportation: Design and Planning”, Kasilingam (1998) wrote about the density of a product (i.e., its volume-toweight ratio) and about the consequences of density on transportation, storage, and billing (page 25). 8.

(21) 1 REVENUE MANAGEMENT IN AIR CARGO. Kasilingam also noted the importance of grouping products, which “may be done based on their similarity in product characteristics such as weight [and] volume […].” The book has a section about data aggregation, similarity measures, and clustering methods (ibid., pages 27 and 29-33). Furthermore, it has some information on logistics metrics and notes that it is crucial to use the right measurement units (ibid., page 230). Kasilingam also writes about the consolidation business (ibid., page 179), and the contents of his 1996 article are again presented (on pages 189-199). However, most of the book is not sufficiently detailed to capture the specifics of air cargo. In 1998, in the United States, Talluri filed a patent application entitled “Revenue Management System and Method” (patent number US 6,263,315). The patent concerns multidimensional lookup tables of access price values and, according to Talluri, it has an application in Air Cargo Revenue Management (Talluri 1998, column 10). Also in 1998, Hamoen published a paper about combination carriers and a dedicated air-cargo hub-and-spoke network (Hamoen 1998). Although this paper is not focused on Cargo Revenue Management, it does contain some interesting information about the economics of air cargo, including network types, deregulation, and market segmentation. Karaesmen’s Ph.D. thesis about Revenue Management also has a chapter on cargo, entitled “Using Bid Prices in Air Cargo Revenue Management”. Karaesmen (2001) claimed on page 4 to “show how a practical airline seat inventory control model can be adapted by air cargo to control both weight and volume capacities.” Furthermore, she claimed that “the model for air cargo requires a continuous linear programming formulation” (ibid., page 4), even though she then went on to refer to the discretisation of the solution space as the most effective way of obtaining numerical results. The focus of her work, however, was not on finding the best discretisation of the weight and volume space, but to prove, among other things, that “any […] discretization with the same asymptotic property (all regions get smaller in both dimensions […]) can be used” to approximate the infinite dimensional linear programming problem (ibid., page 24; see also pages 23 and 56). Moreover, she claims “that under certain topological conditions, there is no duality gap for our optimization problem [the continuous linear programming formulation]” and that bid prices do exist (ibid., page 23). It is worth noting that Karaesmen assumed that the revenues from booking requests are only a function of their weight and volume (see ibid., page 17), ruling out the possibilities that two booking requests with the same weight and volume could end up being charged at different rates. Hence, Karaesmen did not try to differentiate among the booking requests according to their rate (at least not beyond their weight and volume consumption). 9.

(22) PART I: INTRODUCTION. The book “An Introduction to Airline Economics” by William E. O’Connor (currently in its sixth edition) has many profound insights into the subject and a dedicated chapter about the economics of air cargo (see O’Connor 2001, pages 153ff.). The chapter about cargo excels in analysing the demand, identifies what drives the supply, and identifies those factors that determine the rates. In 2001, Gliozzi and Marchetti filed a patent for a “Yield Management Method and System” in Great Britain. This patent application was also filed in the United States under US 2003/0065542 in 2002. In brief, their invention determines “an authorisation to allocate the offered capacity for each capacity variable of each category in the future instance of the service by applying a stochastic model to the historical scenarios according to the corresponding probabilities” (Gliozzi and Marchetti 2003a, page 1). More specifically, they claim to have found an approach that avoids the need for a demand classification by using the original request data and having these sent directly to the optimisation model using multiple stochastic scenarios. A paper by Gliozzi and Marchetti, entitled “A New Yield Management Approach for Continuous Multi-Variable Bookings: The Airline Cargo Case”, concerns the implementation of a complete Cargo Revenue Management System (Cargo RMS) that was “going to be fully operational in 2002 at a major European airline” (Gliozzi and Marchetti 2003b, page 386). The paper describes various aspects of managing revenue in air cargo (including the existence of a density mix; ibid., pages 380-381), and emphasises that “both the variables [i.e., the weight and the volume] have to be treated symmetrically and at the same level in the definition of the models” (ibid., page 372). Their “New Yield Management Approach for Continuous Multi-Variable Bookings” is based on the 2001 patent application “Yield Management Method and System” by Gliozzi and Marchetti (2003a). An excellent chapter about the economics of airfreight can be found in Doganis’ book “Flying Off Course” (Doganis 2002). In this chapter, the demand for airfreight services is analysed by considering, for example, the demand for emergency freight, such as spare parts for machinery; the demand for legal papers and artwork; the demand for transporting valuables, such as gold and jewellery (because of the added security); the demand for transporting perishables, and, of course, the demand for transporting ‘regular’ freight (ibid., pages 300ff.). Further, the book has a chapter on the economics of supply and another about the pricing of airfreight. In the same year, Radnoti published his book “Profit Strategies for Air Transportation” (Radnoti 2002). The book gives a broad overview of various aspects of air transportation and does not shy away from cargo, even though some of the presented data appeared to be obsolete (they were from the 1960s and 1970s). Still, the book has a hands-on approach and provides many insights into the subject. 10.

(23) 1 REVENUE MANAGEMENT IN AIR CARGO. A 2002 paper by Elliott provides some background information on the economic trends in air cargo and recommends basing Cargo Revenue Management on three “strategic realities”. Strategic reality #1 is (according to Elliott) that “Revenue Management is an ongoing business function”, strategic reality #2 is that “Revenue Management helps manage the crisis”, and strategic reality #3 is that “Revenue Management opportunities can still be found, even in a depressed market” (see Elliott 2002, pages 7ff.). The book “Straight and Level: Practical Airline Economics” by Holloway (2003), another book about airline economics, not only has a chapter about Revenue Management but also gives some information concerning how to manage freight revenues. In 2003, Hendricks and Elliott put a short paper titled “Implementing Revenue Management Techniques in an Air Cargo Environment” on the Internet. The paper is clearly written, and it “reviews the techniques of Revenue Management and how they relate to the specific nature of the Air Cargo Business” (Hendricks and Elliott 2003, page 1). The paper “Securing the Future of Cargo”, from the series “Mercer on Travel and Transport”, provides some useful information on why only a few carriers use a Cargo Revenue Management System (Kadar and Larew 2003). On page 5 of the paper, the authors, Kadar and Larew, summarise that “cargo capacity is volatile”, that “cargo demand is multidimensional”, that “cargo customers are concentrated”, and that the “returns on investments are lower for air cargo carriers [than for passenger airlines]” because the cargo carriers are usually smaller in size. The paper “On an Experimental Algorithm for Revenue Management for Cargo Airlines” by Bartodziej and Derigs (2004) is about an itinerary-based network model that not only considers the routing options in air cargo, but is also able to calculate the bid price of a booking request (pages 60-64). Slager and Kapteijns wrote a practice paper in 2004 entitled “Implementation of Cargo Revenue Management at KLM”. The paper describes the concept and the implementation of a new Cargo Revenue Management System at KLM Airlines after a failed attempt that “had focussed too much on IT and a scientific approach” (Slager and Kapteijns 2004, page 82). The new approach seems to centre on the setting of so-called Shipment Entry Conditions (SEC). “The SEC”, they wrote on page 86, “can be set per cubic metre for volume constrained flights, or per kilo for payload restricted flights” but, unfortunately, the paper has no information on how to deal with flights that are expected to be restricted in both weight and volume. Their paper also failed to mention instruments that are available to increase the cargo revenue of a flight, beyond to “protect high margin cargo, on top of eliminating low margin cargo” (ibid., page 90). Additional information on Revenue Management at KLM Cargo can be found in Couzy (2004). 11.

(24) PART I: INTRODUCTION. In their paper “Fleeting with Passenger and Cargo Origin-Destination Booking Control”, Klabjan and Sandhu (2005) compare Passenger Revenue Management and Cargo Revenue Management, and present a so-called Cargo Mix Bid Price Model. Among other topics (which are only loosely connected to cargo), they focus on the possibility of transporting cargo via different routings (ibid., pages 6ff.). An earlier presentation of their approach was given in Klabjan and Sandhu (2004). Cooper et al. (2005) model the Cargo Revenue Management problem as a Markov Decision Process and explicitly take into account that the volume of a booking request is, in practice, a random variable because its value “is learned only just before the flight’s departure” (ibid., page 1). They published a revised version of their paper in 2006 (Cooper et al. 2006). In the last chapter of his 2005 Ph.D. thesis “Revenue Management: New Features and Models”, Pak presented his approach for managing revenue from air cargo under the title “Bid Prices for a 0–1 Multi Knapsack Problem”. This approach claims—not unlike the one by Gliozzi and Marchetti —to “treat the cargo shipments as the unique items that they are” (Pak 2005, page 9). According to Pak, “the weight, volume and profit of each booking request [per kilogram] are random and continuous variables” (ibid., page 111), and “the fundamental difference between Cargo and Passenger Revenue Management, is that cargo shipments are uniquely defined by their profit, weight and volume whereas passengers generally belong to one of a limited number of price classes” (ibid., page 141). He also states that “profit, weight and volume are related to each other since they all reflect the size of the shipment” (ibid., page 128), but does not elaborate on what is meant by the size of a shipment, if not its weight. An earlier version of Pak’s work was published in 2004 (Pak and Dekker 2004). Although the paper “Profit Maximization in Air Cargo Overbooking” by Cakanyildirim and Moussawi (2005) is mostly about overbooking, they do include some basic cargo definitions, as, for example, the definition of the density of a piece of cargo, as well as a definition of its chargeable weight. They also mention the phenomenon that is elsewhere known as the density mix (ibid., pages 6-10). One of the more recent papers about Cargo Revenue Management is by Huang and Hsu (2005), entitled “Revenue Management for Air Cargo Space with Supply Uncertainty”. This paper takes into account the supply uncertainty of available air cargo space on a flight and the incurred penalty for denied boarding (in the air cargo industry, the term ‘denied boarding’ is known as ‘offloads’), but their dynamic programming model is one-dimensional, based on weight.. 12.

(25) 1 REVENUE MANAGEMENT IN AIR CARGO. They are aware of the business practice of selling chargeable weight, but their statement is that airlines sell cargo space in terms of tonnes or kilograms and that the “airlines are not sure that the aircraft can handle the shipments for the space sold” (Huang and Hsu 2005, page 572). Other papers include those by Bazaraa et al. (2001: a general overview of Cargo Management), Chew et al. (2002: Cargo Revenue Management from the perspective of the forwarder), Feller (2002: Revenue Management as a Dynamic Stochastic Knapsack Problem with multidimensional resources), and Billings et al. (2003: a discussion of various aspects of Cargo Revenue Management). The paper by Gallego and Phillips (2004) about the Revenue Management of flexible products also claims to have applications in air cargo. Further papers include those by Chen et al. (2003: about Cargo Revenue Management and routing), Kimms and Müller-Bungart (2004: an article about the construction of multidimensional booking classes), Narayanan (2004: a presentation mainly about the Bayesian forecasting of cargo demand), and Derigs et al. (2006; another paper about Revenue Management and routing). The Publications by the Author on the Subject In 1999, my first thoughts on the subject of Cargo Revenue Management were documented in an unpublished working paper (“for internal use only”) by Lufthansa Cargo. In this paper, the instruments that are available to increase the revenue of a flight are described as the rate mix, the load mix, overbooking, pre-flying shipments, rebooking shipments, and short-term capacity adjustments (Blomeyer 1999, page 5). Further publications have included several patent applications. The results of this dissertation have fed into German patent application DE 10 2004 023 833.2 (priority date 13.05.2004), European patent application EP 1 596 317 A1 (publication date 16.11.2005), and United States patent application US 2006 001 5396 A1 (publication date 19.1.2006).. 13.

(26) PART I: INTRODUCTION. 14.

(27) 2 Preliminary Notes This chapter has two sections. The first is about the general notation used, and the second section is more specific concerning quantity units and value ranges.. 2.1 Notation The names of the variables, parameters, and constants are case-sensitive and their meaning may depend on the subscript. R, for example, is the revenue, r is a rate, and rb is the rate of the booking request b. Furthermore, the concepts can play different roles in various parts of the dissertation. Flight revenue, for example, is mostly treated as a variable, but in the chapter about booking request control with stowage loss, flight revenue is used as a parameter. The role of the symbols should, however, be clear within their context. Units, where applicable, are given in brackets, and the term [unitless] indicates that a value has no units.. 2.2 Primary and Secondary Units There are two kinds of quantity units used in this dissertation: primary quantity units and secondary quantity units. So-called primary units are generally preferred, but sometimes secondary units are also used. In these cases, the use of the secondary units is justified either by an attempt to be compatible with the industry’s naming conventions, or by an attempt to give a concise presentation of the subject. Primary Units: euro+ + + kilogram+ + chargeable kilogram+ cubic metre+ +. + + + +. [€]+ + [kg]+ + [chkg]++ [mc]+ +. currency+ + weight++ + chargeable weight+ volume+ +. + + + +. 123,456.78 123,456 123,456 123.456. Secondary Units: tonne+ + + chargeable tonne+ pound+ + + cubic foot+ + cubic inch+ +. + + + + +. [t]+ [cht]+ [lb]+ [cft]+ [ci]+. weight++ + chargeable weight+ weight++ + volume+ + volume+ +. + + + + +. 123.456 123.456 123,456 123,456 123,456. + + + + +. The preferred number formats are also given. The preferred number format for the cubic metre, for example, is “123.456” (or “###. ###”, if the non-specific number sign is used), and 123,456 litres are equal to 123.456 cubic metres. The comma in the number formats is used as a thousands separator, while the full stop operates as a decimal point. 15.

(28) PART I: INTRODUCTION. If the decimals of a number are suppressed, the number has a decimal point but no decimals (e.g., “123.”). This number format is mainly used in illustrations to save space. Another sign used to save space is the double tilde which denotes an approximate value (e.g., π ≈ 3.14). Finally, a dash, as in “123.– euro”, replaces the zeros after the decimal point. . . Please note that the term [mc] has been chosen as an abbreviation for the cubic metre to avoid confusion with the term [cm] used for centimetres. The format [m3] is inconvenient because of its superscript, and the term ‘m3’ could be misleading if it is used as a prefix: m3 45, for example, could be easily read as either 45 cubic metres or 345 metres. The Date and Time Format The preferred date and time formats are day.month.year and hour:minute, as in 31.12.2003 and 12:34. The Rounding Rules Aside from the preferred formatting, it would be prudent to explain any rounding rules used in the air cargo industry. Reasons for using a rounding rule might be, for instance, a legal requirement, a prevalent business practice, an attempt to achieve numerical stability, or an attempt to simplify the reading of a number. To give an example, a simple rounding rule, which is based on a prevalent business practice, will be presented below. In air cargo, the chargeable weights of bookings and booking requests are rounded up to the next half chargeable kilogram (see IATA Resolution 502). A chargeable weight of 100.1 chargeable kilograms, for example, will be rounded up to 100.5 chargeable kilograms, while a chargeable weight of 100.6 chargeable kilograms will be rounded to 101 chargeable kilograms. Accordingly, the formula for calculating the rounded chargeable weight is 0.5 2 chargeable weight. Despite their importance in the specification of a real-world Cargo Revenue Management System, rounding rules are not further considered in this dissertation because they are beyond the scope of this dissertation. The Conversion Rules To convert primary units into secondary units (and vice versa), several conversion constants are needed. The tonne conversion constant is used to change tonnes into kilograms, and the chargeable tonne conversion constant changes chargeable tonnes into chargeable kilograms. Both constants are formally introduced below. Tonne and Chargeable Tonne Conversion Constants: tc+ 1,000 [kg/t]+ + tonne conversion constant chtc+ 1,000 [chkg/cht]+ chargeable tonne conversion constant. 16.

(29) 2 PRELIMINARY NOTES. The next set of constants is the cubic inch conversion constant, the cubic foot conversion constant, and the pound conversion constant. Their values are not exact but adequate approximations. Cubic Feet, Cubic Inch, and Pound Conversion Constants: 35.3 [cft/mc]+ cubic feet conversion constant 61,000 [ci/mc]+ cubic inch conversion constant 2.2 [lb/kg]+ pound conversion constant. The above conversion constants do not have a dedicated symbol since they are used ‘as is’. The next part of the dissertation concerns initial and derived air cargo properties.. 17.

(30) PART II: AIR CARGO PROPERTIES.

(31) 3 Initial and Derived Properties in Air Cargo Managing revenue in air cargo is primarily a matter of confirming the ‘advantageous’ booking requests and rejecting the ‘disadvantageous’ ones. How this should be done will be the subject of a later chapter but, clearly, any plan to control the confirmation of a booking request has to do with its initial air cargo properties. The initial air cargo properties are the weight, the volume, and the revenue of an item. The initial air cargo properties are accompanied by so-called derived air cargo properties. Derived air cargo properties are, for example, not only the density of an item and its chargeable weight, but also the weight and volume coefficients of the chargeable weight, as well as its rate. Later in the chapter, a simple set of derived air cargo properties will be presented, and this simple set will then be compared with an extended set. The chapter concludes with a consideration of the contribution made to the field.. 3.1 Weight, Volume, and Revenue The weight and volume of bookings, booking requests, and flight capacities are typically expressed in kilograms and cubic metres, or [kg] and [mc], while the revenue of bookings and booking requests is typically expressed in euro, or [€]. The weight, the volume, and the revenue are considered to be initial air cargo properties because they are real quantities in air cargo. The symbols and value ranges of these initial air cargo properties are stated below. Weight, Volume, and Revenue: W+ [0, ∞) [kg]+ + weight V+ [0, ∞) [mc]+ + volume R+ [0, ∞) [€]+ + revenue. All quantities have a lower bound of zero because there is no reason, as yet, to believe that negative weight, volume, or revenue quantities make any sense. The given value ranges do not, however, take account of any specific limitations, as, for example, the payload restrictions of an airplane. In the next section, some derived air cargo properties are introduced.. 3.2 Density, Standard Density, and Chargeable Weight The most important derived air cargo properties are the density and the chargeable weight of a piece of freight (or of any other item which has a weight and volume). Both quantities are considered to be derived since they are calculated from the initial air cargo properties of weight and volume. Despite its status of being ‘derived’, the density is a well-known and well-established figure for describing the volume-to-weight ratio of 19.

(32) PART II: AIR CARGO PROPERTIES. bookings and booking requests in air cargo. The chargeable weight is also well-known in air cargo, but only implicitly and not as an explicit figure. This is because the chargeable weight is the greater of two figures, namely the actual weight and the volume weight. If the volume weight is higher than the actual weight, the volume weight simply replaces the actual weight in certain calculations (for example in the calculation of the booking request’s rate; see www.tci-transport.fr/volum_uk.htm). Prior to discussing the chargeable weight, however, the density and the standard density will be considered. The Density The cargo density reflects the bulkiness of an item with bulky items having large volumes per weight, whereas items which are comparatively dense have less volume than one might expect for their weight. Contrary to the definition of density in physics, the density in air cargo is defined as ‘volume divided by weight’. Definition of the Density in Air Cargo: d = 1,000 V/W. The conventional unit of density in air cargo is cubic metres per tonne, the symbol is d, and the value ranges from ‘pure weight’, with a density of zero, to ‘pure volume’, with a density of infinity. Density: d+ [0, ∞] [mc/t]+ +. density. Even though the above density definition is perfectly adequate for many calculations, it cannot deal with items that have zero weight. In other words, the density definition must be modified to be able to calculate a density for items (or entities) that have zero weight, and this is achieved by stating that the combination of positive volume and zero weight equates to an infinite density. Items (or entities, for that matter) with zero or infinite densities are, incidentally, not uncommon in air cargo. The bookable flight capacities at departure, for example, are often zero in weight or in volume. Booking updates, which are another entity used in air cargo, can have a zero or an infinite density if only additional weight or additional volume is being requested. However, there are entities in air cargo that may have no defined density at all. If, for example, the remaining weight and volume capacities of a flight are both zero, the density of the bookable capacity is, in fact, indeterminate. By being able to deal with entities that have a positive volume but zero weight, the generic density definition overcomes the arbitrariness of using an entity’s volume divided by its weight as a measure of its density. To be specific, a density which is calculated as a volume divided by a weight will 20.

(33) 3 INITIAL AND DERIVED PROPERTIES IN AIR CARGO. be indeterminate for a zero weight, and the more conventional density, which is calculated as a weight divided by a volume, is indeterminate for a zero volume. However, although the first fraction can handle the zero volume case and the second fraction can handle the zero weight case, neither fraction can handle both. Therefore, there is a fundamental need to define density in air cargo generically and so avoid the necessity of having to work with two definitions. If the density in air cargo is defined generically, it no longer matters whether the density is expressed as a volume divided by its weight, or as a weight divided by its volume. A generic density definition of the volume-divided-by-weight type is given below. Density as a Function of Weight and Volume: if+ W = 0 and V = 0+ then d is indeterminate elseif+ W > 0 and V ≥ 0+ then d = (V/W) tc elseif+ W = 0 and V > 0+ then d = ∞. As can be seen, the generic density definition makes use of the tonne conversion constant to achieve unit consistency. It should be noted that the actual density values are rarely affected by the limits placed on weight and volume value ranges. This is because the density is a fraction, and neither the limited value range for the nominator of that fraction, nor the limited value range for its denominator, necessarily lead to a limited density value range. In the world of air cargo, the density range of an item is probably more often restricted by the physical limits on the density itself. Real freight, for example, cannot have a zero density because any tangible cargo has at least some volume and, for a similar reason, it is very unlikely that a physical piece of cargo has an infinite density. The Standard Density The standard density is a very important figure in air cargo because it is used for the calculation of the chargeable weight of freight, and the freight’s chargeable weight, in turn, is the basis for the revenue the carrier aims to earn. Although the value of the standard density is, at least in principle, negotiable, all airlines which are members of the International Air Transport Association (IATA) have agreed on a common value. Physically, the standard density refers to what is considered as the average density of regular freight. As such, the standard density has not only an effect on the calculation of the freight’s chargeable weight but also on nearly all other aspects of managing and transporting freight in the air cargo industry. The optimum volume-to-weight ratio of the cargo hold of commercial cargo airplanes, for example, is similar to the volume-to-weight ratio of the standard density in order to maximise freight carrying opportunities. Further elaborating on the subject, O’Connor refers to planes that have been designed to be freighters from the drawing board onwards as ‘dedicated’ or ‘uncompromised’ cargo aircraft (O’Connor 2001, page 162). 21.

(34) PART II: AIR CARGO PROPERTIES. Dedicated freighters differ significantly from freighters that were converted from passenger use or were made at the factory as freighters but using the basic designs of a passenger aircraft because “an aircraft whose initial design was premised on the requirements of passenger service will, when used as a freighter, usually become filled to capacity with respect to space well before the maximum permissible payload weight is reached”, while a dedicated cargo aircraft “should be designed to reflect the usual trade-off between cube [i.e., the volume] and the weight of the cargo that travels in major markets” (ibid., pages 162f.). More information about this subject can be found in Holloway (2003, pages 500f.), Roskam (1989, pages 76ff.) and Wood et al. (2002, page 192). Besides serving as a guideline in the design of an uncompromised cargo aircraft, the IATA Interline & Revenue Management Services Newsletter (2003, page 14) provides an additional reason why it is important to have a standard density: “… it facilitates the design and the production of standard aircraft containers, pallets and handling equipment, simplifying the movement of shipments from one aircraft type to another, and from one airline to another.” The symbol for the standard density is sdc, and its value is 6 cubic metres per tonne as formally defined below. IATA Standard Density: sdc+ 6 [mc/t]+ +. standard density constant. If the IATA standard density were to be expressed as an inverse (i.e., conventional) density in pounds per cubic inch, its value would be approximately 0.006 [lb/ci], while if the standard density were to be expressed as an inverse density in pounds per cubic feet, its value would be approximately 10.4 [lb/cft]. The aforementioned value of 6 cubic metres per tonne has been valid since October 1981; prior to that date, the IATA standard density was 7 cubic metres per tonne. In May 2002, the IATA Composite Cargo Tariff Coordinating Committee suggested changing the standard density from 6 cubic metres per tonne to 5 cubic metres per tonne (see the Composite Resolution 502 from the IATA Composite Cargo Tariff Co-ordinating Committee 2002) in order to “incite improvements in the efficiency of packaging methods to reduce the volume of their shipments using more compact […] packaging” because “this would allow airlines to increase capacity with only a marginal increase in operating costs” (IATA Press Release Low Density Cargo March 2005, page 1). Another reason that an update to the standard density was proposed was that “aircraft performance has improved significantly in the 20 years since this standard was last changed—with more powerful engines able to lift more weight, while the space available in the cargo hold has remained 22.

(35) 3 INITIAL AND DERIVED PROPERTIES IN AIR CARGO. static”, so that many flights “cube out” before they “weigh out” (ibid., page 1). However, Composite Resolution 502 was withdrawn at the Special Composite Cargo Conference in 2005 and never implemented (see IATA 2005, page 1). Also mentioned in the initial resolution was the fact that the types and overall nature of air cargo have changed. “In the past, air cargo contained heavy machinery and similar commodities and these have been replaced by high-technology products such as computers, software […] and other electronic equipment. Virtually none of these products existed when the first Boeing 747 entered service over 32 years ago. These goods are typically lighter, but are higher in value than most items traditionally shipped by air in the past” (IATA Press Release Low Density Cargo March 2005, page 1). Hence, there is a mismatch between the possibility of lifting more weight and the need to accommodate more volume. More information about the recent developments in the density of freight can be found in Sulogtra (2002). For a detailed discussion on the motives and consequences of a standard density change, see ACCC (2004). However, for the time being, the value of the standard density remains 6 cubic metres per tonne. Although this value is assumed throughout the dissertation, great care has been taken to make a distinction between the standard density function and its actual value so as to be able to handle future changes without any difficulties. In comparison, the standard densities in sea and road cargo are currently 1 and 3 cubic metres per tonne respectively. Densities below the standard density are referred to as high densities (even though the numerical values are lower), and densities above the standard density are called low densities (even though the numerical values are higher). Simply put, high-density items are comparatively heavy, and lowdensity items are comparatively bulky. The explicit definition of what are considered as high, standard and low densities in air cargo is given below. High, Standard, and Low Densities in Air Cargo: if+ 0 ≤ d < sdc+ + then d is a high density elseif+ d = sdc+ + then d is a standard density elseif+ sdc < d ≤ ∞+ + then d is a low density. Typical density figures for various goods are given in Wood et al. (2002) on page 192.. 23.

(36) PART II: AIR CARGO PROPERTIES. For practical purposes, it is useful to further classify these densities into smaller subgroups. A classification with three subgroups for the highdensity category and three subgroups for the low-density category is suggested below. Moderate, Medium, and Extreme Densities in Air Cargo: if+ 0 ≤ d < 2.4+ + then d is an extremely high density elseif+ 2.4 ≤ d < 4.8+ + then d is a medium high density elseif+ 4.8 ≤ d < 6+ + then d is a moderately high density elseif+ d = 6+ + + then d is a standard density elseif+ 6 < d ≤ 7.5+ + then d is a moderately low density elseif+ 7.5 < d ≤ 15+ + then d is a medium low density elseif+ 15 < d ≤ ∞+ + then d is an extremely low density. Even though this classification might look somewhat arbitrary, it is not. Rather, the density classification is based on the unified density. Unified density is a concept which will be explained in Chapter 5 and, as a result of having based the density classification on the unified density, each highdensity subgroup is as extreme, medium or moderate as its counterpart among the low-density subgroups (and vice versa). Furthermore, the suggested classification is symmetric and centred around the standard density of 6 cubic metres per tonne.. 0.. 8. c/t. t c/. m. 0. m .66. 2. 1. 0 mc/t. 0 0. 1. 2. 3. 4. 5. 6. Weight [t] Figure 2: Weight, volume, and density. 4.00 3.50 3.00 Rate [euro/chkg]. c/ t m. 1.3. 1. 3m. c/t 2m. /t 4 mc. Volume [mc]. 3. # mc/t. c/ t. 4. 2.50 lumpy bid price rate. 2.00 1.50 1.00 0.50 0.00. 1) standard. density (dashed): 6 cubic metres per tonne. An illustrated example of different densities, including several extremely high densities, one moderately high density, the standard density, and one extremely low density, is given in Figure 2. The figure shows the weight and volume combinations of the following densities (from left to right): ∞, 4, 2, 1.33, 1, 0.8, 0.66, and 0 [mc/t]. The standard density, of 6 cubic metres per tonne, is shown as a dashed line.. 0. 10. 20. Supply an. 1). Booking class sizes as a fu. According to the definitions of high, standard, and low densities, any combination of weight 4.00and volume that is located to the left of the standard4.00 density line in Figure 2 has a low density, while all combinations of weight3.50 3.50 3.00 Rate [euro/chkg]. Rate [€/chkg]. 3.00. 24. Wk – w. 2.50 2.00 1.50. 2.50. 1.50. 1.00. 1.00. 0.50. 0.50. 0.00. lumpy bid price rate. 2.00. 0.00 0. 20. 40. 60. 80. Chargeable Weight [cht]. 100. 120. 0. 10. 20. Supply an.

(37) 3 INITIAL AND DERIVED PROPERTIES IN AIR CARGO. and volume that are located to the right of the standard density line have a high density. Infinite densities are located on the ordinate of the graph, zero densities are located on its abscissa, and the zero weight / zero volume combination is located at the graph’s origin. From the meeting of the density lines, it is clear that the zero weight / zero volume combination can have any density, and hence it does make sense to say that the density of the zero weight / zero volume combination is indeterminate. The Chargeable Weight The chargeable weight of freight is also known as its billable or dimensional weight. The symbol for chargeable weight is cw, and its unit is the chargeable kilogram. The chargeable weight and its quantity unit are specified below. Chargeable Weight: cw+ [0, ∞) [chkg]++. chargeable weight. The value range for the chargeable weight goes from zero chargeable kilograms to, strictly speaking, less than infinite chargeable kilograms. It may be possible to tighten this value range by taking the particular context of an item into consideration but, more likely, the value range of the chargeable weight will be restricted by certain weight and volume limits. Without invoking a dedicated chargeable weight unit (and, in fact, without bothering about the units at all), the chargeable weight is the maximum of an item’s actual weight and its volume divided by the standard density. For generic usage, however, this definition is enhanced by using explicit weighting factors for weight and volume (instead of using only the standard density), and by using real units (instead of not using units at all). The result, a generic definition of chargeable weight, is given below. Chargeable Weight as a Function of Weight and Volume: cw = max {W/wc, (V/vc) chtc}. The generic chargeable weight definition uses three constants: the chargeable tonne conversion constant chtc, the weight constant wc, and the volume constant vc. The chargeable tonne conversion constant has a value of 1,000 chargeable kilograms per chargeable tonne and is only used to achieve unit consistency. The weight constant has a value of 1 kilogram per chargeable kilogram and is used to indicate how many kilograms of pure weight can be tendered for each chargeable kilogram, while the volume constant has a value of 6 cubic metres per chargeable tonne and is used to indicate how many litres of pure volume can be tendered for each chargeable kilogram. Hence, the weight and volume constants form the upper bounds of how many kilograms and litres are allowed in one chargeable kilogram. The weight and volume constants are formally introduced on the next page. 25.

(38) PART II: AIR CARGO PROPERTIES. Weight and Volume Constants for the IATA Standard Density: wc+ 1 [kg/chkg]+ weight constant vc+ 6 [mc/cht]+ volume constant. Although the standard density can be derived from the weight and volume constants by means of simple division, the weight and volume constants cannot be derived solely from the standard density. This is because the weight and volume constants have not only to relate to each other but also to the chargeable weight. In other words, the weight and volume constants are the weight and volume weighting factors in calculating an item’s chargeable weight and, even though there may be many weight and volume constants with a volume-to-weight ratio equal to the standard density, there is only one set of weight and volume constants that has volume-to-chargeable weight and weight-to-chargeable weight ratios that match the definition of chargeable weight. The use of the weight and volume constants not only has the advantage that the weighting factors are now readily available, it also has the benefit that the weight and volume constants can be used independently, as in the generic definition of the chargeable weight above. Essentially, the purpose of computing the chargeable weight of freight is to marry the weight of an item with its volume to create a broader basis for revenue calculation. If the revenue calculation were based on weight or volume alone, either low-density freight or high-density freight would be unfairly penalised. O’Connor describes chargeable weight as “the dimensional weight policy of an airline” (O’Connor 2001, page 191). He continues: “For articles of very low density, such as cut flowers and empty plastic bottles, the carriers assume a weight higher than the actual weight and compute the rate on that presumed higher weight. That is, the cube [i.e., the volume] of the shipment is measured, and what is really a fictitious weight is used when looking up the rate in the general commodity rate schedule” (ibid., page 191; see also Holloway 2003, page 142). The chargeable weight of an item can also be used as a proxy for its size. Furthermore, the demand for transporting items can be measured in terms of their chargeable weights. To illustrate the concept of chargeable weight, Figure 3 gives some weight and volume combinations which lead to the same chargeable weight. One hundred chargeable kilograms, for example, could be 100 kilograms with a volume up to 0.6 cubic metres, or 0.6 cubic metres with any weight up to 100 kilograms.. 26.

(39) 3 INITIAL AND DERIVED PROPERTIES IN AIR CARGO 50. 40. 60. 30. 20. Although Vo the main reason for computing chargeable weight is to have a lume [mc] comprehensive basis for calculating revenue, the chargeable weight offers more: it is a universal economic term, it can be used to reduce the number Weight,of volume and chargeable weightand (6:1) it has a favourable dimensional scaling. different units,. 10. 4. 50%. 2. 300 chkg 200 chkg. 1. 0%. 6:1. 400 chkg. 100 chkg 0. 6. 8. 10. …. 0. 1. 2. 3. sity [mc/ton]. o a change of standard density. 5. 6. Figure 3: Weight, volume, and chargeable weight. 1). Since these features of the chargeable weight are somewhat complex, they Chargeable Weight [chkg] 5:1 6:1 are discussed in more 10000 detail below.. ble Weight [chkg]. 6:1 9000. 9000. ❖. 8000. Chargeable weight is a universal economic term. 8000 7500. 7000. 7000 To prepare the discussion on this feature, some background infor6000 mation on the use of the chargeable weight in practice will first be 5000 5000 considered. Commonly, chargeable weight is only calculated for 4000 bookings and booking requests, and not for flight capacities. In other 3000 2500 words, the demand of a customer is stated as a request for a charge2000 able weight with a1000 certain density, whereas the supply of the air cargo carrier is stated0as an available weight and volume. These values, i.e., of supply and demand as well20as the30 weights and cannot 0 10 40 50 the volumes, 60 Volume [mc] be directly compared since they have different units. Weight [kg]. 6000. 000. 30. 4. Weight [t]. 1) standard. 100%. Volume [mc]. 150%. 500 chkg. 3. 200%. density: 6 cubic metres per tonne. 600 chkg. 40. 50. 60. lume [mc]. nd chargeable weight (6:1). Weight, volume and chargeable weight (5:1). 6:1. Weight [kg]. 6:1. Fortunately, and this is the point where the chargeable weight steps in as a universal economic term, the chargeable weight can be also 6:1 used to describe the space offered by an air cargo carrier. More 10000 specifically, the flight capacities, which are usually expressed in Density weight and volumeHigh units, can be transformed into a product offer Booking Requests 4:1 7500 • Thus, • • the available weight capacity of a with an economic •unit. flight will be converted into a chargeable weight offer that has a 5000 the available volume capacity will be converted zero density, and into a chargeable weight d = 2 offer that has an infinite density.. • • • •. Low Density Booking Requests. 2500 chkg •. 2500. • d=8 3333 chkg. • • • •. Low Density Booking Requests. 0 30. 40. 50. ume [mc]. Low Density Booking Requests. 60. 0. 10. 20. 30. 40. 50. Volume [mc] Volume critical due to High Density Capacity. 60. 27.

(40) PART II: AIR CARGO PROPERTIES. From this point of view, a customer is not buying a certain weight and volume but a bundle of two different goods, namely some chargeable weight that has a zero density and some chargeable weight that has an infinite density. Rather, the air cargo carrier is not offering mere capacities but some marketable products. Flight capacities of, say, 50 tonnes and 600 cubic metres can be sold as 50,000 chargeable kilograms that have a zero density and as 100,000 chargeable kilograms that have an infinite density (in practice, however, they are sold together). Having restated the supply in terms of chargeable kilograms, the weight supply can be compared with the volume supply, and both can be compared with the demand. As an example, we will consider the demands of two booking requests of 1,000 and 3,000 chargeable kilograms with densities of 4 and 9 cubic metres per tonne respectively. Clearly, in terms of chargeable kilograms, the demand of the second booking request is three times higher than the demand of the first booking request. Now, if the first booking request is confirmed, it will use 1,000 chargeable kilograms of the zero-density supply and 666 chargeable kilograms of the infinitedensity supply, while the second booking request, if confirmed, will use 2,000 chargeable kilograms of the zero-density supply and 3,000 chargeable kilograms of the infinite-density supply. Hence, the volume consumption of the second booking request is three times greater than the weight consumption of the first booking request, and if both requests are confirmed, the remaining weight and volume supply will be 47,000 and 96,334 chargeable kilograms, respectively. In other words, the remaining volume supply will be more than twice as high as the remaining weight supply. It might be argued that a chargeable kilogram of pure weight (i.e., a chargeable kilogram that has a zero density) cannot be easily compared with a chargeable kilogram of pure volume (i.e., with a chargeable kilogram that has an infinite density) but, from an economic point of view, kilograms and cubic metres are only the physical aspects of what can be sold to the customer, and what can be sold to the customer is the chargeable kilogram (albeit with different densities). The benefit of this economic view of weight and volume is also supported by the fact that rates in the air cargo industry are usually quoted per chargeable weight. ❖. Chargeable weight can be used to reduce the number of diﬀerent quantity units. This feature is closely related to the first because any universal term is likely to replace other terms and, in turn, their units. With regard to the chargeable weight, there are two situations:. 28.

(41) 3 INITIAL AND DERIVED PROPERTIES IN AIR CARGO. Where the weight and volume dimensions are independent (as with the weight and volume of flight capacities), a reduction in the number of different units can be achieved by converting all occurrences of weights and volumes into quantities that have a chargeable weight of either zero or infinite density. In addition, where the weight and volume dimensions are not independent (as in the weight and volumes of booking requests), a reduction in the number of different units can be achieved by converting all combinations of weight and volume into quantities that have one chargeable weight and one density. Admittedly, the weight and volume units are not yet completely removed since they are still used in the quantity unit of density (cubic metres per tonne). In Section 2 of Chapter 5, however, this regular density will be replaced by a unitless unified density. ❖. Chargeable weight has favourable dimensional scaling. This feature is mainly used to even out the noticeably different magnitudes of the weight and volume scales, even though in the fifth chapter the scaling feature of the chargeable weight will also be used in developing the unified density. The scaling feature of the chargeable weight is based on the weight and volume consumption of cargo that has a standard density, and the idea behind the dimensional scaling is to use the chargeable weight as a universal scale for weight and volume. From this remark, it is clear that the dimensional scaling is closely connected with other features of the chargeable weight (i.e., the unit reduction feature and the universal term feature). To demonstrate the attraction of dimensional scaling, an example is provided: cargo that has a density of 6 cubic metres per tonne (i.e., cargo that has a standard density) has a weight-to-volume ratio of approximately 166:1, if expressed in kilograms and cubic metres. If expressed in chargeable kilograms, however, the ratio of weight and volume consumptions is only 1:1 (i.e., one chargeable kilogram of zero density per one chargeable kilogram of infinite density). Since the density of typical freight is generally around the standard density, the volume consumption of regular freight—if expressed in chargeable kilograms—does not differ that much from its weight consumption (which should also be expressed in chargeable kilograms in order for it to be comparable).. 29.

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