- Email: [email protected]
Estimation of the occurrence of “short-shipping” of air cargo
Journal of Air Transport Management 16 (2010) 315e319
Contents lists available at ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Estimation of the occurrence of “short-shipping” of air cargo Shinya Hanaoka a, *, Ekachai Phoosanabhongs b a
Department of International Development Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8550, Japan b Transportation Engineering Field, School of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand
a b s t r a c t Many airlines use the main deck of aircraft to carry passengers and belly capacity to accommodate cargo and baggage. When problems regarding the weight and balance requirements of the aircraft arise, the cargo is the first to be considered for unloading: a practice is known as “short-shipping”. This paper develops a simulation model for estimating the probability of occurrence of short-shipping. Risk analysis is used to estimate the uncertainty of several factors such as the weight of passengers, baggage, and fuel. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Since the beginning of commercial aviations, airlines have used the main deck of their planes to carry passengers and the belly hold to accommodate cargo and baggage.1 When weight and balance constraints are exceeded, cargo is generally the first to be considered for unloading largely because cargo does not complain.2 Cargo is also sometimes sacrificed in other situations, e.g., when there are several go-show passengers, there is excess overbooking, or when there is bad weather. “Short shipping” occurs when consignments that are planned to be carried on a selected flight are not loaded for onward delivery on that flight. Flights are planned and monitored by load controllers prior to departure who are responsible for distributing loads and checking whether the aircraft is balanced and in accordance with the load plan. Typically, load planning is performed several hours or days prior to departure, depending on each airline’s policy. This procedure relies on the number of booked passengers to plan operating flights. There can be times when load controllers only leave a small under-load as slack during load planning and hence, if there is a large unplanned increase in the weight of passengers, their baggage, or fuel, short-shipping of cargo will probably occur. Dealing with short shipping is a problem because it is difficult to
* Corresponding author. Tel./fax: þ81 3 5734 3468. E-mail address: [email protected] (S. Hanaoka). 1 The importance of air cargo in international trade has long been recognized (Eaton, 1994) but the economics of the interaction between cargo and passenger traffic has been little studied. 2 Many countries also have legal requirements to compensate passengers who are taken of a contracted flight. In terms of air cargo, routing is normally left to an airline and missing any particular flight does not imply any direct compensation for forwarders or shippers. 0969-6997/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2010.03.007
predict, given the uncertainty in these factors, when it will be undertaken. For example, the weight of passengers and their baggage is a major factor in determining of an aircraft’s cargo capacity but this weight may be different at take-off than estimated during bookings. The paper looks at the economic efficiency of short shipping practices making use of risk analysis within a simulation framework.3 2. Methodology We take as the basis of our analysis the load planning process of a single airline using routine procedures. Two international routes e Bangkok to London and Bangkok to Seoul e are selected because they carry the most passengers on intercontinental flights at Bangkok airport. On average, the weight of passengers and their baggage accounts for almost 70% of aircraft load on both routes. The general characteristics of flights on the two routes are shown in Table 1. The simulation models applied to the two routes are developed separately to reflect their specific characteristics.4 Two main types of information are used (Fig. 1): these concern daily flights and the characteristics of the aircraft used. The former used to develop the simulation model, and the latter to calculate supplementary parameters. These two categories were linked through the procedure for aircraft weight calculation.
3 Strict management of yield has failed to catch on widely in the cargo industry: of the top 20 belly carriers, only five had installed such systems by 2000, and those are limited in scope or are based on outdated technology (Sobie, 2000). 4 Fuel and aircraft balance calculations for each flight are omitted because of inadequate data.
316
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Table 1 General characteristics of the routes studied. Bangkok to
London Seoul
Aircraft type
Boeing 747-400 Boeing 777-200
Seating capacity First (F) class
Business (C) class
Economy (Y) class
All classes
14 N/A
50 55
325 303
389 358
Average distance (km)
Average flying time (h:min.)
Operating day
9540 3686
12:05 05:25
Daily Daily
Fig. 1. Simulation framework.
Daily information on flights was collected from load sheets for three months, November 15, 2004, to February 16, 2005 (see Table 2).5 The sheets for the two studied routes were printed out each day after the departures. The sheets’ data are divided into two periods. The load sheets collected for November 15th to January 16th are used for data analysis and model development and those from January 17th to February 16th are used for model validation. The aircraft registration and type are matched to determine such things as weight limitations (Table 3). A two-sample t-test was used look at differences between data collected on weekdays and weekends. The number of passengers
5 Load sheets are documents reporting the location and weight of all loads on an aircraft, including balance indices and the weight limitations.
and the amount and weight of baggage were initially believed to be higher on weekends than on weekdays; passengers tend to travel on weekends rather than on weekdays. Fridays are considered part of the weekend because flights on both routes were scheduled to depart late at night. The differences between the number of check-in passengers and booked seats (Diff. PAX) by seat class were focused on for each flight. A positive difference implies that the number of go-show passengers is greater than no-shows. The Diff. PAX values by class on the Bangkok to London and Bangkok to Seoul routes are graphically illustrated in Figs. 2 and 3, respectively. It is noted the Indian Ocean Tsunami happened on 26th December 2004. Similarly, the amount and weight of check-in baggage is examined. The planned weight of baggage is calculated by multiplying the number of passengers by the standard weight for
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319 Table 2 Information on flights.
Booked passengers
Check-in passengers
Number and weight of check-in baggage Weight of cargo
Trip fuel (TF)
Take-off fuel (TOF)
Collected to examine the inherent characteristics of operating aircrafts such as basic empty weight (BW), weight limitations, etc. Number of pilots and flight attendants. The weight of the empty aircraft including standard, version, route, and pantry equipment and the crew weight. Manually recorded before beginning load planning. The number recorded two days before departure was set as the controlled parameter. Number of passengers who actually checked in aboard the flights. Basically, the standard weights of passengers were used to convert the number to weight. The amount of baggage actually contained in the compartment of operating aircrafts. The entire cargo weight contained in the belly of the operating aircraft, which was separated by the weight of freight and mail in kg. Details on cargo such as dimensions and individual weights were ignored due to inaccessibility in this study. The estimated amount (kg) of fuel needed for an operating aircraft taking off from the origin to the destination. The amount (kg) of fuel on board when the aircraft is ready for take-off on the runway. It is summed from all fuel used for achieving flight.
baggage on a seat class basis. Because there are no significant differences between weekends and weekdays no adjustment factor is needed. Statistical approaches were used to manipulate the data suitable for modeling and chi-square (chi-sq), Anderson-Darling (A-D), and Kolmogorov-Smirnov (K-S) tests used to select suitable probability distributions. The Diff. PAX value and the difference between the actual and estimated weight of containers (Diff. Containers) are used as variables in the load planning process. Diff PAX is also subdivided by three seat classes: Diff. First PAX, Diff. Business PAX, and Diff. Economy PAX. Table 4 gives details of the calculations.6 The ranges of the probability distributions are truncated to conform to the nature of the variables. The majority of the probability distributions have limits at either positive or negative infinity that are changed to reflect the minimum or maximum possible occurrences. The selected probability distributions are used in the simulation. The probabilistic values are summed across the number of booked seats and weight of the projected containers to deduce the number of check-in passengers and weight of actual containers. Regression analysis is used to identify relationships between the input variables. The relationships between the number of passengers and their weight, the number of passengers and baggage weight, and zero fuel weight (ZFW) and amount of trip fuel (TF) are examined.7 The expected values calculated by substituting independent values into the regression equations are treated as the means of possible occurrences. The residuals are considered the uncertainty
6
For chi-sq tests, differences are significant if the P-value is less than 0.05. The values for A-D and K-S show how well the probability distribution fits with the assigned data set. The chi-sq tests have no P-value lower than 0.05, and the A-D and K-S tests indicate the probability distribution fits the data set. 7 ZFW is the weight of an aircraft including all loads except fuel, and TF is the estimated amount of fuel needed to reach the destination. The weight of passengers, baggage, and TF were set as dependent variables predicted by the independent variables such as the number of passengers, number of passengers by class, and the ZFW. All three relationships were focused on individually for each route.
Set according to the seat class, which are first, business, and economy. Generally, the seat configuration differs according to the aircraft version. Configuration and capacity Depends on the number of containers and pallets of compartments used for holding cargo in the compartments. Basic empty weight Weight of the airframe, engines, and all items of (BW) operating weight that have fixed locations and are permanently installed in the aircraft. This weight is generally added to the weights for catering, equipment, and crew for the dry operating weight (DOW). Maximum landing Maximum permitted weight of the aircraft at weight (MLAW) landing. It is limited by the structure of the aircraft, especially the landing gear. Maximum take-off Maximum permitted weight of the aircraft at brake weight (MTOW) release for take-off. It is limited by the structure of the aircraft and thrust of its engines. Maximum zero fuel Maximum weight of the aircraft with load on board weight (MZFW) except fuel. It is limited by the structure of the wing joints (where the wings are attached to the fuselage of the aircraft). Seating capacity
Difference between Check-in and Booking Passengers
Crew Dry operating weight (DOW)
Table 3 Aircraft characteristics.
60 40 20 0 -20 -40 -60
Variable Diff. F Diff. C Diff. Y
-80 -100
Day 15 20 Month Nov.
25
30
5 10 Dec.
15
20
25
30
4 9 Jan.
14
Fig. 2. Differences between the number of check-in and booked passengers: Bangkok to London.
Difference between Check-in and Booking Passengers
Aircraft version and registration
317
50 40 30 20 10 0 -10 -20 -30
Variable Diff. C Diff. Y
-40 -50
Day 15 20 Month Nov.
25
30
5 10 Dec.
15
20
25
30
4 9 Jan.
14
Fig. 3. Differences between the number of check-in and booked passengers: Bangkok to Seoul.
318
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Table 4 Probability distributions of variables. Variables
Distribution
Parameters of distribution
Min
Bangkok to London Diff. First PAX Diff. Business PAX Diff. Economy PAX Diff. Containers
Log-logistic Log-logistic Logistic Logistic
(11.05, 11.55, 9.67) (13.46, 13.98, 8.32) (15.68, 7.40) (126.52, 82.59)
5 7 50 600
10 15 20 600
Bangkok to Seoul Diff. Business PAX Diff. Economy PAX Diff. Containers
Log-logistic Extreme value Log-logistic
(6.73, 8.33, 3.05) (15.80, 12.26) (1052, 1102.5, 4.38)
6 40 900
30 30 2200
in the expected value and are assumed to be normally distributed. The standard deviation of the residuals are used to define the shape of the normal distribution modeled as the uncertainty in the expected value. The uncertainty distribution functions for the two Table 5 Uncertainty in terms of probability distributions. Uncertainty in Probability distribution weight of (b0 þ b1x1 þ b2x2., s) Bangkok to London Passenger Normal (78*Check-in PAX, 125) Baggage Normal (625 þ 57*Check-in F þ 26*Check-in C þ 23*Check-in Y, 375) Trip fuel (TF) Uniform (46382 þ 0.773*ZFW-7000, 46382 þ 0.773*ZFW þ 5500)
Range of residual
R2
(300, 300) 0.99 (1000, 1000) 0.95 (7000, 5500) 0.59
Bangkok to Seoul Passenger Normal (78*Check-in PAX, 200) (600, 600) 0.99 Baggage Normal (740 þ 20*Check-in C þ 11*Check- (1000, 1000) 0.76 in Y, 410) Trip fuel (TF) Uniform (0.166*ZFW-1500, 0.166*ZFW (1500, 2000) 0.54 þ 2000)
Max
Chi-Sq (P-Value)
A-D
K-S
5.97 15.93 13.31 13.59
(0.65) (0.05) (0.10) (0.09)
0.88 1.39 0.41 1.32
0.153 0.160 0.065 0.122
15.40 (0.05) 5.83 (0.67) 8.86 (0.35)
0.48 0.34 0.86
0.110 0.076 0.095
routes are shown in Table 5. Standard weights for passengers are used to convert the number of passengers into the weight; the standard passenger weights being 78, 35, and 10 kg for adults, children, and infants. The uncertainty in the passenger weight is small compared with the actual weight, which is why the R2 values for the weight of the passengers on both routes are relatively high. When load controllers begin load planning, they estimate the baggage weight by multiplying the weight quota by the number of booked seats according to seat classes; in this case, the weight quotas are 30, 30, and 20 kg for first, business, and economy class. Then, the estimated baggage weight is replaced with the actual weight when passengers checked in baggage at the airline counter. The strong relationship between the baggage weight and number of passengers on the Bangkok to London route indicates that the majority of passengers fully utilized their weight quotas. The R2 value are high given the small dispersion. In general, the TF weight tends to rely on the ZFW, however, weather conditions, flight path, and flight profile are also taken into account. The lack of information about these effects causes uncertainty in the TF weight; for both routes, the relationship between
Fig. 4. Structure of the simulation model.
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Fig. 5. Generated probability distributions for under-load on the Bangkok to Seoul Route.
the TF weight and ZFW is weak. A uniform distribution is used to model the TF uncertainty instead of a normal distribution based on R2 values. Due to the range of the residuals, the flight to London has a larger dispersion than the one to Seoul; the former has a greater chance of encountering a wide variety of situations given the longer flight distance. The simulation models replicate the procedure for the aircraft weight calculations. Variables in the form of probability distributions and the uncertainties modeled by regression equations were applied to the developed it. A schematic of the process for aircraft weight calculation in the simulation model is seen in Fig. 4. Parameters needed as inputs to the simulation model include the number of booked seats by class and the weight of the freight, mail, and extra fuel. Operating flight characteristics such as the number of crew-members and weight limitation were also required. Monte Carlo simulations were performed to generate probability distributions using @Risk 4.5 Professional (Palisade Corporation, 2004).
3. Results The flight selected the Bangkok to Seoul route had 52 and 302 booked seats in business and economy classes and it carried 16,455 kg of the freight and no mail. The aircraft required 12,300 kg of extra fuel. The simulation was then run to generate the probability distribution of the under-load (Fig. 5).
319
Determination of the threshold under-load value that may cause short-shipping is based on interviews with airline employees. The amount of cargo being shorted seems to be depend on the type of container; container maximum gross weights range from 1500 to 6000 kg for all aircraft types. If there are any problems regarding the weight and balance requirements, then the smallest container (1500 kg) is the first unloaded; the threshold under which shortshipping is seen to occur is thus set at 1500 kg. The probability distribution for under-loading shown in Fig. 5 shows there was a 91.6% possibility that the under-load was lower than 1500 kg with a mean for all possible occurrences of an 149.3 kg overload. The number of check-in passengers is 348 in this case. The generated probability distribution indicated a 39% possibility that the number of check-in passengers was over 348, with a mean of 344. In this situation, the load controllers should reduce the weight of the cargo. Sensitivity analysis for the assigned weight of the cargo may assist controllers to estimate and decide on the weight of incoming cargo to avoid short-shipping. The airline would not disclose the data on real occurrences of short-shipping and, therefore, for model validation, the simulation of under-load for each day are run individually, and the results were compared with the actual data, two-sample t-tests being used for validation. The results of validations show that the model offers good estimates the means of under-loading with P-values of 0.919 and 0.774 for the t-tests for the Bangkok to London and to Seoul routes, respectively indicating no significant difference between the means of the generated probability distributions of under-load and the actual under-load. 4. Conclusions Simulation models are used to estimate the occurrence of shortshipping in two case studies with the aim of providing load controllers with better information to estimate the probabilities of short-shipping being needed. If load controllers assess that there is little possibility of short-shipping being needed, they may decide to increase the weight of incoming cargo in their load plans. Much depends, however, on the inherent characteristics of each route. References Eaton, J., 1994. The crazy economics of air freight. Intereconomics 29, 33e37. Palisade Corporation, 2004. @Risk 4.5 professional. Palisade Corporation, New York. Sobie, B., 2000. Freight’s yield signs. Air Cargo World 9 (7) Available from. http:// www.aircargoworld.com/archives/feat1_jul00.htm.
Contents lists available at ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Estimation of the occurrence of “short-shipping” of air cargo Shinya Hanaoka a, *, Ekachai Phoosanabhongs b a
Department of International Development Engineering, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8550, Japan b Transportation Engineering Field, School of Engineering and Technology, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, Thailand
a b s t r a c t Many airlines use the main deck of aircraft to carry passengers and belly capacity to accommodate cargo and baggage. When problems regarding the weight and balance requirements of the aircraft arise, the cargo is the first to be considered for unloading: a practice is known as “short-shipping”. This paper develops a simulation model for estimating the probability of occurrence of short-shipping. Risk analysis is used to estimate the uncertainty of several factors such as the weight of passengers, baggage, and fuel. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Since the beginning of commercial aviations, airlines have used the main deck of their planes to carry passengers and the belly hold to accommodate cargo and baggage.1 When weight and balance constraints are exceeded, cargo is generally the first to be considered for unloading largely because cargo does not complain.2 Cargo is also sometimes sacrificed in other situations, e.g., when there are several go-show passengers, there is excess overbooking, or when there is bad weather. “Short shipping” occurs when consignments that are planned to be carried on a selected flight are not loaded for onward delivery on that flight. Flights are planned and monitored by load controllers prior to departure who are responsible for distributing loads and checking whether the aircraft is balanced and in accordance with the load plan. Typically, load planning is performed several hours or days prior to departure, depending on each airline’s policy. This procedure relies on the number of booked passengers to plan operating flights. There can be times when load controllers only leave a small under-load as slack during load planning and hence, if there is a large unplanned increase in the weight of passengers, their baggage, or fuel, short-shipping of cargo will probably occur. Dealing with short shipping is a problem because it is difficult to
* Corresponding author. Tel./fax: þ81 3 5734 3468. E-mail address: [email protected] (S. Hanaoka). 1 The importance of air cargo in international trade has long been recognized (Eaton, 1994) but the economics of the interaction between cargo and passenger traffic has been little studied. 2 Many countries also have legal requirements to compensate passengers who are taken of a contracted flight. In terms of air cargo, routing is normally left to an airline and missing any particular flight does not imply any direct compensation for forwarders or shippers. 0969-6997/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2010.03.007
predict, given the uncertainty in these factors, when it will be undertaken. For example, the weight of passengers and their baggage is a major factor in determining of an aircraft’s cargo capacity but this weight may be different at take-off than estimated during bookings. The paper looks at the economic efficiency of short shipping practices making use of risk analysis within a simulation framework.3 2. Methodology We take as the basis of our analysis the load planning process of a single airline using routine procedures. Two international routes e Bangkok to London and Bangkok to Seoul e are selected because they carry the most passengers on intercontinental flights at Bangkok airport. On average, the weight of passengers and their baggage accounts for almost 70% of aircraft load on both routes. The general characteristics of flights on the two routes are shown in Table 1. The simulation models applied to the two routes are developed separately to reflect their specific characteristics.4 Two main types of information are used (Fig. 1): these concern daily flights and the characteristics of the aircraft used. The former used to develop the simulation model, and the latter to calculate supplementary parameters. These two categories were linked through the procedure for aircraft weight calculation.
3 Strict management of yield has failed to catch on widely in the cargo industry: of the top 20 belly carriers, only five had installed such systems by 2000, and those are limited in scope or are based on outdated technology (Sobie, 2000). 4 Fuel and aircraft balance calculations for each flight are omitted because of inadequate data.
316
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Table 1 General characteristics of the routes studied. Bangkok to
London Seoul
Aircraft type
Boeing 747-400 Boeing 777-200
Seating capacity First (F) class
Business (C) class
Economy (Y) class
All classes
14 N/A
50 55
325 303
389 358
Average distance (km)
Average flying time (h:min.)
Operating day
9540 3686
12:05 05:25
Daily Daily
Fig. 1. Simulation framework.
Daily information on flights was collected from load sheets for three months, November 15, 2004, to February 16, 2005 (see Table 2).5 The sheets for the two studied routes were printed out each day after the departures. The sheets’ data are divided into two periods. The load sheets collected for November 15th to January 16th are used for data analysis and model development and those from January 17th to February 16th are used for model validation. The aircraft registration and type are matched to determine such things as weight limitations (Table 3). A two-sample t-test was used look at differences between data collected on weekdays and weekends. The number of passengers
5 Load sheets are documents reporting the location and weight of all loads on an aircraft, including balance indices and the weight limitations.
and the amount and weight of baggage were initially believed to be higher on weekends than on weekdays; passengers tend to travel on weekends rather than on weekdays. Fridays are considered part of the weekend because flights on both routes were scheduled to depart late at night. The differences between the number of check-in passengers and booked seats (Diff. PAX) by seat class were focused on for each flight. A positive difference implies that the number of go-show passengers is greater than no-shows. The Diff. PAX values by class on the Bangkok to London and Bangkok to Seoul routes are graphically illustrated in Figs. 2 and 3, respectively. It is noted the Indian Ocean Tsunami happened on 26th December 2004. Similarly, the amount and weight of check-in baggage is examined. The planned weight of baggage is calculated by multiplying the number of passengers by the standard weight for
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319 Table 2 Information on flights.
Booked passengers
Check-in passengers
Number and weight of check-in baggage Weight of cargo
Trip fuel (TF)
Take-off fuel (TOF)
Collected to examine the inherent characteristics of operating aircrafts such as basic empty weight (BW), weight limitations, etc. Number of pilots and flight attendants. The weight of the empty aircraft including standard, version, route, and pantry equipment and the crew weight. Manually recorded before beginning load planning. The number recorded two days before departure was set as the controlled parameter. Number of passengers who actually checked in aboard the flights. Basically, the standard weights of passengers were used to convert the number to weight. The amount of baggage actually contained in the compartment of operating aircrafts. The entire cargo weight contained in the belly of the operating aircraft, which was separated by the weight of freight and mail in kg. Details on cargo such as dimensions and individual weights were ignored due to inaccessibility in this study. The estimated amount (kg) of fuel needed for an operating aircraft taking off from the origin to the destination. The amount (kg) of fuel on board when the aircraft is ready for take-off on the runway. It is summed from all fuel used for achieving flight.
baggage on a seat class basis. Because there are no significant differences between weekends and weekdays no adjustment factor is needed. Statistical approaches were used to manipulate the data suitable for modeling and chi-square (chi-sq), Anderson-Darling (A-D), and Kolmogorov-Smirnov (K-S) tests used to select suitable probability distributions. The Diff. PAX value and the difference between the actual and estimated weight of containers (Diff. Containers) are used as variables in the load planning process. Diff PAX is also subdivided by three seat classes: Diff. First PAX, Diff. Business PAX, and Diff. Economy PAX. Table 4 gives details of the calculations.6 The ranges of the probability distributions are truncated to conform to the nature of the variables. The majority of the probability distributions have limits at either positive or negative infinity that are changed to reflect the minimum or maximum possible occurrences. The selected probability distributions are used in the simulation. The probabilistic values are summed across the number of booked seats and weight of the projected containers to deduce the number of check-in passengers and weight of actual containers. Regression analysis is used to identify relationships between the input variables. The relationships between the number of passengers and their weight, the number of passengers and baggage weight, and zero fuel weight (ZFW) and amount of trip fuel (TF) are examined.7 The expected values calculated by substituting independent values into the regression equations are treated as the means of possible occurrences. The residuals are considered the uncertainty
6
For chi-sq tests, differences are significant if the P-value is less than 0.05. The values for A-D and K-S show how well the probability distribution fits with the assigned data set. The chi-sq tests have no P-value lower than 0.05, and the A-D and K-S tests indicate the probability distribution fits the data set. 7 ZFW is the weight of an aircraft including all loads except fuel, and TF is the estimated amount of fuel needed to reach the destination. The weight of passengers, baggage, and TF were set as dependent variables predicted by the independent variables such as the number of passengers, number of passengers by class, and the ZFW. All three relationships were focused on individually for each route.
Set according to the seat class, which are first, business, and economy. Generally, the seat configuration differs according to the aircraft version. Configuration and capacity Depends on the number of containers and pallets of compartments used for holding cargo in the compartments. Basic empty weight Weight of the airframe, engines, and all items of (BW) operating weight that have fixed locations and are permanently installed in the aircraft. This weight is generally added to the weights for catering, equipment, and crew for the dry operating weight (DOW). Maximum landing Maximum permitted weight of the aircraft at weight (MLAW) landing. It is limited by the structure of the aircraft, especially the landing gear. Maximum take-off Maximum permitted weight of the aircraft at brake weight (MTOW) release for take-off. It is limited by the structure of the aircraft and thrust of its engines. Maximum zero fuel Maximum weight of the aircraft with load on board weight (MZFW) except fuel. It is limited by the structure of the wing joints (where the wings are attached to the fuselage of the aircraft). Seating capacity
Difference between Check-in and Booking Passengers
Crew Dry operating weight (DOW)
Table 3 Aircraft characteristics.
60 40 20 0 -20 -40 -60
Variable Diff. F Diff. C Diff. Y
-80 -100
Day 15 20 Month Nov.
25
30
5 10 Dec.
15
20
25
30
4 9 Jan.
14
Fig. 2. Differences between the number of check-in and booked passengers: Bangkok to London.
Difference between Check-in and Booking Passengers
Aircraft version and registration
317
50 40 30 20 10 0 -10 -20 -30
Variable Diff. C Diff. Y
-40 -50
Day 15 20 Month Nov.
25
30
5 10 Dec.
15
20
25
30
4 9 Jan.
14
Fig. 3. Differences between the number of check-in and booked passengers: Bangkok to Seoul.
318
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Table 4 Probability distributions of variables. Variables
Distribution
Parameters of distribution
Min
Bangkok to London Diff. First PAX Diff. Business PAX Diff. Economy PAX Diff. Containers
Log-logistic Log-logistic Logistic Logistic
(11.05, 11.55, 9.67) (13.46, 13.98, 8.32) (15.68, 7.40) (126.52, 82.59)
5 7 50 600
10 15 20 600
Bangkok to Seoul Diff. Business PAX Diff. Economy PAX Diff. Containers
Log-logistic Extreme value Log-logistic
(6.73, 8.33, 3.05) (15.80, 12.26) (1052, 1102.5, 4.38)
6 40 900
30 30 2200
in the expected value and are assumed to be normally distributed. The standard deviation of the residuals are used to define the shape of the normal distribution modeled as the uncertainty in the expected value. The uncertainty distribution functions for the two Table 5 Uncertainty in terms of probability distributions. Uncertainty in Probability distribution weight of (b0 þ b1x1 þ b2x2., s) Bangkok to London Passenger Normal (78*Check-in PAX, 125) Baggage Normal (625 þ 57*Check-in F þ 26*Check-in C þ 23*Check-in Y, 375) Trip fuel (TF) Uniform (46382 þ 0.773*ZFW-7000, 46382 þ 0.773*ZFW þ 5500)
Range of residual
R2
(300, 300) 0.99 (1000, 1000) 0.95 (7000, 5500) 0.59
Bangkok to Seoul Passenger Normal (78*Check-in PAX, 200) (600, 600) 0.99 Baggage Normal (740 þ 20*Check-in C þ 11*Check- (1000, 1000) 0.76 in Y, 410) Trip fuel (TF) Uniform (0.166*ZFW-1500, 0.166*ZFW (1500, 2000) 0.54 þ 2000)
Max
Chi-Sq (P-Value)
A-D
K-S
5.97 15.93 13.31 13.59
(0.65) (0.05) (0.10) (0.09)
0.88 1.39 0.41 1.32
0.153 0.160 0.065 0.122
15.40 (0.05) 5.83 (0.67) 8.86 (0.35)
0.48 0.34 0.86
0.110 0.076 0.095
routes are shown in Table 5. Standard weights for passengers are used to convert the number of passengers into the weight; the standard passenger weights being 78, 35, and 10 kg for adults, children, and infants. The uncertainty in the passenger weight is small compared with the actual weight, which is why the R2 values for the weight of the passengers on both routes are relatively high. When load controllers begin load planning, they estimate the baggage weight by multiplying the weight quota by the number of booked seats according to seat classes; in this case, the weight quotas are 30, 30, and 20 kg for first, business, and economy class. Then, the estimated baggage weight is replaced with the actual weight when passengers checked in baggage at the airline counter. The strong relationship between the baggage weight and number of passengers on the Bangkok to London route indicates that the majority of passengers fully utilized their weight quotas. The R2 value are high given the small dispersion. In general, the TF weight tends to rely on the ZFW, however, weather conditions, flight path, and flight profile are also taken into account. The lack of information about these effects causes uncertainty in the TF weight; for both routes, the relationship between
Fig. 4. Structure of the simulation model.
S. Hanaoka, E. Phoosanabhongs / Journal of Air Transport Management 16 (2010) 315e319
Fig. 5. Generated probability distributions for under-load on the Bangkok to Seoul Route.
the TF weight and ZFW is weak. A uniform distribution is used to model the TF uncertainty instead of a normal distribution based on R2 values. Due to the range of the residuals, the flight to London has a larger dispersion than the one to Seoul; the former has a greater chance of encountering a wide variety of situations given the longer flight distance. The simulation models replicate the procedure for the aircraft weight calculations. Variables in the form of probability distributions and the uncertainties modeled by regression equations were applied to the developed it. A schematic of the process for aircraft weight calculation in the simulation model is seen in Fig. 4. Parameters needed as inputs to the simulation model include the number of booked seats by class and the weight of the freight, mail, and extra fuel. Operating flight characteristics such as the number of crew-members and weight limitation were also required. Monte Carlo simulations were performed to generate probability distributions using @Risk 4.5 Professional (Palisade Corporation, 2004).
3. Results The flight selected the Bangkok to Seoul route had 52 and 302 booked seats in business and economy classes and it carried 16,455 kg of the freight and no mail. The aircraft required 12,300 kg of extra fuel. The simulation was then run to generate the probability distribution of the under-load (Fig. 5).
319
Determination of the threshold under-load value that may cause short-shipping is based on interviews with airline employees. The amount of cargo being shorted seems to be depend on the type of container; container maximum gross weights range from 1500 to 6000 kg for all aircraft types. If there are any problems regarding the weight and balance requirements, then the smallest container (1500 kg) is the first unloaded; the threshold under which shortshipping is seen to occur is thus set at 1500 kg. The probability distribution for under-loading shown in Fig. 5 shows there was a 91.6% possibility that the under-load was lower than 1500 kg with a mean for all possible occurrences of an 149.3 kg overload. The number of check-in passengers is 348 in this case. The generated probability distribution indicated a 39% possibility that the number of check-in passengers was over 348, with a mean of 344. In this situation, the load controllers should reduce the weight of the cargo. Sensitivity analysis for the assigned weight of the cargo may assist controllers to estimate and decide on the weight of incoming cargo to avoid short-shipping. The airline would not disclose the data on real occurrences of short-shipping and, therefore, for model validation, the simulation of under-load for each day are run individually, and the results were compared with the actual data, two-sample t-tests being used for validation. The results of validations show that the model offers good estimates the means of under-loading with P-values of 0.919 and 0.774 for the t-tests for the Bangkok to London and to Seoul routes, respectively indicating no significant difference between the means of the generated probability distributions of under-load and the actual under-load. 4. Conclusions Simulation models are used to estimate the occurrence of shortshipping in two case studies with the aim of providing load controllers with better information to estimate the probabilities of short-shipping being needed. If load controllers assess that there is little possibility of short-shipping being needed, they may decide to increase the weight of incoming cargo in their load plans. Much depends, however, on the inherent characteristics of each route. References Eaton, J., 1994. The crazy economics of air freight. Intereconomics 29, 33e37. Palisade Corporation, 2004. @Risk 4.5 professional. Palisade Corporation, New York. Sobie, B., 2000. Freight’s yield signs. Air Cargo World 9 (7) Available from. http:// www.aircargoworld.com/archives/feat1_jul00.htm.