Optimizing the load factor for cargo ﬂights by using standby containers

(1)

Optimizing the load factor for

cargo flights by using standby

containers

Master’s Thesis Operations Research

November 22, 2011

Author:

S. Meijer Timmerman Thijssen

(2)

Master’s Thesis Econometrics, Operations Research and Actuarial Studies

(3)

Optimizing the load factor for cargo flights by using

standby containers

Steven Meijer Timmerman Thijssen

Abstract

At KLM Cargo, freight is delivered at the Schiphol hub daily. Some freight arrives by truck and is loaded onto an aircraft. Other freight arrives by air and is either transferred to a connecting flight or loaded onto a truck. For outbound flights the freight has to be repacked onto special air transport containers and pallets, after which the goods are transported to the aircraft.

Due to, for instance, delayed shipment arrivals, customs checks or incomplete paperwork, it may happen that the planned cargo cannot be loaded onto the planned flight, reducing the average load factor. On most flights passengers and cargo are hauled. If less passengers show up than expected or if the total amount of baggage is less than planned, additional cargo capacity may be available. The use of standby containers can mitigate this effect. Such containers hold cargo which is planned to be on a later flight but is already present in the warehouse. These standby containers are transported to the aircraft along with the other freight, and until several minutes prior to departure the decision can be made whether a standby container will be loaded.

Currently, there is insufficient manpower to build standby containers for all flights, so choices need to be made on which standby containers to build. The goal of this research is to optimize the load factor for outbound flights by the use of standby containers, under the given capacity restrictions. A standby con-tainer does not directly increase the load factor. By loading a standby concon-tainer the shipments in the container are transported before the date they were booked on. Hence, flights should be selected for which the created container position can be resold in order to increase the load factor. By computing the probability that a standby container is loaded, a ranking can be made of possible standby containers.

(4)

(5)

Introduction

Most airlines combine passenger transport with freight transport, especially on long-haul flights. Nearly all commercial passenger aircraft have a cargo section in the belly, where for instance passengers’ luggage is stowed. In middle- and long-range aircraft a rather large space is left which can be filled with cargo, as these are mostly wide-body aircraft. There are also aircraft which are mixed, so-called combi-aircraft; the front section is configured for passengers and the rear for cargo. Finally there are full freighters, which carry cargo only. KLM operates the largest fleet of combi-aircraft of all airlines, along with a large number of ordinary passenger aircraft. KLM also owns a small number of full freighters, but these have been leased to Martinair which is also part of Air France-KLM, but operates as an individual company. In order to get a clear view on the problem, this chapter discusses the process at KLM Cargo, the department in charge of freight transport.

The transport of freight by air involves several parties. The company that wants to ship a parcel from A to B is called the shipper. The shipper contracts an agent to arrange the transport for him. In turn, the agent books a flight with an airline, and takes care of the required documents. The airline delivers the cargo at the destination airport, where it is collected by the broker. The final step is that the broker delivers the cargo at the receiving party; the consignee. Figure 1.1 shows this process schematically.

Figure 1.1: Schematic representation of parties involved

The involvement of KLM starts by deciding which routes to operate the

(8)

ing season (summer/winter). These decisions are made without direct influence of KLM Cargo. Once the schedule has been made and the different types of aircraft have been assigned to the routes, the revenue management department (RM) comes into play. Although volume is often the constraining factor, cargo is priced based on its weight, so RM decides on the rate per kilo that should be charged for each different route. For low-density shipments a rule of thumb is applied to ensure enough revenue. For shipments with a density of less than 167 kilos per cubic meter the price is based on volume instead of weight. The price for a cubic meter of low-density freight is then 167 times the per kilo price for that destination.

Using this information so-called entry conditions are computed. These are the minimum prices that have to be charged for a cubic meter, which are com-puted separately for each flight (date and destination). Based on this price and expected demand, RM decides which percentage of the cargo hold will be sold in fixed contracts to large clients, and which percentage may be sold freely. Also, a small part of the available space is reserved for light packages (< 100 kg) and high yield shipments. This last part can be sold to clients willing to pay a high price in order to ship a package last-minute.

Once the sales transactions have been completed, the bookings are handed over to the operations department 24 hours prior to departure. This depart-ment is in charge of hauling the freight from the different European outstations to Amsterdam, and loading it onto the designated flight, and vice versa. If all goes well trucks arrive at a preset time, after which ready-made pallets and containers are stored in the Physical Cargo Handling System (PCHS), an auto-mated storage system in the warehouse. Arriving freight that has yet to be built onto a ULD (Unit Load Device, see Section B.2) can be stored in designated buffers in the warehouse. Several hours prior to departure, a planner at one of the Worldports (WP1/WP2) checks if all cargo is on site, and makes sure it is loaded onto the correct pallets and containers. Once this has been done the ULDs are again stored in the PCHS. An hour prior to departure, the ULDs are picked up by the transport department and brought to the aircraft.

Unfortunately several issues can occur, causing this process not to function optimally. For instance, the volume and weight given in the booking information may differ from the actual volume and weight. If a shipment is larger than booked it may not fit, if it is smaller the aircraft will be underloaded. Also, there can be issues with the documents, or customs can delay or even prohibit a certain shipment from being transported. Even though a flight is fully booked in the planning, it may well be that in practice a shipment is left behind, leaving the aircraft with an open position in the cargo hold.

(9)

open positions, which leads to more available space for cargo, albeit in the very last stage prior to departure. It has previously been shown at KLM that there is room for improvement here; there either may still be cargo in the warehouse with the same destination, or the sales department could have sold more capacity. Air cargo capacity is perishable; once an aircraft departs, unused capacity is lost irrevocably. Hence, airlines are eager to utilize all such opportunities.

One way to take advantage of these opportunities is the use of so-called standby containers (SBCs). An SBC is an extra container prepared for a flight, filled with freight for the same destination but booked on a later flight. This SBC is transported to the platform along with the other cargo. In the very last stage the Team Leader Turn-around (TLT) decides whether the SBC can be loaded on the aircraft. If it is loaded, this opens up a position on the flight on which the cargo was originally booked. If not, the contents will be loaded onto the flight they were originally booked on.

An SBC can cost slightly more time to build than an ordinary container. Depending on what shipments are loaded in the SBC, the planning department has to change the bookings for this freight, and the builders have to gather these parcels from the warehouse. Ideally, once an SBC has been built for a certain destination, it is loaded onto the first flight departing to that destination. If there is no empty position, it will be returned to the warehouse, where there are three options. Either it can be re-used as a standby container the next day, or all the shipments are booked on tomorrows flight so it can be loaded as an ordinary container. The third option is that some, but not all contents are booked on the flight tomorrow, so these shipments may have to be offloaded from the container. Offloading or breaking down a container costs extra time, so preferably a container can be re-used as SBC until at some point it can be loaded.

We need to find a way to select the appropriate flights for which we want to build these containers, and which freight to use. On the one hand we need to have a sufficient amount of cargo in the warehouse in order to be able to fill an entire container. Given that the number of standby containers that can be built is limited, the ones that are built should be as full as possible. On the other hand we want to do this for the flights with a high probability for actually loading the SBC. A third aspect of the problem is the sales department. If freight can be hauled before the date that it is booked on, this does not directly improve the load factor. Only when the created open position is resold will there be additional profits.

(10)

(11)

Chapter 2

Problem description

This research focuses on the operations in the Schiphol hub. The following sections include an analysis of the processes in the hub, and a more precise explanation of the problem at hand.

2.1 Current situation

In the air transport sector there is an urge to work more cost efficiently due to high fuel prices and the competitiveness of the market. At KLM Cargo this leads to a number of initiatives, such as improving productivity and thereby decreasing personnel expenses. One of these initiatives is researching the possi-bility to increase the load factor, since the more capacity sold (at a competitive price), the higher the revenue. In order to optimize the load factor on outgoing flights several aspects are being researched at the hub, one of which focuses on the use of standby containers. Currently, there is no framework on which the decision to build an SBC is based. It is up to the planner in charge to decide if an SBC should be built and what freight should be loaded in this SBC. However, the expectation is that the load factor can be improved by building a decision model in order to optimize the use of SBCs. Currently SBC are built for flights which are fully booked. If a flight is fully booked the expectation is that a container position created by the use of standby containers can easily be resold.

The KLM Cargo hub at Schiphol Airport is formed by a collection of three interlinked warehouses. Freight Building 1 focuses on mail, ‘high speed’ and otherwise special freight such as live animals and valuables. These shipments demand extra speed and attention, so they are handled separately. Freight

(12)

Figure 2.1: Warehouse Layout

Building 2 (Europort) handles the incoming flights from all over the world. From here, freight is transported to KLM’s European outstations by truck or delivered directly to the consignee. Another fraction of the cargo is transferred to Freight Building 3 (Worldport 1 & 2), where the outbound flights are prepared. Freight Building 3 receives the balance of its freight by truck from European locations, where it is prepared for air transport to global destinations. The main focus of this paper will be on the decisions made in the Worldports, partially based on the flow of goods from Europort. Figure 2.1 gives a schematic overview of the warehouse. All together, there are some 800 people working in the Amsterdam hub operation, handling a daily average of 60 outbound flights.

2.2 Research lay-out

(13)

way to utilize a number of these opportunities, whilst not wasting precious resources such as time and money.

In 2008 KLM conducted an experiment on the use of standby containers. Ini-tially two destinations were chosen for which standby containers were deemed beneficial. For these destinations the planners were instructed to build an SBC if enough freight was available. Gradually the number of destinations was in-creased to twelve, but these destinations were fixed. It was shown that the use of SBCs was beneficial, although the additional revenues were hard to measure. Building and loading an SBC does not directly imply an increase in revenues. The open position created by the use of an SBC needs to be resold to increase revenues. The first three years the statistics were updated by hand, on a monthly basis, keeping record of when SBCs were built, loaded and when opportunities were missed. At that time, the outgoing freight handling was organized dif-ferently, with three flows instead of the current two Worldports (WPs). The experiment was conducted in one of these flows, and with the reorganization of the flows the planners were reassigned to one of the WPs. Instead of a dedicated team, the planners who knew how to use SBCs were spread out over WP1 and WP2, diminishing the use of their knowledge.

An important observation to make here are the boundaries of the possibil-ities. One extreme would be to build all opportunity freight into containers, and send all available containers for a specific destination to the aircraft. This way, if enough freight is available, every open position can be filled by a standby container. The other extreme is not to build standby containers at all, thereby possibly having aircraft depart with open positions whilst having freight in the warehouse. Both of these options have clear (dis)advantages. The first option utilizes a maximum number of opportunities, but implies a large amount of work which currently is infeasible. The second option requires no additional work, but does not utilize any opportunities. Our goal is to find a scheme somewhere in the middle, where resources are used efficiently, yet taking advantage of empty positions when they arise.

2.2.1 Freight availability

(14)

is delayed it might result in a position remaining empty on an outbound flight. The trucking also has an important advantage. Take for example a truck originating in Milan, containing freight for several different flights departing from Amsterdam. There might be freight on this truck that is booked on a flight one or several days later than the trucks planned arrival at Schiphol. This freight will be stored in the warehouse, awaiting the moment of its planned flight. This freight might be suitable for use in a standby container; it is already at hand, and is not ‘hot’, i.e. it does not necessarily have to be on a flight within the next 24 hours.

Another source for freight to be used in SBCs are transit shipments. If a shipper books a cargo shipment say from Los Angeles Airport (LAX) to Hong Kong International Airport (HKG) at KLM Cargo, the freight will be flown to Schiphol first, and be transferred to a flight to HKG. It may happen that this shipment is booked on a flight to HKG two days later than the arrival from LAX. This shipment will then be stored in the warehouse and be retrieved several hours prior to the departure of the flight to HKG. This freight is most likely suitable for building standby containers, as it is not expected to arrive at HKG for another 48 hours.

We should note that not all freight in the warehouse is suitable for standby containers. It must be taken into account that some cargo is expected to fly as booked, so it cannot be forwarded. Take for instance valuables; the cargo handler at the destination might not have a vault, so the broker must be on site to accept the goods. If it is decided to ship these goods a day earlier than planned, it is not sure the goods can be collected by the broker, so this cannot be done without the broker’s permission. Another issue is storage cost; if goods arrive on site early and are not picked up within 24 hours, the handler will typically charge storage costs to the broker. Currently these costs are passed on to the consignee, even if the airline decides to deliver earlier than planned. Hence when selecting parcels to build a standby container, it has to be made sure the parcels are suitable for early delivery.

2.2.2 Loading probability

(15)

loaded onto the lower deck. This is the section of the aircraft underneath the passengers. Secondly, we have lower deck pallets (LDPs), which are also loaded on the lower deck, but have a larger footprint, and consist of a floor panel only which can be loaded up to 162cm. Finally, there are main deck pallets (MDPs), which are exactly the same as lower deck pallets, except they are built up to a higher level (mostly 230cm, depending on cargo door), and can only be loaded onto an aircraft’s main deck. Note that there are two sizes of floor panels for LDP/MDPs, which differ slightly in width but are mostly interchangeable. A more precise description of the different ULD types is included in Appendix B.2. In previous experiments, only AKE containers were used for standby con-tainers. As they are much smaller than, for instance, LDPs, if any cargo cannot be loaded on a flight an AKE will fit in its place. Although an AKE can only be loaded on a lower deck position, it can still be used if a main deck pallet (MDP) is offloaded. In case this happens, a lower deck pallet (LDP) will be shifted to the main deck. This can be done as these pallets have the same footprint, only the height of the load differs. Next, if the LDP is loaded on the main deck the AKE can be placed in a lower deck position on the aircraft. In fact, if either a LDP or MDP is offloaded, two AKE containers can fit on the empty position. Another advantage is that with limited freight available in the warehouse, it is often easier to fill an entire AKE (4m3_{) than an LDP (10m}3_{) or an MDP}

(18m3).

Once the ULD type has been decided on and an SBC has been built the load control department comes into play. The load control department is in charge of balancing the aircraft, and advising to what extent an aircraft should be refueled. These decisions depend mostly on the number of passengers on board and the amount of baggage they carry. Weather conditions also have a large impact. A transatlantic flight with a strong headwind will need more fuel than the same route with a tailwind, reducing cargo capacity. Based on these numbers the load control department decides how many kilos of cargo can be stowed, and in which positions, within the limited volume of the cargo hold. Within these constraints they try to optimize the use of capacity.

(16)

2.2.3 Added revenues

In this research the goal is to increase the load factor on outgoing flights. In 2008 an experiment was conducted on the use of standby containers. Although it was shown that standby containers were loaded, it turned out to be difficult to measure revenues. By using SBCs the capacity sold can be increased, which in turn increases the load factor. Given that a flight is deemed suitable for building an SBC, the load factor is only increased when the sales department can resell the created open position. If the volume and weight information on an Air Waybill (AWB) provides an accurate representation of the true volume and weight of a shipment, an increase in the load factor can be measured. Note that an empty container position can be sold directly, or a container booked on tomorrows flight can be loaded today, giving the sales department more time to sell the capacity.

The current way of computing the main load factor does pose some problems. The main load factor, LFmain, is defined in Equation (2.1), based on the volume

and weight load factors, LFvol and LFwgtrespectively.

LFmain= min(100, max(LFvol, LFwgt)), (2.1)

where

LFvol=

aggregate of AWB volumes

volume capacity on aircraft× 100% and

LFwgt=

aggregate weight of all cargo

weight capacity on aircraft × 100%.

Here LFwgtis the most exact, as all cargo is weighed in the warehouse. However,

LFvol is based on the AWB volumes, which unfortunately are not always equal

to the true volumes. It happens that the aggregate AWB volumes exceed the aircraft capacity, yet still can be loaded as the true volumes do not exceed the capacity. This way LFvol can be over 100%. When computing LFmain the

maximum of LFvoland LFwgt is taken and cut off at 100%.

The discrepancies in volume are an issue, but loading an additional ULD generally will increase LFmain. The problem lies in the cut off at 100%. A

(17)

in (2.2).

LFpos=

number of ULD positions used

number of ULD positions on aircraft× 100% (2.2) Every type of aircraft has a number of different container configurations. These configurations are chosen by the revenue management department, and are used to compute LFpos. By counting the number of positions used, the position

load factor does overcome the discrepancies the main load factor tends to have. However LFpos also has an important drawback. If a container is filled with

for instance a single small 10kg parcel, the position load factor is effectively increased. What is not taken into account though is to what extent the con-tainer was filled. In fact, the only information LFpos yields is the number of

ULDs loaded, full or empty. In order to overcome this problem, LFpos can be

measured, were a minimum load for a standby container is imposed. This way every time an SBC is loaded, and the created position is resold, an increase will be measured. If at some point the volume load factor becomes more reliable, this could also be used as indicator.

(18)

(19)

Chapter 3

Literature

This research project is to a large extent based on predicting the probability of loading an SBC. The subject seems to be closely related to predicting the no-show rate of passengers, an important piece of information used to determine to what extent a flight may be overbooked. Rothstein (1985) discussed the use of binomial distributions to model the no-show rate of passengers. Later, normal distributions were used more often as mentioned by for instance Gorin, Brunger, and White (2006). In their paper they propose a new method for passenger no-show predictions, namely using a combination of a normal distribution and a prediction based on Passenger Name Record (PNR) data.

Although the air cargo situation seems similar, it is more complex than the passenger situation. Passengers are fairly predictable; they generally use one seat and the amount of luggage they bring with them is also limited. With air cargo however, the shipments differ widely. Cars and jet engines are shipped, but small parcels of only several kilos are also transported. Kasilingam (2009) mentions four important differences. First of all, the capacity is uncertain. The available weight and volume is not fixed, depending for instance on the number of passenger bags and the weather conditions. Secondly, the capacity is three-dimensional as opposed to the one-three-dimensional passenger case. Both volume and weight, as well as container positions are to be taken into account. A third difference is the itinerary; where passengers prefer to follow their planned route, cargo can be shipped through another route without great consequences. Fi-nally, we have to deal with allotments. These are fixed capacities on destinations reserved for specific (large) clients. Hence instead of selling all positions freely, the size available for allotments has to be decided on, and sold separately.

Popescu, Keskinocak, and Johnson (2006) discuss the air cargo booking processes, and the overbooking in particular. Popescu et al. (2006) fit a number

(20)

of distributions to the show-up rate: the percentage of passengers that shows up at departure. They show that the normal, gamma, beta, Weibull, log-normal and exponential distributions fail to fit the sample data properly. Popescu et al. (2006) propose using a nonparametric model instead. According to them a histogram would provide the most easy to use model. It is shown that the nonparametric model provides a better fit than a normal distribution would have. However, they note that the nonparametric model is more complex to fit than most parametric models and might not be suitable in practice.

Luo, C¸ akanyildirim, and Kasilingam (2009) use a two-dimensional approach to cargo overbooking, where the dimensions are used for weight and volume. In doing so, they seek a parameterization for the distribution of the two-dimensional show-up rate. This entails a thorough analysis of the data at hand, which is not straightforward. Becker and Wald (2008) discuss overbooking based on the Shipment Information Record (SIR), which would be similar to basing a model on PNR data. To some extent the models are comparable, however we still have the issue of multi-dimensionality versus the one-dimensional passenger forecasting model.

Bakar, Othman, Ismail, and Abdullah (2009) provide a prediction model for the number of offloads using rough set theory. In their research a model is suggested which predicts the number of AWBs that will be offloaded on a specific flight. This prediction is shown to be 100% accurate, although the prediction is not a point estimator, but an interval in which the true value lies. Since the volume and weight of an AWB differ widely, this is not directly of great use for this research. In fact, we want to predict whether a position is open in order to load an AKE container.

(21)

Chapter 4

Model

Using historic data on the number of open positions on outbound flights, we make a prediction of future open positions. Combined with AWBs currently in the warehouse, we construct a model to make an optimal decision on which SBCs to build given the amount of time available on a given day. The following sections describe these decisions in more detail.

4.1 Freight availability

In order to build a standby container, we will start by investigating the freight at hand. We start with the setup currently used at KLM, where at most one standby container is built per flight. Later, we extend this to multiple contain-ers per flight. When it is decided to build an SBC, a snapshot of the freight currently in the warehouse is made. This freight can be listed according to their AWBs, which contain most of the relevant information. An AWB has informa-tion on the origin, the destinainforma-tion, the flight the freight is booked on, volume, weight, and a categorization of the contents of the shipment. For instance, if a shipment contains dangerous goods, this would be stated on the AWB. As already mentioned in Chapter 1, freight is paid for per kilo, unless the density is under 167 kilos per cubic meter. This rule implies that for shipments with densities over 167 kilos per cubic meter, the volume is less important than the weight in the booking process. Therefore discrepancies show in the volumes of shipments.

Once the snapshot of the freight in the warehouse is made, a filter is applied to select the shipments suitable for use in a standby container. An AWB is considered an opportunity for a standby container for a given flight if:

(22)

• it is booked on a later flight with the same destination,

• it is available in the warehouse at least 5 hours prior to departure, this provides enough time to gather the parcels and build a container, • all required documents are present,

• the location of the shipment in the warehouse is known, • its dimensions do not exceed container dimensions, • no other restrictions apply (e.g. must fly as booked).

The final bullet refers to shipments such as valuables and dangerous goods. For these shipments it is required that they fly on a specified date. Regarding the dimensions of a shipment, these are not always exactly known until it is retrieved from storage prior to building. Therefore it is left to the planner and builders to judge whether a shipment will fit in a container. In order to ensure that enough freight is available to fill an AKE container, we assume that at least 4m3 _{of opportunity freight should be available.}

4.1.1 Container contents: pure or mixed

Given a particular flight and a list of suitable AWBs, the next step is the selec-tion of the freight to be loaded into a potential standby container. Since every parcel should be hauled to the destination airport no later than the flight it is originally booked on, an AWB considered for a standby container has an ‘expi-ration date’. Depending on which parcels are loaded onto a standby container, this unit as a whole will also have an expiration date. If we cannot load the SBC onto an aircraft before this date, we need to make sure that the packages which are reaching their expiration date are loaded onto the flight they are originally booked on. If the SBC is composed of only parcels with the same expiration date, the entire container can be loaded onto the flight these packages were originally booked on. This leads to two basic ways to build an SBC:

• Pure container: container filled with parcels with equal expiration dates. • Mixed container: container filled with parcels where different expiration

dates are allowed.

Both types have advantages; if a pure container could not be loaded onto a flight before its expiration date, it can be loaded onto the flight its contents were booked on originally. This way the only additional costs are for transporting the container back and forth to aircraft it was not loaded on.

(23)

always be built in a way that it has an equal or later expiration date than a pure container for the same flight. The downside is that if a mixed container is not loaded before its expiration date, it may have to be broken down in order to retrieve the parcels that have met their expiration date. In that case the additional costs of building the SBC are transportation costs, building costs and possible breakdown costs. However, it is possible more often to build a mixed container, as it imposes less restrictions on the available freight. Given the characteristics of these different types of SBC, a decision has to be made which type of container to build if both are possible.

Given that building time for standby containers is limited, pure containers are preferred. A mixed container may have a later expiration date than a pure container, but the number of opportunities that will be missed by building a pure instead of a mixed container is small. Such a pure container will either be loaded as SBC or loaded as ordinary container. Given that there is little or no overlap in the container contents, the mixed container may still be built. Moreover, in the meantime new opportunity AWBs will most likely have arrived, creating new possibilities for building pure containers.

4.1.2 Containers with different expiration dates

Now that we have decided to build pure containers only, one possible decision remains. If for a flight there are two possible pure standby containers, which one should we build?

As mentioned in Section 2.2, there are two extreme options: build all possible standby containers, or build none. Since the time available for building standby containers currently is limited, we want to use this time in an efficient way. Since the goal is to increase the load factor, this implies we want to build SBCs which have the highest probability of being loaded before their expiration. In order to make the decision between two possible pure standby containers for one flight, we want to prove two relations. The first is that if we decide to build the standby container with the nearest expiration date, the fraction of containers that we build that is loaded before expiring is lower than if we decide to build the other container. The second relation is that if we build that standby container with the nearest expiration date, the fraction of opportunities that is used is higher than if we build the other container.

(24)

an SBC for this flight, we have to decide on one of these options.

• Scheme A: On day 1 build SBC1. If there is an open position on day 1, SBC1 is loaded. If not, it is loaded on day 2 as an ordinary container, so it is no longer on standby. Then on day 2 SBC2 can be built, following the same process. This way 2 SBCs are built, and an SBC is available both days.

• Scheme B: Build SBC2 on day 1. Now if there is an open position on day 1, SBC2 will be loaded. If not, SBC2 can be re-used on day 2 in a similar way as the previous option. If SBC2 is loaded on day 1, it may happen that a position is open on day 2, but we cannot be sure enough freight is available to build a new SBC. When choosing for this option, initially only one container is built, but an opportunity may be lost on day 2.

In order to quantify the difference between the two schemes, several expected values are defined in Equation (4.1), where the subscripts of the expected values represent the different schemes. Here p1 denotes the probability of an open

position on day 1, p2for an open position on day 2, and pnewis the probability

of having enough freight for a new container on day 2.

EA[# of containers to build] = 2 (4.1)

EA[# of opportunities used] = p1+ p2

EB[# of containers to build] = 1 + p1pnew

EB[# of opportunities used] = p1+ (1 − p1)p2+ p1p2pnew

E[total # of opportunities] = p1+ p2

Using these expected values, the fraction of containers that were loaded as standby container can be computed. Also, the fraction of total opportunities used can be measured. These are all shown in (4.2)-(4.5).

(25)

EA[fraction of opportunities used] =

EA[# of opportunities used]

E[total # of opportunities] (4.4) = 1

EB[fraction of opportunities used] =

EB[# of opportunities used]

E[total # of opportunities] (4.5)

=p1+ (1 − p1)p2+ p1p2pnew p1+ p2

We want to show that EA[fraction used as SBC] ≤ EB[fraction used as SBC].

Rewriting the inequality yields

p1+ p2 2 ≤ p1+ (1 − p1)p2+ p1p2pnew 1 + p1pnew (4.6) (1 + p1pnew)(p1+ p2) ≤ 2(p1+ (1 − p1)p2+ p1p2pnew)

p1+ p2+ p21pnew+ p1p2pnew≤ 2p1+ 2p2− 2p1p2+ 2p1p2pnew

p2₁pnew≤ p1+ p2− 2p1p2+ p1p2pnew

p1pnew(p1− p2) ≤ p1(1 − p2) + p2(1 − p1).

Since p1 ≤ 1, it follows that (p1− p2) ≤ (1 − p2). As pnew ≤ 1, we have

that p1pnew(p1− p2) ≤ p1(1 − p2). Using that p2(1 − p1) ≥ 0 we have that

(4.6) holds true for all p1, p2, pnew ∈ [0, 1]. The next step is to show that

EA[fraction of opportunities used] ≥ EB[fraction of opportunities used].

Rewriting this inequality yields (4.7).

EA[fraction of opportunities used] ≥ EB[fraction of opportunities used] (4.7)

1 ≥ p1+ (1 − p1)p2+ p1p2pnew p1+ p2 1 ≥ p1+ p2− p1p2+ p1p2pnew p1+ p2 1 ≥ 1 +−p1p2+ p1p2pnew p1+ p2 p1p2 p1+ p2 ≥ pnew p1p2 p1+ p2

Which holds true for all p1, p2, pnew ∈ [0, 1], since pnew ≤ 1. Note that when

pnew = 1, the inequality becomes an equality. Intuitively this makes sense: if

pnew = 1 there will be enough freight available on day 1 to build a (new) SBC

(26)

reasoning would apply.

This is the result we expected; scheme A maximizes the expected number of opportunities used, but the per-container performance is lower than in scheme B. In scheme B, the per-container performance is high, but possibly some op-portunities are missed. Given the limited number of containers that (currently) can be built per day, scheme B is the better choice. This implies that if mul-tiple there are mulmul-tiple options for a single flight, the container with the latest expiration date should be built. This way the limited amount of time results in the highest probability of actually increasing the load factor. Scheme B entails another more implicit advantage. By building containers with a longer interval before expiration, the sales department will have more time to resell the created position. The reasoning for following scheme B extends to cases with more than two options, which we will not explain in detail.

4.2 Booking level

The use of standby containers does not directly increase the load factor, it simply shifts booked shipments forward. This way an open position is created a number of days ahead. In order to increase the load factor, the open position has to be resold. Only then will freight be transported in addition to the amount that would have been hauled without using standby containers.

For some destinations it is ‘known’ that they are always fully booked, and created positions can be resold. This result is based on the employees’ empirical knowledge, and not always easy to verify. In order to select those flights that will yield an increase in the load factor, we want to use a quantitative approach to decide whether we can expect to resell a position created by using SBCs.

The revenue management (RM) department has all sorts of information on the booking levels of flights. One of the indicators used is the so-called daily flight monitor, which includes forecasts of the load factors for the next two weeks. The load factor forecast gives an intuitive indication for the probability of reselling the created position. If the forecast is over 80% a flight is called constrained, and we can be almost sure that the created position will be resold. By filtering out the destinations for which this threshold is not met, we can be fairly sure open positions will be resold once created. This implies that when a standby container is loaded revenues are increased.

(27)

4.3 Loading probability

The probability of loading an SBC on a particular flight has a large influence on the decision of building one. Once a flight has departed, a number of details is recorded about the flight, such as the number of empty cargo positions and the achieved load factor. Since it is hard to give a precise prediction of open positions from booking information, we will make a forecast per destination based on historical data.

The starting point in this research will be based on building at most one AKE container per flight, as this was proven to work well in the 2008 experiment. Section 4.4 will discuss the process if we allow for two containers to be on standby for a single flight. For the forecast there are two types of flights: flights with an opportunity, and flights without. If an SBC is loaded, there was an open position, but this will no longer be seen in the data, so when the use of SBCs is implemented this is to be taken into account in the forecast, by counting a loaded SBC as an empty position.

The number of open positions can fluctuate heavily, mostly due to external factors such as seasonality, but also due to more severe impulses as for instance the 2010 ash cloud. In order to respond to these fluctuations, we will use ex-ponential smoothing to forecast the number of open positions per flight. This method is closely related to a moving average, but it attaches the highest weight to the most recent observation, decreasing the weights with the age of the obser-vation. This ensures the forecast reacts to shocks faster than a moving average does. A possibility would be to make separate forecasts for different days of the week, as the amount of freight hauled fluctuates throughout the week. How-ever, since most standby containers last for more than one day a single forecast suffices. The definition of exponential smoothing, as explained in for instance Axs¨ater (2006), is

ˆ

xt+1= (1 − α)ˆxt+ αxt (4.8)

where

α = smoothing constant (0 < α < 1) xt= indicator for open position

ˆ

xt+1= prediction for open position.

This forecast is updated every day a specific flight occurs, so ˆxt+1 will give

an estimate for the presence of an empty position on the next flight. As α ∈ (0, 1) and xt ∈ {0, 1} it follows that ˆxt+1 ∈ (0, 1), so it can be interpreted

(28)

exponential smoothing, the smoothing constant α has to be set. Ghiani, Laport, and Musmanno (2003) note that α is typically set between 0.01 and 0.3. In Axs¨ater (2006) it is stated that when comparing to a moving average, α = _{N +1}2 , with N the number of observations in the average. We tested for different values of α between 0.1 and 0.3, finding little difference in the outcomes. Therefore we set α = 0.2, which following the line of reasoning of Axs¨ater (2006) is the exponential smoothing equivalent of a moving average over 9 flights. A further explanation can be found in Appendix C.1.

The next step is to combine this one-day loading probability with the expira-tion date of the SBC at hand. Let X be the number of open container posiexpira-tions on a flight, and s be the number of flights until the container expires. The total loading probability for this single container over the interval is given in (4.9).

P1,s= s X i=1 P (X = 0)i−1P (X ≥ 1) (4.9) = s X i=1 (1 − P (X ≥ 1))i−1P (X ≥ 1) = s X i=1 (1 − ˆxt+1)i−1xˆt+1

Now we have a list with all flights for which we are certain we can sell a created position, and the probability that an SBC built for those flights will be loaded as such. The final step is to sort this list by the loading probability, and start building SBCs from the top of the list.

4.4 Allowing multiple containers per destination

So far we have only considered building a single SBC per flight. However, multiple container positions may be empty on a flight, so it could be optimal to have more than one standby container per flight. For instance two AKE containers fit on the position of one LDP/MDP. If for a certain destination it often occurs that more than one position is empty, it may be beneficial to have more than one container on standby for that flight.

(29)

more intricate than is the case with a single container, but the basic idea is the same. Once again we let X represent the number of open container positions on a flight, and r, s the expiration dates of two possible containers. Without loss of generality we assume r ≤ s. We then have the probability that at least two containers can be loaded before r:

r X i=1 P (X = 0)i−1P (X ≥ 2) + r X i=1 i − 1 1 P (X = 0)i−2P (X = 1)P (X ≥ 1).

If r < s, it is also an option that one container is loaded before r, and the other between r and s. This yields

r 1 P (X = 0)r−1P (X = 1)P1,s−r= s−r X i=1 rP (X = 0)r+i−2P (X = 1)P (X ≥ 1).

Combining these two, the probability that both containers are loaded before they expire is given in (4.10).

P2,(r,s)= r X i=1 P (X = 0)i−1P (X ≥ 2) (4.10a) + r X i=1 (i − 1)P (X = 0)i−2P (X = 1)P (X ≥ 1) (4.10b) + s−r X i=1 rP (X = 0)r+i−2P (X = 1)P (X ≥ 1) (4.10c)

If r = s, the summation in (4.10c) is an empty sum, hence equal to zero (Ingham (1990)).

If r = 0, which means that that container has expired, P2,(0,s)= 0.

Summa-tions (4.10a) and (4.10b) will be empty sums, (4.10c) has a term r, hence will be zero as well. In case r = 1, (4.10b) will be zero, since then (i − 1) = (1 − 1). This also makes sense; if one container has already expired, the probability of loading both is equal to zero. Nevertheless the probability of loading the second container can be positive, and is equal to P1,s. What remains is (4.10a) for

the probability both containers are loaded in the first period, and (4.10c) for the probability that one container is loaded in the first period and the second container is loaded before s.

(30)

today. The other possibility is that one container is built today, and a second one seems beneficial as well.

(31)

Chapter 5

Results

Now that we have set up a decision support model in order to optimize the use of standby containers, the final step is to verify if the model works correctly. Ideally, we would have implemented the model and collected the results. How-ever, as this research was conducted in only five months, there was too little time to set up an experiment and base a conclusion on the outcome. Therefore, the choice was made to use a historic dataset, which we used as input for a simulation study. Each day of the simulation the model reads the data that would have been available that day, and virtually builds standby containers if they are desirable according to the model. These virtual containers are stored in a list, until a flight occurs which is not weight-constrained and has an open position, after which the container is counted as successful.

The longest available interval contained data assembled over a 90-day period starting in July 2010. This data consists of the opportunity AWBs for outgo-ing KLM flights, as well as the different load factors and the number of open container and pallet positions per flight. Combining this with the 2010 summer schedule, we have all the required inputs for the model except the load factor forecasts from the daily flight monitor. We covered for this lack of data by using historic load factors, which is explained in more detail later in this section.

In order to use this data for testing the model, we applied a 10-day warm-up period for the forecast. Ideally this would be longer, but the longer the warm-up the shorter the test. Exponential smoothing theoretically depends on an infinite number of historic observations. After ten days the forecast will consist of data older than ten days for at least 11%, depending on how often the flight is operated. We do not have that data, so in order to cover for this we investigated three possibilities:

(32)

• start warm-up on day 1 with a 10 day average as initial value, • start warm-up on day 1 with a 90 day average as initial value.

The first possibility has a clear disadvantage. By not using an initial value, on day 11 we lack at least 11% of the input. If for instance a flight had an open position each of the first ten days, the forecasted probability of an open position will still not exceed 0.89. With the second possibility we can cover for this problem, by using the average over the first ten days as initial value. For flights which are operated daily this can give a reasonable forecast for day 11, using only historic data. However for flights operated for instance twice a week, this method gives an initial value based on only three observations. Moreover, the first forecast will depend on this value for over 50%.

The final possibility is using an average over the entire 90 days at hand as initial value. This does cover for the drawbacks of the other possibilities as far as possible, but does lead to another issue. Since the start-up value is based on the entire 90 days, a forecast for day 11 will be based partly on the true value of the observation of day 11, which is impossible in practice.

Since the first two possibilities have clear disadvantages for non-daily flights, we chose to use the third possibility. The performance of the model is almost 2.5% better than the other possibilities, as it gives a more reliable forecast for the first number of days after the warm-up period. Note that when the model is implemented, a longer warm-up period should be used as we will not have similar data.

Apart from the length of the interval, another drawback of the data at hand is that the demand forecasts as explained in Section 4.2 are not available. In order to still make a selection of flights where we expect open positions to be resold, we must therefore use another type of filter. By selecting only flights which over the last five flights have shown a load factor greater than a certain threshold, we rule out flights which are never constrained. Again, this is not optimal, but at least this way we can provide some insight on the performance of the model, and the sensitivity of the parameters. These results are presented in the following sections.

For the simulation we assume a base case, which has a darker shade in Figure (5.1)-(5.3). In the base case a maximum of three containers can be built per day, which all should have a minimum loading probability of at least 80%. In addition, we require the average load factor for all containers to be at least 80% and we allow only one SBC per flight. Note that we have no information on the exact dimensions of shipments. In practice a planner would assess whether a parcel would fit into a container. It turns out that in most cases the available volume is well over 4m3_{, so we assume that amongst the available shipments}

(33)

Using the chosen parameters, we run the model every day of the simulation. Once a list of suitable flights is generated, we start building containers from the top of this list, until either the maximum number of containers we allowed to build is reached, or the loading probability of the containers no longer meets the minimum loading probability. The built containers are stored in a list, and it is checked whether they could have been loaded onto a flight. If not, the data on remaining containers is used when generating a new list of suitable flights for building standby containers.

Starting with the base case, we varied the parameters to gain insight on how the model reacts. Leaving the other parameters from the bases case the same, we ran the model several times varying:

• the minimum loading probability • the minimum average load factor

• the maximum number of containers to build per day

• the minimum loading probability, with maximum number of containers to build per day fixed at 10

• the minimum loading probability, allowing two standby containers per flight.

In the graphs in this chapter, a number of properties indicating the perfor-mance of the model are shown. First, there is the number of containers that were loaded as standby containers, thereby creating an open position, indicated by ‘loaded as SBC’. Next, there are the containers that were built as SBC, but were not loaded before their expiration; these are indicated by ‘loaded as normal’. Finally, there is the ‘success rate’, which shows the performance per container. This is the fraction of all containers that where built as SBCs and were eventually loaded as such. Hence the percentage gives a measure for the probability that a container is in fact loaded as SBC.

5.1 Minimum loading probability

(34)

Figure 5.1: Model performance for different minimum loading probabilities, allowing a single SBC per flight, a maximum of 3 SBCs to be built daily and an average load factor over 80%. The shaded bars indicate the base case.

number of container passes the filter, decreasing the total number of containers built.

In the base case over a 75-day period 195 SBCs were built, of which 172 were loaded as a standby container. The remaining 23 were loaded on the flight they were originally booked on. This leads to a success rate of 172₁₉₅ ≈ 88%. In the base case standby containers were returned to the warehouse 270 times, so each container was returned on average 270₁₉₅≈ 1.4 times, or 270

172 ≈ 1.6 times per

successful SBC.

The success rate should be at least as high as the minimum loading probabil-ity. Unfortunately this is not true, which can have several causes. One possible cause is a positively biased forecast. Also, the data contains some blank spots on empty positions, which are interpreted as zeroes (no empty positions). If more data were available, a greater simulation would be advisable to find the cause of this underperformance.

5.2 Minimum average load factor

(35)

Figure 5.2: Model performance for different minimum average load factors, allowing a single SBC per flight, a maximum of 3 SBCs to be built daily and a minimum loading probability over 80%

higher the threshold, the smaller the number that passes through the filter. The fraction of containers which are loaded as SBC remains over 80%, although the discontinuity in the graph forces us to be careful with conclusions.

5.3 Maximum number of containers to build

Next, we vary the maximum number of containers we allow to be built per day. Once again we start with the base case, so only one container per destination, a minimum loading probability of 80% and an average load factor of at least 80%. In practice this number will vary daily based on the availability of time, however for this analysis the results are easier to interpret in a fixed setting. Figure 5.3 shows the results. Given that the maximum number of containers to build is low, the performance per container is high. The more containers we allow to be built each day, the lower the performance per container is.

(36)

Figure 5.3: Model performance for different maximum number of containers to build, allowing a single SBC per flight, a minimum loading probability over 80% and an average load factor over 80%

Figure 5.1.

5.4 Multiple containers per flight

(37)

Figure 5.4: Model performance for different minimum loading probabilities, allowing a single SBC per flight, a maximum of 10 SBCs to be built daily and an average load factor over 80%

(38)

5.5 Financial benefits

The costs for implementing and using the proposed standby container model consist of three components; labor, transportation and IT integration costs. The setup of the model implies that the containers are to be built using ex-cess building capacity. This way the model lays no additional pressure on the workforce, but does increase labor utilization. When using standby containers, transportation to the platform is inevitable. As transportation is inevitable, it was left out of the optimization, however for the financial results it should be accounted for. The third component is formed by costs for implementing the model into the current Hub Planning (HubPla) tool.

5.5.1 Labor

Currently, manpower is are scarce at KLM, so the focus is on using resources which are already available. As the demand for manpower fluctuates during the day, it is clear that standby containers should not be built during peaks in work pressure. As standby containers have the lowest priority in the building process, they should only be built when there is excess building capacity, for instance in the evenings. By doing this, on the one hand we ensure that standby containers are available, but on the other hand the work load is also evened out. By building a standby container today, this container will not have to be built on the day it is originally booked on. This time can then be used to build an additional container, if the created empty position has been resold. By using this setup, excess building capacity is used, and along the way the work pressure is slightly evened out. Hence given the current labor planning, no additional costs will be made to build standby containers. We should note though that if this planning is to be changed, or if for instance workers are laid off, there may be no capacity left to build standby containers. To give an idea of the labor demand; it costs on average 25 minutes with two workers to build an AKE container, and in the different settings on average 3-5 containers are built daily.

5.5.2 Transportation costs

(39)

container, costing in total around 30 minutes. Adding expenses for petrol, the total expense will then be at moste 25. It is important to emphasize that this is the very ‘worst’ case, generally costs will be lower. If we look at the previously explained base case, a successful SBC requires on average almost 1.6 round trips to the aircraft before it can be loaded. Hence, the average transportation costs in the base case are at moste 40. Given that a successful SBC results in 4m3

which can be sold, these costs can easily be covered.

5.5.3 IT integration costs

Currently, only a prototype of the model is available, a screenshot of which is shown in Figure C.2. So far the model has not been linked to a live data feed, but this is currently being attempted. In order to reap the benefits from the model, two interlinked systems have to be put in place. The first is basically the same as the prototype, but ideally this will be integrated into HubPla, a tool which is currently used by the planners. This way it will simply be an additional option in an existing framework. The second system has to keep track of the standby containers once they have been built. On the one hand this is part of the input for the first system, because if an SBC is already at hand, a second one may be less interesting. On the other hand it will provide information on performance of the model. A similar system is built into the prototype, however for technical reasons it is better to set these systems up separately. The second system can also contain an interface for the mail division. Currently, the allocations for air mail are often too small to meet demand, so mail is frequently sent to an aircraft on standby. If the mail devision has access to the second system, they can easily gain insight on which standby containers from the Worldports are in place, and decide whether to build one.

HubPla is developed and maintained within KLM Cargo, so integrating the model will have no direct costs. Since a working prototype is already available, it should cost no more than two full work weeks to include it in HubPla. On the other hand the users of HubPla need to be informed about the workings of the model, which will demand some time. A KLM expert estimated the maximum costs for the entire integration process ate 50.000.

5.5.4 Revenue increase

(40)

revenue = additional sales − transportation costs − IT integration costs. (5.1)

For the additional sales, we assume that all created capacity can be resold, as standby containers are only built on constrained flights. By using the shipment contribution reports from the period at hand, we found a price per m3 _{for all}

destinations. We know the capacity of an AKE container is 4m3_{, and how many}

standby containers where used on which destinations. Combining the two, we computed the additional sales that could have been made, and extrapolated the results to a one-year interval. We would like to stress that since the results are based on a 75-day interval, they are not as reliable as desired. True revenues may hence deviate from these numbers in either way. However, they do give an idea of the size of the opportunity, and the difference between the setups.

In the base case, where at most 3 containers were built daily, and a single container was allowed to be on standby per flight, 172 SBCs would be success-fully loaded. In order to attain this, 23 containers would be built but loaded as ordinary containers and 270 transports would be needed. Extrapolating this to a one-year interval yields

revenue ≈e 940.000 − e 35.000 − e 50.000 = e 855.000. (5.2) If we use the same setting with a single container on standby per flight, but allow 10 containers to be built daily, 242 SBCs would be loaded. 404 transports would be needed and 41 containers would be built and loaded as ordinary containers, which would give

revenue ≈e 1.325.000 − e 50.000 − e 50.000 = e 1.225.000. (5.3) By building at most 3 containers per day, but allowing 2 containers to be on standby for the same flight, 194 SBCs would be loaded. Only 14 containers would loaded on their original flights and 377 transports would be needed. This yields

revenue ≈e 1.045.000 − e 50.000 − e 50.000 = e 945.000. (5.4) By allowing two containers on standby for a single flight, and building at most 10 containers per day, 337 SBCs would successfully be loaded. 39 contain-ers would be built and loaded as ordinary containcontain-ers, and 691 transports would be needed with this setup. This leads to

(41)

Chapter 6

Conclusion

In the simulation the model has proven to successfully improve the load factor and increase revenues. The process to integrate the model into HubPla has started, and approval has been given to fully implement the system.

The benefits of the model have been expressed in the number of additional containers that will be hauled. This was chosen as this gives the most clear pic-ture of the improvements made. Obviously, by transporting additional freight, the load factor will improve. Once the model has been implemented, the overall load factors should improve.

In the setting where 2 containers are allowed to be on standby for one flight and a maximum of 10 containers per day is built, on average 4.5 SBCs will be loaded daily, which corresponds to 18m3_{. In interval where the simulations}

were run, on average 3450m3 _{of freight was hauled on outbound flights daily,}

leaving 1100m3 unused. Hence the proposed model leads to a 0.5% increase in the volume load factor. What is even better is that this increase is attained on constrained flights only. So this increase is made on flights which already show a main load factor over 80%.

The number of containers loaded as SBC and the success rate remain good indicators for the model performance once implemented. On the one hand it gives insight in the overall number of additional containers transported, on the other hand the performance per container shows how much effort is put into at-taining that result. Eventually it is up to the management team to find a balance in these two indicators. As mentioned previously, there are two extreme cases. The first is building all opportunity AWBs into containers, thereby creating a large amount of standby containers. By doing this a maximum of opportuni-ties will be used, but it is clear that this approach costs a lot of manpower and money, and will not be very efficient. The second approach is to build no

(42)

standby containers, giving no additional risk, but also no additional profits. The key to success in using standby containers lies in finding a balance in the two performance measures, yielding a process somewhere in the middle of these two extreme cases.

6.1 Areas for further research

Although this model leads to a substantial increase in both the load factor and revenues, the opportunities might be exploited even more. Previous research has shown that for instance creating an additional buffer for each destination, where opportunity AWBs are placed, will increase the load factor. This way, if a pallet or container cannot be entirely filled, a shipment booked for a later flight can be used to fill the gaps. The volume lost on a pallet or container (stacking loss) is decreased, thereby increasing the load factor. Currently creating these additional buffers is not an option due to the limited surface available in the warehouse, so this idea has not been implemented. Until this can be done, there are also some possible improvements to the model for standby containers.

Based on the 2008 experiment with standby containers, the initial concept was to build a maximum of one standby container per flight. We have shown that extending this to two containers per flight is beneficial, and presented the framework for extending this to three and four containers. The primary goal will be to implement the system with a maximum of one container per flight, so increasing this number to three, four and beyond is currently not within the scope of this research. However, it might be advisable to explore this area in future research.

Another choice made previously was to focus on AKE containers only. It is known however, that open pallet positions also occur every now and then. If enough freight is at hand, it might be beneficial to also build standby pallets, either lower or main deck. Presumably the loading probability will be smaller than for standby containers. Nevertheless if a standby pallet is loaded, it creates an open pallet position, which is more valuable.

(43)

6.2 Concluding remarks

Summarizing the results, the advice to KLM is to implement the model as explained in Chapter 4, allowing one container to be on standby per flight. An important requirement for the success of the project is to gain support from the workforce in the hub operation. Therefore it is advisable to start with a single container on standby per flight, and increase this once the model has proven itself.

(44)

(45)

Bibliography

Axs¨ater, Sven (2006). Inventory control. Springer Science + Bussines Media, LLC.

Bakar, Azuraliza Abu, Zalinda Othman, Ruhaizan Ismail, and Ros-mawati Muhamad Abdullah (2009). Managing the air cargo offload prob-lems using rough set theory. In 2009 International Conference on Electrical Engineering and Informatics, 5-7 August, Selangor, Malaysia.

Becker, Bjoern and Andreas Wald (2008). Air cargo overbooking based on the shipment information record. Journal of Revenue and Pricing Management Vol. 7, pp. 242–255.

Boeing (2010, May). Cargo pallets and containers. http://www.boeing.com/ commercial/startup/pdf/CargoPalletsContainers.pdf.

Ghiani, Gianpaolo, Gilbert Laport, and Roberto Musmanno (2003). Introduc-tion to logistics systems planning and control. John Wiley & Sons, Ltd.

Gorin, Thomas, William G. Brunger, and Mary Michele White (2006). No-show forecasting: a blended cost-based PNR-adjusted approach. Journal of Revenue and Pricing Management Vol. 5, pp. 188–206.

Ingham, Albert Edward (1990). The distribution of prime numbers. Cambridge University Press.

Kasilingam, Raja G. (2009). Air cargo revenue management: characteristics and complexities. European Journal Of Operational Research Vol. 96, pp. 36–44.

Luo, Sirong, Metin C¸ akanyildirim, and Raja G. Kasilingam (2009). Two-dimensional cargo overbooking models. European Journal Of Operational Research Vol.197, pp. 862–883.

(46)

Popescu, Andreea, Pinar Keskinocak, and Ellis Johnson (2006). Estimating air-cargo overbooking based on a discrete show-up-rate distribution. Interfaces Vol. 36 No. 3, pp. 248–258.

(47)

Appendix A

Abbreviations &

terminology

AKE Lower deck container, see Appendix B.2 for a description.

AWB Air Waybill, document accompanying a shipment with all booking information.

European Locations in Europe where agents deliver freight, outstation KLM then uses trucks for transport to Schiphol. Europort Flow of inbound flights and trucking into Europe.

LDP Lower Deck Pallet, see Appendix B.2 for a description.

MDP Main Deck Pallet, see Appendix B.2 for a description.

Pax (Number of) passengers

PCHS Physical Cargo Handling System (pallet storage system).

RM Revenue Management Department.

SBC Standby Container.

Stacking loss Volume loss on ULD due to dimensions of packages.

(48)

TLT Team Leader Turn-around (TLO), manager of operations on the platform in charge of i.e. loading and refueling. ULD Unit Load Device (generic term for containers and pallets).

(49)

Appendix B

Aircraft and container

properties

B.1 Aircraft layouts

KLM Cargo operates a number of aircrafts which carry ULDs, of which the specifics are listed in Table B.1. Note that the number of AKE’s reserved for passenger luggage is an estimate based on a 100% load rate for passengers and 18kg luggage for each passenger. As the amount of fuel differs depending amongst others on the weather, the weight of the cargo allowed might be less than initially planned.

Aircraft Type Pax/ Pax Payload MDP LDP AKE AKE

Cargo (kg) bags cargo

A 330-200 Pax 251 13.900 0 6 8 1 B 747-400 Pax 426 12.500 0 5 14 2 B 747-400M Combi 278 35.300 6 7 9 1 B 747-400ERF Cargo - 103.100 30 9 - 2 B 777-200ER Pax 327 15.300 0 6 11 3 B 777-300ER Pax 422 21.600 0 6 14 6 MD11 Pax 294 16.000 0 6 10 4

Table B.1: Aircraft Specifics; A = Airbus, B = Boeing, MD = McDonnell Douglas

(50)

B.2 Containers and pallets

Figure B.1: AKE Container, source: Boeing (2010)

Figure B.2: P1P Main Deck Pallet/Lower Deck Pallet

(51)

Appendix C

Additional sections

C.1 Forecast

In the model exponential smoothing is used in order to gain insight in the probability of an open position occurring on today’s flight. The smoothing parameter is set to α = 0.2, which is justified in the following way. Over a period of 70 days the top 10 flights were recorded, filtering out SBC opportunities with P1,r < 0.8, as in practice these will not be built. The number of times a flight

shows up in the top 10 is divided by the number of flights in the interval in order to have a fair comparison. By comparing these records varying α from 0.1 to 0.3, an insight is created on the sensibility of α. Figure C.1 shows these different records. As can be seen the value of α does not have great influence on the top 10 flights, hence α is set at 0.2.

Figure C.1: Top 10 flights recorded daily for different values of α

(52)

C.2 Maximum number of containers per flight

As explained in Section 4.4, the more containers one involves, the longer the computations for the probabilities are. The following sections state the formula’s for using three and four containers.

C.2.1 Three containers

Let q ≤ r ≤ s. Then P3,(q,r,s) is given by

P3,(q,r,s)= q X i=1 P (X = 0)i−1P (X ≥ 3) (C.1a) + q X i=1 i − 1 1 P (X = 0)i−2P (X = 1)P (X ≥ 2) (C.1b) + q X i=1 i − 1 1 P (X = 0)i−2P (X = 2)P (X ≥ 1) (C.1c) + q X i=1 i − 1 2 P (X = 0)i−3P (X = 1)2P (X ≥ 1) (C.1d) +q 1 P (X = 0)q−1P (X = 1)P2,(r−q,s−q) (C.1e) +q 1 P (X = 0)q−1P (X = 2)P1,s−q (C.1f) +q 2 P (X = 0)q−2P (X = 1)2P1,s−q (C.1g)

This probability is an extension of the probability P2,(r,s) (Equation (4.10)).

Therefore there are again some ‘special’ situations to give attention to here. For similar reasons, if q = 0 it follows that P3,(0,r,s) = 0. If q = 1 only term

(C.1g) is equal to zero as 1₂ = 0. Again this makes sense since this term indicates the probability of having an opportunity for a single container twice before q, which is impossible if q = 1.

If q = r > 1, only the term (C.1e) is influenced as explained in the previous section. The same holds if r = s > 1, only then P2,(r−q,s−q) changes in a

different manner. If it happens that q = r = s > 1, terms (C.1e-g) are zero due to the properties of P1,s−q and P2,(r−q,s−q).

Optimizing the load factor for cargo ﬂights by using standby containers