Truck arrival scheduling for air cargo terminals: Modelling a slot allocation policy to alleviate congestion and improve performance

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Truck arrival scheduling for air cargo terminals:

Modelling a slot allocation policy to alleviate

congestion and improve performance

25th of June, 2018

Lisa van Casteren, s2537621 lisavancasteren@hotmail.com

Thesis MSc. Technology & Operations Management

University of Groningen, Faculty of Economics and Business First supervisor: dr. I. Bakir

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Abstract

Air cargo terminals often become congested as flight departures and concentrated truck arrivals demand workload simultaneously. This leads to long waiting times for trucks and shipments missing their flights. Literature suggests that the workload can be spread by coordinating truck arrivals using a slot allocation policy. This thesis aims to assess the effect of using a slot allocation policy on air cargo terminal performance. To find this effect, the air cargo terminal operations are formulated as an integer programming (IP) problem and modelled in CPLEX. The objective is to find an optimal truck unloading schedule that minimizes the total penalties issued for storage time, truck waiting time and shipments missing their flights. The IP is illustrated with a case study of a world leading air cargo terminal. Numerical experiments reveal that the slot allocation policy can improve air cargo terminal performance when it only allows trucks which require high unloading times and carry many shipments to request a slot.

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Preface

This thesis is the concluding work to my Master’s degree in Technology & Operations Management at the University of Groningen. My long-lasting interest in aviation motivated me to find a research topic in that direction. Upon contacting the ground handler Swissport International, its project manager Thierry Huizing proposed to do research on alleviating the congestion in their air cargo terminal. Driven by this real-world problem, I formulated a research topic which dr. Ilke Bakir was glad to supervise. By taking a quantitative approach in the research project, I had the opportunity to further develop my abilities in modelling and using optimization software. As a result, this thesis not only forms the capstone of my studies, it also represents my drive to keep looking for skills to develop.

I would like to express my greatest thanks to dr. Ilke Bakir for her great enthusiasm, valuable feedback and interactive discussions. I thank Thierry Huizing for proposing this interesting research topic and providing me with the opportunity to research an actual air cargo terminal. The people I would like to thank for their input and data provision are Eljas Oulad (warehouse manager at Swissport), Guy Driebeek (managing director at SmartLOXS, the provider of the truck registration software at Swissport), Jan Carel Paro (Black Belt at Amsterdam Airport Schiphol), Erik Nagel (managing director at R. Nagel, trucking company) and Robin de Block (station manager Schiphol at Wallenborn, trucking company). Lastly, I would like to thank my boyfriend, family and friends for their support.

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1. Introduction

The air cargo industry accounts for transporting 35% of the value of all goods traded globally. As a key facilitator of globalization, its volume has doubled every 10 years since 1970 and it is forecasted to continue growing by an average 4.2 percent per year over the next two decades (Boeing, 2017). Combined with the increasing customer demand for more flexible, reliable and faster deliveries at a competitive price, the aviation industry faces a tremendous challenge to efficiently manage their air cargo operations (Meng et al., 2010; Rahman et al., 2017).

In order to face this challenge, it is crucial that each link of the air cargo supply chain works efficiently and effectively. According to Feng, Li and Shen (2015), who performed a comprehensive literature review on air cargo operations and its problems in practice, a specific part of the air cargo supply chain that requires more research is the air cargo terminal (ACT). An ACT is located directly at an airport and provides airlines with the service of (un)loading cargo aircrafts and trucks, (re)consolidation of the shipments and temporary storage. In addition to the challenges described above, the ACT experiences extra complexity and pressure due to tight flight schedules of airlines, short connection times, unpredictable arrival of trucks, a wide variety in shipment weights and sizes and the inherent uncertainty of the airline environment (Ou, Hsu and Li, 2010).

Managing the ACT workload over time proves to be a vast managerial challenge (Rong and Grunow, 2009; Selinka, Franz and Stolletz, 2016). The departures and arrivals of cargo flights are clustered around certain fixed times of the day and at certain days of the week. During these hours, ACT workload peaks as aircrafts have to be (un)loaded and the shipments have to be sorted (Rong and Grunow, 2009; Selinka, Franz and Stolletz, 2016). In off-peak hours, on the other hand, the ACT has to deal with largely idle capacity.

These peaks in ACT workload are amplified by the arrival pattern of trucks that deliver shipments. Trucking companies are free to decide when they deliver their shipments to the ACT, as long as they meet the delivery deadline. In practice, the shipments are most often delivered close to this deadline, which is just hours before the flight departure time (Ou, Hsu and Li, 2010; Ladier and Alpan, 2016). Their required unloading and shipment sorting intensify the ACT workload during the hours that are already busiest for handling the flights and the likelihood on ACT congestion increases. Trucks start queuing on the parking lot and, as the cargo flights’ departure times cannot be delayed, shipments could miss their flights (Ou, Hsu and Li, 2010; Ladier and Alpan, 2016). This harms the service level which the ACT and the airlines agreed upon, also deteriorating the ACT’s competitive position. It is therefore essential for an ACT to prevent its operations from becoming overloaded and congested.

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1. Introduction

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increase, as the performance of ACT operations depends majorly on the arrival rate of work (Hall, 2001; Konur and Golias, 2013). Also trucking companies are in need of truck arrival coordination. By having an allocated unloading time, a truck no longer needs to queue for multiple hours under the ACT’s first come, first served (FCFS) policy. However, slot allocation policies have failed in the past as they did not consider the truckers’ concerns and availability (Zhao and Goodchild, 2010). To make the truck arrival coordination work well in practice, the truckers’ availability needs to be taken into account as well.

Yet, the lack of a proper model for truck arrival scheduling forms one of the biggest research opportunities within air cargo operations, according to the extensive literature research of Feng, Li and Shen (2015). Their research agenda suggests a time slot design to shape the truck scheduling model. Time slot scheduling (or appointment scheduling), in the maritime sector, was found to flatten peak demand, reduce trucker waiting time and shorten container storage time (Chen, Govindan and Yang, 2013). It also seems to be effective even when a good portion of the arrivals are walk-ins or late (Huynh, 2009). To study the true impact of such a policy on ACT performance, Feng, Li and Shen (2015) suggest that the truck scheduling model should integrate the three key ACT decision problems (truck scheduling, cargo routing through the ACT facility, and manpower scheduling). Existing ACT articles fail to do so: by only focussing on one decision problem, the effect cannot be measured realistically.

In this Master’s thesis, we aim to develop this mathematical model that determines the optimal allocation of time slots to arriving cargo trucks, while integrating all key ACT decision problems. Through this model, we aim to assess the impact of a slot allocation policy on the ACT performance. We compare this to the ACT performance under the currently employed FCFS policy to see whether an ACT can benefit from employing a slot allocation policy. The contribution will also have major practical relevance as this research was initiated by one of the world’s biggest air cargo handlers, Swissport International (hereinafter called Swissport). The problem of congestion is faced by their ACTs worldwide. In order to make the contribution, this thesis will answer the following research question:

To what extent can a slot allocation policy for arriving trucks at an ACT improve ACT performance?

a) What should be included in the slot allocation model to make it representative for ACT operations in practice?

b) How can the impact of truck slot allocation on ACT performance be measured?

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this thesis as it makes the research more applicable to other ACTs in the world in order to help them alleviate congestion.

The scope of this research comprises the truck arrival and unloading process at the ACT. The basic operations within the ACT are included as well, as this research aims to incorporate all three key ACT decision problems. Lastly, the scope only includes export shipments as the truck arrivals for picking up import shipments are not as much related to flight departure or arrival: trucks often perform pick-ups when they are at the ACT for unloading export shipments.

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2. Theoretical background

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2. Theoretical background

In order to develop a slot allocation model that builds on and extends existing knowledge, this chapter maps out the current state of affairs in this field of research. The first two sections briefly describe the context of ACT operations. Section 2.1 provides a system description of the air cargo supply chain. Section 2.2 narrows down and describes the operations within an ACT to highlight the interdependencies of operations that influence the scheduling of truck arrivals. Section 2.3 then zooms in on the focus area of this research, the truck arrival and unloading process. Section 2.4 forms the main focus of the theoretical background. It critically reviews the models in literature that are relevant to ACT truck scheduling. It provides insight in the existing knowledge base and identifies the missing aspects in the context of this research. The latter creates the opportunity for contribution by this Master’s thesis. A reader who is familiar with the air cargo supply chain and ACT operations may proceed reading at Section 2.3.

2.1. Air cargo supply chain

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airport. Upon arrival at the destination airport, the cargo is unloaded and checked in the local ACT. Finally, it is moved to a local warehouse for final delivery by a trucking company or it is picked-up by the consignee itself.

Figure 2.1 – The transportation of an air cargo shipment

Figure 2.1 also emphasizes the importance of taking a system wide view when regarding the transportation of air cargo. Inefficiencies in an individual part of the chain can result in system wide delays and force the airline to alter its delivery commitment to the customer (Hall, 2001).

2.2. Air cargo terminal operations

As is evident from Figure 2.1, an ACT can take several roles in the transportation of cargo: it can transfer the shipment from truck to aircraft; from aircraft to aircraft; and from aircraft to truck. Typical activities performed in an ACT are the following: (un)loading of trucks; performing inspection and document verification for acceptance; temporarily storing the shipments and ULDs; sorting the shipments according to their destination, volume, weight and type; build-up and break-down of the shipments on ULDs; the positioning of ULDs on the aircraft line-up area; and the (un)loading of aircrafts (Hall, 2001; Rong and Grunow, 2009). The visual representation of these operations, for export shipment only, is presented in Figure 2.2.

Figure 2.2 – The ACT export operations

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and aligned, the more competitive service an ACT operator can offer to its airline customers, in order to capture a larger share of the express market.

As briefly mentioned in Chapter 1, the coordination of ACT operations involves three key decision problems: truck scheduling, internal cargo routing trough the facility and manpower scheduling. Although most often separately investigated in literature, these sub-decisions are in practice all interdependent (Feng, Li and Shen, 2015). Inefficiencies in one of them can lead to complications in the others. This emphasizes that, although this research focuses on truck scheduling, it is important to take all key ACT decision problems into account.

2.3. Truck arrival and unloading process at air cargo terminals

The arrival and unloading of trucks at the ACT docks has some specific characteristics. These can complicate the allocation of unloading slots to trucks, but should also be taken into account in order to develop a realistic model for truck slot allocation.

The truck arrivals at an ACT are, as mentioned in Chapter 1, characterized by their concentrated pattern. The peaks are somewhat predictable, but the actual arrivals are subject to uncertainty and randomness (Hall, 2001; Ou, Hsu and Li, 2010; Selinka, Franz and Stolletz, 2016).

The unloading process of trucks is characterized by three aspects. First, the service capability for unloading the trucks at the docks is limited, as it depends on the number of docks in use, the number of scheduled employees and the number of material handling equipment available (Ladier and Alpan, 2014; Feng, Li and Shen, 2015). Most often, the unloading process follows a FCFS policy (Selinka, Franz and Stolletz, 2016). Second, each truck can carry shipments for a number of different flights. As a result, some shipments go directly to the build-up area and their flight, while others have to be temporarily stored (Ou, Hsu and Li, 2010). Third and last, the shipments a truck contains can widely vary in size, weight, number of pieces and shipment type (for example temperature-controlled or dangerous shipments) and can be delivered either loose or already palletized on a ULD (Ou, Hsu and Li, 2010). This causes variety in required unloading time per truck and thus increases the need for flexibility at the ACT unloading and sorting processes. Regarding the time-critical nature of the truck arrivals, using variable unloading times has a great impact on the practical relevance of the model. Note that the number of available employees in the first aspect and the cargo routing in the second aspect are two of the key ACT decision problems identified by Feng, Li and Shen (2015).

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2.4. Existing models on truck scheduling for air cargo terminals

This section reviews the models in literature that are relevant to ACT truck scheduling. To the best of our knowledge, only two articles written by Hall (2001) and Ou, Hsu and Li (2010) model ACT operations specifically for scheduling truck arrivals. The few other articles that mathematically model ACT operations are mainly focused on the cargo routing problem within the ACT (Lee et al., 2006; Xu et al., 2014) or the scheduling of manpower (Nobert and Roy, 1998; Yan, Chen and Chen, 2006; Rong and Grunow, 2009). These articles solely focus on one of the key ACT decision areas and take the others as a given, thus failing to model the ACT operations as an integrated system as Feng, Li and Shen (2015) described. Other articles that offer input later in this review originate from the research area of cross-docking, as an ACT can be seen as a cross-dock (Belle, Valckenaers and Cattrysse, 2012; Selinka, Franz and Stolletz, 2016).

Hall (2001) was the first author to address the interaction between the arrival of trucks and the processing of shipments. He schedules trucks to arrive at a reasonable constant rate with the goals of keeping the sorting process productive and minimizing the queue of shipments waiting to be processed. He models this as a stochastic work conserving single server queuing system with random bulk arrivals. Ou, Hsu and Li (2010) use time-indexed integer programming to schedule trucks to arrive such that the total handling and storage costs for all shipments are minimized. Upon arrival, shipments may either go directly to the ULD build-up area and departing flight, or they have to be temporarily stored.

Both Hall (2001) and Ou, Hsu and Li (2010) incorporate variable unloading times and, especially Ou, Hsu and Li (2010), internal routing. However, by not including a limitation on the storage capacity, the internal cargo routing is presented less realistic. They also both fail to include all three key ACT decision problems as emphasized previously. Lastly, both articles do not incorporate the trucker’s preferred unloading time window, undermining the importance of taking a more system wide view as stressed in Section 2.1. Due to the complexity of a trucker’s route among different ACTs, shippers and consignees, imposing an unloading time that only incorporates the ACT’s constraints is likely to result in many missed slots.

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incorporation of both is important in our model: when the storage facility is full or material handling is fully occupied (i.e. the ACT gets congested), trucks can no longer unload at the docks and need to wait. Taking the above limitations in consideration, the following cross-docking articles provide two relevant additions to our model.

A cross-docking article that, in contrast to Hall (2001) and Ou, Hsu and Li (2010), takes the trucker’s preferred unloading time window into account for truck scheduling is written by Ladier and Alpan (2014). The earliest possible arrival time and the latest possible departure time for each truck are, however, incorporated as soft constraints that can be violated at a cost. That is because internal shipment flows might prove unfeasible if the wishes of the trucking companies were granted directly. By incorporating the truckers’ preferred unloading time window, we also take a more integrated supply chain view.

The articles of Boysen, Briskorn and Tschöke (2013) and Tootkaleh, Ghomi and Sheikh Sajadieh (2016) on cross-dock truck scheduling include the departure times of outbound trucks as hard constraints, which makes them suggest to include a constraint that allows shipments to miss their flight. This aspect should also be included in our model, as delivery reliability is identified as one of the key factors in ACT performance (Rahman et al., 2017). In our context, concentrated truck arrivals and insufficient ACT capacity to unload and process shipments can lead to shipments missing their flights. Incorporating this aspect should result in more feasible solutions and brings the model closer to reality.

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3. Methodology

In order to assess the effect of a slot allocation policy on ACT performance, relative to the effect of the benchmark FCFS policy, this thesis will formulate an integer programming (IP) problem. Mathematical modelling is also used as a method in the articles reviewed in Section 2.4 and, more general, in truck scheduling articles in cross-docking (Belle, Valckenaers and Cattrysse, 2012). Mathematical modelling enables the generation of quantitative results and the exploration of the policy’s effect without interfering with the current ACT operations or making any initial investments (Robinson, 2014). The wide availability of quantitative data at Swissport is an additional motivation to perform this type of study.

A truck-to-slot allocation problem forms the basis of the deterministic IP and is complemented by constraints representing the aspects identified in Chapters 1 and 2. As the model is driven by empirical findings and measurements, this research is considered a model-based empirical research (Karlsson, 2016). This type of research aims to capture the behavior of real-life operational processes. It can be used to predict the future state of the modelled process, which aids the decision making process faced by ACT managers in real-life.

The structure of methodology chapter is as follows. Section 3.1 contains the informal problem definition. Section 3.2 contains the formal problem definition, which includes the declaration of the decision variables, parameters and assumptions. It also describes how the aspects identified in Chapters 1 and 2 are included in the IP. Section 3.3 then defines the slot allocation IP. Section 3.4 discusses model verification and validation. Section 3.5 describes the solution method to generate solutions from the model in the next chapter.

3.1. Informal problem definition

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shipment and because a truck is assumed to be more important when it carries more shipments (i.e. its waiting is higher penalized). Our goal is to find a schedule for the trucks that minimizes the total penalties issued for the amount of shipments missing their flights and the total number of periods shipments spend in storage, while being as close as possible to the requested unloading time of the trucking company. This objective takes both the ACT and truckers’ perspectives into account.

3.2. Formal problem definition

The integrated slot allocation IP can be formally defined as following. Consider a set of discrete time periods. Within this time horizon, consider a set of flights where each of these flights has a fixed departure time that is given. Also consider a set of trucks where each truck has a given number of shipments it delivers for flight . A shipment consists of all goods a shipper sends to a consignee at a certain moment. It consists of one or more pieces, either loose shipments or palletized as one ULD and it can have any weight and volume. Note that each truck can deliver shipments for several flights and that each flight can be loaded with shipments delivered by several trucks.

We face the problem to schedule all arriving trucks in such a way that the penalties issued for storing shipments, randomly arriving truck waiting time, slot requesting truck waiting time and late shipments are minimized. The weights given to each of these sub objectives, respectively and , create a priority of certain trucks over others in the allocation of slots.

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number of time periods the truck spends waiting after . Both penalties are multiplied by the number of shipments in the truck to prioritize trucks carrying more shipments. The preferred unloading time window is considered a soft constraint that can be violated at a cost, as strictly adhering to the requested time windows might result in infeasible cargo flows inside the ACT. When it is not feasible to allocate a slot requesting truck to a time slot it prefers, it is allocated to the first available slot in order to minimize the total penalty issued. Through this cost construction, slot requesting trucks will have some priority over randomly arriving trucks in the allocation of slots, as is also reasonable in practice.

Also consider a set of inbound docks , representing the doors where the set of trucks can be unloaded. Each truck needs a given time slots for unloading, where each time slot is one time period in length. The IP ensures all needed time periods are scheduled consecutively and at the same dock. We assume that once unloading starts, the truck is unloaded without interruptions.

Even though all truck arrival times are assumed to be deterministic and in time, shipments may still miss their flight. When the maximum material handling or storage capacity has been reached, the capacity of the ACT may be insufficient to unload all trucks in time. As a result, a truck may be too late to deliver shipments for a certain flight , triggering the binary variable to be 1. The corresponding shipments are assumed to be lost business and penalized at cost . Assuming that is a relatively high cost, trucks carrying time-critical shipments will have highest priority in the allocation of slots.

After unloading, for each shipment is decided whether it can proceed directly to the line-up area of its flight or whether it needs to be temporarily stored until departure. This reflects the key ACT decision problem of internal cargo routing. Shipments can proceed to the aircraft line-up area between and time periods before flight departure, as the line-up area is then open. The ACT storage facility has a maximum capacity of shipments that can be stored in each time period . Storing one shipment costs per period of time. The ACT facility has a maximum capacity of shipments that can be moved during time period due to constraints in the number of available material handling equipment and scheduled employees. This reflects the key ACT decision problem of manpower scheduling.

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The remaining assumptions are the following:

a) In this deterministic model, all trucks are assumed to arrive on their known arrival time.

b) The required unloading periods and exact contents of each truck are known at the beginning of the time horizon.

c) Shipments from a truck proceed to the ACT floor only after complete unloading of

the truck. This is a reasonable assumption, as in reality all shipments first have to be gathered for documentation and inspection, making them simultaneously available to the ACT floor. The inspection and documentation of shipments are assumed to be included in the truck unloading time.

d) Each movement by forklift truck (i.e. to transport a shipment from truck to line-up area; from truck to storage facility; or storage facility to line-up area) is assumed to take 1 period of time.

e) The time for eventual sorting and build-up of loose shipments on ULDs is not included in the model, as this most often takes place in the storage area with the shipments that are already present.

f) Shipments cannot enter and leave the ACT storage facility in the same period of time.

g) The time periods in which a shipment enters or leaves the ACT storage facility are also paid storage costs for.

h) We assume all parameters except for and to be integer.

3.3. Model formulation

Using the notations summarized in Table 3.1, the slot allocation problem can be represented as a deterministic integer program with objective function (1) and constraints (2) - (28). The shipments’ flow in the IP is schematically depicted in Figure 3.1.

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variable is used to indicate and penalize the shipments that missed their flight. Constraints (14) – (20) model the internal cargo routing of shipments through the ACT facility. Constraint (14) ensures that all shipments from a truck move to the ACT floor in the period after the truck has been unloaded. They also ensure that all shipments proceed either directly to their flight if possible, or first to the storage facility. Constraints (15) – (16) ensure that all shipments for a flight move to the line-up area during the time periods it is open. They also ensure that shipments that are able to proceed directly from the truck to the flight will do so and that shipments that have arrived earlier are retrieved from the storage facility. Constraints (17) – (18) ensure that shipments must first enter the storage before they can be retrieved from it and that entering and retrieval happens in different time periods. Constraint (19) limits the material handling capacity of the ACT. Constraints (20) – (21) calculate the amount of shipments in the storage facility, while constraint (22) limits the capacity of the storage facility. Finally, constraints (23) – (28) define the integer and binary nature of all decision variables.

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Indices

Set of inbound trucks Set of outbound flights

Set of docks available for unloading inbound trucks Set of time periods in the planning horizon

Parameters

Weight assigned to the periods of time that shipments spend in storage Weight assigned to the periods of time truckers spend waiting

Weight assigned to the periods that are extra penalized for scheduling slot requesting truckers outside their preferred unloading time window

Weight assigned to the shipments that miss their flight

Type of truck i: 0, if truck arrives randomly; 1, if truck requests a slot Number of time periods needed to unload truck i

Arrival time of truck i

The last time period of the preferred unloading time window indicated by truck i

G Large integer

Departure time of flight o

Time periods before flight o departure that the aircraft line-up area closes

Number of the shipments in truck i destined for flight o

E Time periods before flight o departure that the line-up area opens

Maximum number of export shipments that can be moved during one period of time

Maximum number of the export shipments considered in the time horizon that can be stored during one period of time

Decision variables

Binary variable: 1, if truck i is assigned to dock m at time t ; 0, otherwise

Binary variable: 1, if truck i is assigned to dock m; 0, otherwise

Binary value: 1, if it is the first time period t after which truck i is finished unloading at dock

m; 0, otherwise

Number of the time period in which truck i starts unloading Number of periods for which waiting costs are issued for truck i

Number of periods for which an extra penalty is issued for scheduling slot requesting truck i after its preferred unloading time window

Binary value: 1, if shipments from truck i are not able to make it to flight o; 0, otherwise Number of shipments transferred from truck i directly to flight o at time period t

Number of shipments transferred from truck i to the storage at time period t Number of shipments transferred from the storage to flight o at time period t

Total number of shipments in the ACT storage at time period t

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3. Methodology 21 (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28)

3.4. Model verification and validation

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written code and logic of the model have been extensively discussed with the first thesis supervisor; and while testing the model outcomes are assessed on logic.

Model validity is important in our research as the model and its outcomes should reflect reality to such an extent that they can be used for decision making by ACT managers in practice. The validity can be assessed on multiple aspects: the conceptual model, the data, the model itself, the experiments and the solution (Robinson, 2014). Meetings with Swissport managers and trucking companies were used to increase our understanding of the ACT system. These meetings all increased both conceptual model validation, as the accuracy of content and assumptions used in the model became more realistic, as well as model validation, as their approval was gained for the elements included in the developed model. The use of quantitative data, complemented with terminal observations and managers’ opinions, enhanced the data validity of this research as it increased the accuracy of the collected real-life data. Experiment validity is enhanced by the direct input of real-world data. Solution validation is enhanced as the model outcomes under the FCFS policy can be compared to Swissport’s current performance, as it currently employs this policy.

By covering all validation dimensions, the model is believed to reflect reality sufficiently accurate to be used by ACT managers in decision making. It should be noted that, although Swissport’s processes are representative for ACTs in general, there inevitably are differences that affect the model. Chapter 4 accounts for this aspect by documenting the collection of data.

3.5. Solution method

In order to obtain solutions from the IP, it has been implemented in the software of IBM ILOG CPLEX Optimization Studio (version 12.8), hereafter called CPLEX. The model was tested on a personal computer with a 64-bit processor with 6GB of workable memory. Given the number of tests to run, a runtime of maximum 30 minutes was assumed to be acceptable. However, due to the limited amount of workable memory and the amount of variables and constraints taken into account, the runtime is quite large. Datasets containing 70 trucks, 3 flights and 84 time periods (representing 3 hours of truck arrivals on the Wednesday afternoon); 24 trucks, 3 flights and 84 time periods; 24 trucks, 2 flights and 84 time periods; and 24 trucks, 2 flights and 41 time periods (representing 1 hour of truck arrivals on the Wednesday afternoon) all had a runtime of over 1 hour, after which the run was aborted. Finally, a dataset containing 12 trucks, 2 flights and 41 time periods took an acceptable 22 minutes of computation time.

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4. Data collection

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4. Data collection

We have collected data at the ACT of Swissport located at Amsterdam Airport Schiphol in order to generate valid input to run the model and realistically explore to what extent the slot allocation policy can increase ACT performance. This ACT is representative for other ACTs worldwide due to its size and because it has to deal with a concentrated arrival pattern of trucks and warehouse congestion at peak times.

The ACT export operations of Swissport can be summarized as follows. In 2017 it handled a total of 13.594 shipments for 37 airlines, of which 56 percent was export. Swissport operates 24 hours per day, 7 days per week. Its peak time for import shipments is in the morning, as the cargo aircrafts mainly land between 7:00 and 11:00. The peak time for export shipments is in the afternoon, as the cargo aircrafts mainly depart between 16:00 and 20:00. Currently, Swissport has no control over the arrival times of the trucks that come to unload and load at the ACT, also because information sharing is limited. A FCFS policy is currently in use, where priority can be given to trucks containing time-critical shipments that need to make it to their departing flight. Currently, the ACT capacity to unload all arriving trucks and move the shipments around the ACT is not sufficient during peak times, and trucks start queuing in front of the ACT.

The values of the IP parameters are estimated based on data collected at Swissport to enhance model validity. Three different data sources are used to create data triangulation and increase the reliability of the data (Karlsson, 2016). The quantitative data is used as a basis, terminal observations and expert opinions are used to verify and clarify the quantitative data. The latter two also provided us with a feel for the overall ACT work environment and systems. The expert opinions are provided by Thierry Huizing, project manager and company supervisor of this thesis, and Eljas Oulad, warehouse manager.

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departure times cannot be discovered. The use of one single company is not necessarily a data limitation, as it enabled the collection of in-depth data for realistically estimating the parameters. The following sections describe per parameter how the data was collected and what assumptions were made to estimate a valid value. This documentation of the data collection process enhances data validity (Robinson, 2014). Chapter 5 describes how the parameter estimates are used for generating test problems for the numerical experiments.

4.1. Flight departure times

: schedule

The scheduled arrival and departure times of cargo aircrafts during a regular week at Swissport can be found in Appendix 9.1.1. The aircraft arrival peak occurs from 7:00 until 14:00, the departure peak from 14:00 until 20:00.

4.2. Expected proportion of trucks requesting a slot

K = 1: 50%

The proportion of trucks that is expected to request a slot is the only parameter that cannot be based on historical data. Instead, it is based on the expert opinion of Thierry Huizing as he is most involved in this research project. Following his assessment, 50 percent of the trucks is expected to request a slot when a proper slot system comes in place. This percentage is expected to increase when truckers are aware of the possibility and benefits of requesting a slot. This estimate is only an initial value to generate input for the experiments in Chapter 5. In reality, this parameter will be equal to the proportion of the trucks that actually requests a slot.

4.3. Truck arrival pattern

: distribution

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Figure 4.1 – Discrete distribution of the truck arrival times

4.4. Number of shipments per truck

: distribution

Data from December 2017 was available for estimating the amount of shipments per truck. The dataset comprises 7,342 arriving trucks and states per truck the amount of shipments it contained. The distribution of shipments per truck is depicted in Figure 4.2.

Figure 4.2 – Distribution of the number of shipments per truck

0% 1% 2% 3% 4% 5% 6% 7% 8% 01: 00: 00 02: 00: 00 03 :00 :00 04: 00: 00 05: 00: 00 06: 00: 00 07: 00: 00 08 :00 :00 09: 00: 00 10: 00: 00 11: 00: 00 12: 00: 00 13 :00 :00 14: 00: 00 15: 00: 00 16: 00: 00 17 :00 :00 18: 00: 00 19: 00: 00 20: 00: 00 21: 00: 00 22 :00 :00 23: 00: 00 00: 00: 00 P er ce nt age of t ruc ks

Truck arrival time at Swissport's gates

Peak for flights 19:40, 20:20 Peak for flight 14:20 Peak for flights 16:05, 16:50 0% 5% 10% 15% 20% 25% 30% 35% 40% 1 2 3 4 5 6 7 8 9 ₁₀ ₁₁ ₁₂ ₁₃ ₁₄ ₁₅ ₁₆ ₁₇ ₁₈ ₁₉ ₂₀ ₂₁ ₂₂ ₂₃ ₂₄ ₂₅ ₂₆ ₂₇ ₂₈ ₂₉ ₃₀ ₃₁ ₃₂ ₃₃ ₃₄ ₃₅ ₃₆ ₃₇ ₃₈ ₃₉ ₄₀ P er ce nt age f re que nc y

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26

4.5. Required unloading time per truck

: distribution

According to Eljas Oulad, the required unloading time of a truck depends not only on the number of shipments per truck, but also on their weights and volumes. As such, the number of shipments per truck identified in Section 4.4 cannot be used to predict the required time to unload a truck; both parameters are estimated independently.

The times a truck starts and finishes unloading are not recorded in ‘Cargospot’. However, Jan Carel Paro (Black Belt at Amsterdam Schiphol Airport) performed a research in February 2017 on the truck processing times at Swissport’s ACT. He analyzed data on the unloading times of the 1,133 trucks that visited the ACT between Tuesday February 21st and Monday February 27th 2017. Upon request, he provided us with the original source data so we could generate the distribution of required unloading times for the analyzed trucks. Of the 1,133 trucks, 434 visited the ACT only for unloading; the other trucks came for loading or a combination of unloading and then loading. The discrete distribution of the required unloading time per truck is depicted in Figure 4.3.

It should be addressed that this data does not originate from the same month as the arrival and shipment number data. However, according to Thierry Huizing and Eljas Oulad this available data provides a sufficiently accurate insight in the required unloading time per truck.

Figure 4.3 – Distribution of the required truck unloading time

0% 2% 4% 6% 8% 10% 12% 14% 16% 0 -5 5 -10 10 -15 15 -20 20 -25 25 -30 30 -35 35 -40 40 -45 45 -50 50 -55 55 -60 60 -65 65 -70 70 -75 75 -80 80 -85 85 -90 90 -95 95 -100 100 -105 105 -110 110 -115 115 -120 P er ce nt age f re que nc y

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4.6. Number of docks

9

Swissport’s ACT has a total of 26 doors for trucks to dock at, as depicted in Appendix 9.1.5. Only 9 are dedicated to unload export trucks, the other doors are dedicated to unload vans, trucks containing ULDs, import trucks or pharmaceutical trucks.

Even though the doors are always open, their unloading capacity depends on the number of employees available to unload the trucks. This factor is incorporated in parameter , the ACT material handling capacity.

4.7. Material handling capacity

: 187 / 300 shipments per hour

The material handling capacity for all shipments at Swissport depends on the number of available employees operating the material handling equipment; the amount of equipment available is sufficient and constant over time. According to Eljas Oulad, each forklift truck operator is able to move 50 shipments per hour, from truck to either storage or line-up area and from storage to line-up area. During the day (6:00 until 22:00), 8 employees are available to operate the forklift trucks for moving shipments. During the night (22:00 until 6:00), generally 5 employees are available to operate the forklift trucks. According to Eljas Oulad, 75 percent of the material handling capacity is used for export shipments, at they require more handling than import shipments. As a result, the material handling capacity for export shipments is 300 per hour during the day and 187 per hour during the night.

4.8. Storage facility capacity

:

As the shipments can have many different dimensions, there is no unambiguous number of shipments that can be stored in the ACT’s storage facility. Also, when running the model for a certain time window, only a fraction of the storage can be used for those particular shipments. According to Thierry Huizing and Eljas Oulad, the ACT cannot store all shipments all trucks deliver: about two third of a truck’s shipments requires storage, the others need to directly proceed to the line-up area.

The storage capacity is fixed over time, as Swissport does not have external storage locations or outsourcing of storage capacity to external parties.

4.9. Opening times line-up area

B: 3 hours F: 0.5 hours

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28

4.10. Objective function weights

: 1, 2, 4, 16

The objective of the IP is to minimize the total number of late shipments and shipments in storage, while being as close as possible to the requested unloading time of the trucking company. It is up to the ACT manager to decide on the relative importance of these often conflicting objectives; this is a strategic decision. A straightforward way to express the relative importance is to link the objectives to their respective costs.

At Swissport, storage costs are a percentage of the shipment’s value, paid per day. Trucker waiting is currently not penalized and the penalty for a shipment that misses its flight is also a percentage of the shipment’s value. In consultation with Thierry Huizing, relative weights are used. A storage period’s penalty is 1; the penalty to keep a randomly arriving trucker waiting is 2; the penalty to keep a slot arriving truck is 4; and the penalty for a shipment that misses its flight is 16.

4.11. Current air cargo terminal performance

s

t

, c

i

,

l

io



W

io

In order to validate the outcomes of the model, the results of the FCFS policy are compared to real-life ACT performance measures. When the experimental outcomes resonate with the outcomes defined here, the outcome validity is considered to be sufficient.

The discrete distributions of the storage time per shipment and for the waiting time a trucker spends upon arrival before it is unloaded can be found in respectively Appendix 9.2.4 and Appendix 9.2.5. Regarding the late shipments, ‘Cargospot’ offers data from December 2017 on the fraction of shipments that are delivered after their latest acceptance time, and thus miss their flight, . On the considered Wednesdays in December, this was 2.2, 1.4, 7.5 and 0.0

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5. Numerical experiments and results

29

5. Numerical experiments and results

Through numerical experiments we aim to explore the solutions generated by the IP under several circumstances in order to determine the effect of the slot allocation policy on ACT performance. In Section 5.1, we describe the experimental design and process for generating test problems from the Swissport data. In Section 5.2, we present and interpret the experimental results. In Section 5.3, we perform a sensitivity analysis to illustrate the impacts of key ACT parameters (number of docks, storage capacity, material handling capacity and proportion of trucks requesting a slot) on the ACT performance (storage periods, truck waiting periods, late shipments and ACT congestion).

5.1. Experimental design

Considering the computational time per run and the number of runs that should be performed per test problem, a total of 10 test problems is generated. Each test problem represents a truck arrival setting and serves as input for two series of experiments: the FCFS policy and the slot allocation policy. The FCFS policy is used as a benchmark to compare the outcomes of the slot allocation policy to, as it represents the current ACT performance under uncoordinated truck arrivals. The FCFS experiments do actually not serve all trucks purely on a first come, first served basis as they also contain the and through which some priority is given to trucks containing many or time-critical shipments, as is also reasonable in practice. Its benchmark function is derived from not having the extra prioritized trucks the slot allocation experiments have.

5.1.1. Generation of test problems

The process for generating parameter values is summarized in Table 5.1. The parameter values regarding the arriving trucks (i.e. and ) will be generated for each test problem by

sampling from their distributions presented in Chapter 4. These parameters characterize the truck arrivals that need to be scheduled and an ACT indeed faces variations in these parameters every day. It is assumed that these parameter values are independent. The parameter values regarding the ACT characteristics (i.e. and policy parameters - ), on the other hand, take the Swissport values determined in Chapter 4. This not only reduces complexity, but it also tests the impact of scheduling in a stable context, making the outcomes more comparable to each other. However, concerning the generelizability of our results to other ACTs in practice, a sensitivity analysis on key ACT characteristics is performed in Section 5.3.

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20:20 (time period 41). This time horizon includes the departures of the last 2 flights that day at 19:40 (time period 33) ad 20:20 (time period 41). The 12 trucks arrive only in the first hour (time periods 1 – 12), the remaining time periods are budgeted for finishing the unloading and cargo routing. The arriving trucks’ parameter values for the test problems are generated as follows. The truck arrival times ( ) form the distinction between the two series of experiments. For the FCFS policy, all arrival times are sampled from the concentrated arrival distribution. As the truck arrival time window covers only 1 hour, a more detailed arrival distribution is generated from Swissport’s truck arrivals between 17:00 and 18:00 on a Wednesday. This distribution is presented in Appendix 9.3.1. The end times ( ) of these trucks’ preferred unloading time windows are equal to the last time period in the time horizon.

The truck arrival times ( ) within the slot allocation policy are generated differently for the two types of trucks (both 50 percent). Every other truck is considered a slot requesting truck. For the randomly arriving trucks the same arrival times are used as under the FCFS policy, to enhance comparability of the two series of experiments. For the slot requesting trucks, the arrival times are evenly divided over the time horizon to simulate their coordinated nature (i.e. at time periods 2, 4, 6, 8, 10 and 12). The end times of their preferred unloading time windows ( ) are all 3 periods (15 minutes) after the start of the time window ( ), which is less than the current average waiting time of 25 minutes to emphasize that requesting a slot should benefit the truck. The number of time periods required to unload a truck ( ) is sampled from the discrete distribution presented in Section 4.5.

The number of shipments each truck contains ( ) is sampled from the distribution presented in

Section 4.4, with a maximum of 25 due to the maximum material handling capacity of 25 shipments per time period. As no Swissport data was available on which flights each truck delivers for, these values are generated as follows. For each truck is randomly generated (both 50 percent probability) whether it delivers for 1 or 2 flights and then for which. Then, the truck’s shipments are evenly divided over these selected flights, rounding up if necessary.

Because of using a smaller dataset, some ACT parameters need to be adjusted to prevent overoptimistic performance measures in the solution. As each of the 12 trucks carries on average 5 shipments, a total of 60 shipments is expected. Following the structure presented in Section 4.8, the storage capacity for this dataset is set at 40 shipments. The number of docks is decreased proportionally: as only half of the trucks that normally arrive between 17:00 and 18:00 on a Wednesday are considered, also half of the docks are taken into account, rounded down to 4. The line-up area opening time is decreased to 6 and 12 time periods before departure, as it would otherwise cover the majority of the considered time horizon.

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Parameter Generation of parameter values

Swissport value: Wednesday 19:40 (time period 33) and 20:20 (time period 41) Swissport value: 50%

Randomly arriving: sampled from distribution presented in Appendix 9.3.1 Slot requesting: arrival times evenly divided over time horizon

Randomly arriving: equal to the end of the time horizon Slot requesting: arrival time plus 3 time periods

Sampled from distribution presented in Section 4.4; then assigning each truck to

flight 1 and/or 2 with 50 percent probability each. Sampled from distribution presented in Section 4.5

Swissport value: 300 per hour (6:00 until 22:00), i.e. 25 per time period Determined to be 40 shipments

Swissport value of 3 hours decreased to 1 hour (12 time periods) Swissport value: 0.5 hour (6 time periods)

Swissport values: 1, 2, 4, 16

12 trucks, i.e. half the arrivals in 1 hour on a Wednesday afternoon

2 flights

Swissport value proportionally decreased to 4

41 time periods (Wednesday 17:00 - 20:20); trucks arrive only in periods 1 – 12 Table 5.1 – The generation of parameter values for test problems

Test pro-blem Total number of shipments (avg. 55) Number of trucks Number of trucks delivering for 2 flights Average unloading time (avg. 5.1) Number of trucks Concentrated pattern of randomly arriving trucks

1 61 1 3 4.2 (low) 1 Yes (middle and end)

2 47 0 (low) 6 (high) 4.4 1 Yes (begin and end)

3 61 1 5 (high) 5.4 1 Yes (begin)

4 72 (high) 1 3 4.1 (low) 1 No

5 41 (low) 1 3 5.8 2 (high) No

6 76 (high) 3 (high) 3 6.3 (high) 1 Yes (begin and end)

7 54 2 (high) 3 5.8 2 (high) No

8 33 (low) 1 4 5.0 1 Yes (begin and end)

9 61 2 (high) 3 4.5 1 Yes (middle)

10 52 1 5 (high) 5.0 2 (high) Yes (begin)

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32 5.1.2. Performance measures

In order to compare the outcomes of the experiments to each other and to draw conclusions on the effect of the slot allocation policy on ACT performance, the ACT performance for each test problem is measured on the dimensions listed in Table 5.3. These 5 performance dimensions also appear in the performance measure overviews of Ladier and Alpan (2016) and Rahman et al. (2017). The measures regarding late shipments, storage periods and truck waiting are also reflected in the objective function of the IP. The measure regarding ACT congestion is added to check whether truck coordination, as suggested by literature, actually lowers the key problem of ACT congestion. The 5 measures ensure that both the ACT’s and truckers’ perspectives are taken into account. Taking this broader view is, as was mentioned in Chapter 2, essential for increasing the system wide performance of the air cargo transportation chain (Hall, 2001).

PS Average number of time periods the shipments spends in the ACT storage facility WR Average number of time periods the randomly arrived trucks wait after arrival to unload

WS Average number of time periods the slot requesting trucks wait after arrival to unload MF Percentage of the total shipments that missed their flight

AC The number of periods in which the ACT is congested, i.e. the utilization exceeds 80 percent (in table 5.4: material handling capacity ( ), storage capacity ( ))

Table 5.3 – The ACT performance measures

5.2. Experimental results and interpretation

Table 5.4 summarizes the results of the numerical experiments per test problem.

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FCFS policy Slot allocation policy

Test problem Nr. of shipments PS WR MF (%) AC PS WR WS MF (%) AC 1 61 3.7 10.3 8.2 2, 0 5.2 13.2 13.8 6.6 2, 4 2 47 4.3 11.7 8.5 0, 0 7.0 12.7 8.3 8.5 0, 0 3 61 9.0 11.6 3.3 2, 10 5.2 14.3 14.0 3.3 2, 1 4 72 4.3 18.0 2.8 1, 0 9.6 10.0 13.3 2.8 2, 8 5 41 12.5 7.1 7.3 1, 2 2.4 17.2 11.5 7.3 0, 0 6 76 2.8 9.6 3.9 1, 0 2.1 16.5 10.0 3.9 1, 0 7 54 8.4 13.1 5.6 0, 6 1.5 11.5 14.8 5.6 0, 0 8 33 7.4 7.3 6.1 0, 0 5.8 9.0 5.0 7.3 0, 0 9 61 8.6 14.3 3.3 0, 12 3.5 10.3 14.0 3.3 1, 0 10 52 4.6 14.8 1.9 1, 0 4.2 6.8 14.2 1.9 1, 0

Table 5.4 – Experimental results

Regarding the results, it is notable that the performance under the slot allocation policy seems lower than under the FCFS policy. It also surprised that in 8 out of 10 FCFS test problems and all slot allocation test problems WR and WS are higher than PS, as truck waiting is more heavily penalized than shipment storage. The congested docks mainly account for these results, but the next two paragraphs also describe the large impact of the required unloading time and amount of shipments per truck on the WR and PS of the resulting truck schedule. The outcome differences between the test problems can mainly be explained by variations in the test problems on truck level, rather than their main characteristics summarized in Table 5.2.

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The height of the truck unloading time also has an impact on truck scheduling as a high unloading time increases the likelihood on dock congestion. Test problems 5, 7 and 10 all contain 2 trucks with a relatively high unloading time (i.e. over 10 time periods). When that truck carries relatively few shipments (test problem 5 and partly 7), unloading priority is given to other trucks carrying more shipments to minimize penalties issued. As a result, all prioritized trucks’ shipments need to be stored and PS increases. A truck that requires relatively high unloading time and carries relatively many shipments (test problem 10 and partly 7), is scheduled such that the shipments can directly proceed to the line-up area in order not to almost fully occupy material handling in two time periods. As other trucks have to wait longer for unloading, WR increases and PS decreases.

Surprisingly, test problems in which relatively many trucks deliver for both flights (test problems 2, 3 and 10) do not have a higher PS as is expected. However, as the line-up area opening times for the first flights are time periods 21 – 28 and for the second flight 29 – 35, there indeed is little time that needs to be spent in storage by the shipments for the second flight.

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5.3. Sensitivity analysis on air cargo terminal characteristics

Sensitivity analyses with respect to the number of docks, the storage and material handling capacity (all three factors that constrain the ACT capacity to handle shipments) and the proportion of trucks requesting a slot are performed to gain insight in the impact of varying ACT characteristics on ACT performance. Due to the required runtime per test, we have chosen to perform the sensitivity analyses only on test problems 1 and 2, which will serve as anchor cases. The interpretation is described in this section; the result tables are included in Appendix 9.4.2. To test the impact of the number of docks on the performance measures, the anchor cases are tested with 3 and 5 docks. The storage capacity was seldom congested as shown in Table 5.4, so to find the effect of its congestion we lowered the storage capacities and tested the anchor cases under storage capacities of 30 and 20 shipments. The material handling capacity was, likewise, not often congested. To find the performance under constrained material handling capacity, we lowered it and tested the anchor cases under material handling capacities of 20 and 15 shipments per time period (i.e. 240 and 180 shipments per hour). To prevent infeasibility in test problem 1, we had to lower the amount of shipments truck 10 carried for flight 2 from 20 to 15 shipments for the test with the material handling capacity of 15.

The results in Tables 9.14 – 9.16 in Appendix 9.4.2 show similar results for the three sensitivity analyses. The here described patterns occur at both the FCFS and slot allocation series of experiments. When the number of docks, the storage or material handling is decreased, PS and MF decrease and WR and WS increase and vice versa. As the ACT then becomes more constrained, trucks need to wait longer to unload at a time period in which a dock is freed or their shipments can proceed directly to the line-up area. In that case, they do not utilize storage space or require double material handling for bringing and retrieving them to and from the storage. This effect is more pronounced for anchor case 1 as it has relatively many shipments and puts more pressure on the ACT capacity.

Lastly, we tested the anchor cases under increasing proportions of trucks requesting a slot, i.e. more coordinated truck arrivals. The anchor cases are tested with 8 and 10 out of 12 trucks being slot requested trucks. Their arrival times are included in Appendix 9.4.1. The results in Table 9.17 in Appendix 9.4.2 show that PS, WR and AC decrease when truck arrivals are more evenly divided. WS, on the other hand, starts to increase. It seems that when more trucks have ‘priority’, those benefits are no longer exclusive and the average waiting time for these trucks increases. However, taking all measures into account, the overall ACT performance improves.

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6. Discussion

For truck scheduling in general, our findings highlight the large impact of trucks which require large unloading times and carry many shipments on the unloading schedule and resulting performance. For the slot allocation policy the findings suggest, although based on small test problems, that if only those trucks are allowed to request a slot, ACT performance increases: the ACT would have fewer shipments in storage, and thus less pressure on the storage and material handling capacity, and the slot requesting trucker would wait shorter than under the FCFS policy as they are now prioritized. The randomly arriving trucks, having low unloading times and few shipments, will indeed have longer waiting times as they would be unloaded earlier otherwise. An ACT could experiment with dedicating a small fraction of the docks to randomly arriving trucks, to see whether that decreases their waiting time while preserving the other benefits. The minimum values for required unloading time and amount of shipments should be determined such that they represent no more than half the amount of arriving trucks. The sensitivity analysis showed that having too many trucks requesting a slot will reduce the positive effects on their waiting times. The sensitivity analysis also shows that, for truck scheduling in general, the ACT performance can be further enlarged by increasing the docks, storage and material handling capacity. All described findings not only hold for ACT truck scheduling, but can also be generalized to cross-dock truck scheduling.

The research question stated in Chapter 1 can be answered with our findings. Only when the model can be adjusted to solve larger and more realistic test problems, we would be able to reliably quantify the effect of the slot allocation policy on ACT performance. Therefore, to express the answer in words, we assess the overall extent to which the slot allocation policy can improve ACT performance to be large enough for academics to further research it and for ACT managers to consider experimenting with a slot allocation policy for large trucks only.

Relating our findings to the existing body of knowledge reviewed in Chapters 1 and 2, we can say that they challenge the articles that claim truck coordination benefits ACT performance (Hall, 2001; Rong and Grunow, 2009; Konur and Golias, 2013) by suggesting that the coordination of truck arrivals at an ACT does not straightforwardly lead to improvements in ACT performance. Our findings refine the circumstances under which that improvement can occur. They support the findings of Chen, Govindan and Yang (2013) as the trucker waiting time and storage time were indeed educed and workload was spread. Our findings cannot support nor challenge the finings of Huynh (2009) on the policy’s effectiveness when a good portion of the arrivals are walk-ins or late, as our model did not include this stochasticity.

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6. Discussion

37

integrates the key ACT decision problems (truck scheduling, manpower scheduling and internal cargo routing) and even the trucker perspective. To do so, we built on existing ACT truck scheduling models (Hall, 2001; Ou, Hsu and Li, 2010), introduced relevant aspects from cross-dock truck scheduling models (Boysen, Briskorn and Tschöke, 2013; Ladier and Alpan, 2014; Tootkaleh, Ghomi and Sheikh Sajadieh, 2016) and used real-world data and observations to validate the model. By also including the trucker’s perspective in the model and policy, we take the wider perspective that is needed for improving supply chain wide performance (Hall, 2001). To relate back to the empirical context set out in Chapter 1, our findings work towards a solution for the concentrated truck arrival problem stated there, although future research is still needed to test the model with larger and more realistic test problems. Then, also a proper design of the policy can be tested. In practice, the ACT should decide upon a policy for trucks that miss their slot and the time until which trucks can request a slot. A more flexible policy in which a truck can pre-announce its upcoming arrival to reserve a slot and confirm the actual arrival and precise truck contents a certain amount of hours before the time of the slot could provide the flexibility that is needed for both trucking companies and ACTs. Increased data sharing, which is now limited mainly from the trucker’s side (Rahman et al., 2017), is also needed in practice. When the ACT has the precise location of the truck and detailed information on its expected arrival time, the performance of the slot allocation policy increases (Zhao and Goodchild, 2010).

6.1. Research limitations

This research modelled ACT operations and explored the effect of a slot allocation policy on ACT performance as had not been done before, but several research limitations should be noted as a critical reflection upon the performed research. As few relevant ACT and cross-docking articles were available on truck scheduling, a small base of existing knowledge was provided to build this research on. Only the essentials of the key ACT decision problems could be adopted, even though this thesis aimed at developing an integrated model. As a result, our model mainly falls short in modelling the manpower scheduling problem well.

Due to the use of a single case and data of only several months, the precision of the data is likely to be overstated. Also assumptions like the deterministic truck arrival times and the material handling capacity being only dependent on the number of shipments (and not the wide variety in volumes and weights) reduce the practical relevance of the model.

Truck arrival scheduling for air cargo terminals: Modelling a slot allocation policy to alleviate congestion and improve performance