Master’s Thesis
Reducing backup capacity fleet for distribution
systems via simulation: A case study
By A.A. Haverkamp Begemann
Dual Degree in Operations Management University of Groningen
Newcastle University
December 12, 2016
Word count: 14,000
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Abstract
Purpose: A small portion of all the routed parcels is not able to reach its destination due to
disruptions in the network. A backup capacity trailer fleet transports these parcels to their destination to ensure a high service level at acceptable costs. Backup capacity planning in hub-and-spoke distribution networks has received little attention in literature, while its impact on costs and service level is significant.
Method: A Monte Carlo simulation based on data provided by PostNL Parcels provides a
framework to generate representative datasets when historical data is limited. In addition, a designed algorithm contains planning procedures to determine the required backup capacity and starting locations. Several hinterland configurations are tested and compared on their costs efficiency and service levels.
Findings: The non-overlapping hinterland structure achieved a costs reduction of ##% on
backup capacity budget compared to PostNL Parcels’ current planning approach. Based on the expected total volume on a day, the developed model determines how many backup trailers should be located at which depots in the hub-and-spoke network.
Contribution: Adopted from Emergency Vehicle Location queueing theory, additional candidate
servers from an overlapping hinterland, covering ### hubs in a hub-and-spoke distribution network, does not lead to a more efficient server allocation.
Keywords: Backup capacity transport, Hub-and-Spoke distribution, Emergency vehicle location,
Monte Carlo Simulation, Overlapping hinterlands.
Definitions
PNP: PostNL Parcels
Flexible trailer: A stand-by trailer that can flexibly be allocated to a specific route on the delivery night where needed
PSD: Postal Service Delivery (provider)
FTL: Full-Truck-Load
LTL: Less-than-Truck-Load
RC: Roll Cage
##: ##################
Demand trip: A transport between two depots, which can not be transported with regular trailers and
is caused by a disruption
Author: A.A. Haverkamp Begemann
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Table of Contents
1 Introduction ... 5
2 Problem description ... 8
2.1
System overview ... 8
2.2
Current planning approach ... 10
2.3
Research Question ... 11
3 Theoretical background ... 12
3.1
Parcel transportation systems ... 12
3.2
Hub-and-spoke networks ... 14
3.3
Emergency vehicle location ... 15
3.4
Research Novelty ... 16
4 Methodology ... 18
4.1
Why a simulation study is chosen ... 18
4.2
Assumptions ... 19
4.2.1
Trip duration ... 19
4.2.2
Connection between demand trips ... 19
4.2.3
Time of arrival ... 20
4.2.4
Miscellaneous trips from or to retailers ... 20
4.3
Monte Carlo simulation to construct data ... 20
4.3.1
Correlation between daily parcel volume and number of demand trips ... 20
4.3.2
Probability matrix ... 23
4.4
Algorithm to process the constructed data ... 23
4.4.1
Assignment of demand trips to hinterlands ... 24
4.4.2
Determine starting location ... 25
5 Results ... 26
5.1
Interpretation ... 26
5.2
Hinterland configurations ... 27
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5.4
Driving time parameter ... 30
5.5
Comparison with PNP’s current approach. ... 32
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Discussion and Limitations ... 33
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Conclusions ... 35
7.1
Further research ... 36
Bibliography ... 37
Appendix A: Map of PNP’s hybrid hub-and-spoke network ... 40
Appendix B: Transportation times between depots ... 41
Appendix C: Probability Matrix ... 42
Appendix D: Simplified overview of model code ... 43
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1
Introduction
Parcel delivery organizations are currently experiencing enormous growth due to a global increase in e-commerce. The total European e-commerce market in 2015 was valued to €477 billion of which 53% was spent on ordering physical goods (Marcus & Petropoulos, 2016). In 2015, the Dutch e-commerce market grew with 23%, resulting in 11.3% more transported parcels compared to 2014 (Autoriteit Consument & Markt, 2016). PostNL, the largest parcel delivery organization in The Netherlands, has experienced a volume growth of 140% during the past decade (Autoriteit Consument & Markt, 2016; PostNL, 2016). Such market growths have not been unnoted which is why one of the characteristics of the Dutch parcel delivery sector is its competitiveness (Rabobank, 2015).
As a result, parcel delivery organizations are constantly trying to achieve more efficient operations in order to gain more market share (Grünert & Sebastian, 2000; Lee & Moon, 2014; Wasner & Zäpfel, 2004). The delivery performance is not only expressed in costs, but also in delivery speed and reliability. Customers usually call for next day delivery within a few hour time window and the demand for these more complicated types of delivery increases every year (Autoriteit Consument & Markt, 2016). Parcel delivery organizations all over the world have designed flexible delivery networks that are able to efficiently transport parcels from the sender to receiver at both high and low volumes (Accenture, 2015). The design of such networks should be able to detect and respond to inefficiencies as early as possible in order to survive in the medium and long term (Wasner & Zäpfel, 2004).
This research is focused on a case study of the largest parcel delivery organization in The Netherlands: PostNL Parcels (PNP). The PNP distribution network for line-haul operations is designed according to the hybrid hub-and-spoke principles. Parcels are transported with trailers between depots and hubs during a few hours in the evening and night. Regular trailers are only allowed to travel on fixed routes on predetermined time schedules. Due to numerous different reasons, some parcels are not able to be transported with regular trailers and are at risk of not being delivered the next day. Backup trailers, hereafter flexible trailers, are available to transport those parcels in order to guarantee that those parcels are also delivered the next day. In this research, a parcel transportation movement by a flexible trailer is defined as a demand trip. ####### ########################### ##############. PNP has to decide for every day how many flexible trailers should be ordered and where those should be located in order to fulfil all demand trips. ####### ####### ##### #### ##### ### ######## ###########.
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destination. A problem analysis revealed that the current planning approach concerning flexible trailer allocation tends to be overly risk averse. Too many flexible trailers are generally ordered for a night which causes some trailers to stay at its starting point during the entire night. Also, flexible trailers often need to travel to the depot where the disruption occurred, indicating that the starting location of the flexible trailers is poorly chosen. Empty trailer movements between depots cause waste in terms of time, costs and environmental sustainability (Lin & Chen, 2008). Therefore, a decision concerning the placement of flexible trailers has to be made in addition to the quantity. The following research question has been established in order to address the problems involved with the current planning approach:
How can backup trailers in a hub-and-spoke distribution network be allocated more efficiently?
One key disadvantage of a hub-and-spoke distribution system is a longer transportation duration because every parcel is passed through a hub (Grünert & Sebastian, 2000; Lin & Chen, 2008; Liu, Li, & Chan, 2003). The hybrid hub-and-spoke network of PNP allows trailers to bypass hubs and consequently reduce transportation time. Flexible trailers are often required to transport parcels to a different hinterland, which could be achieved by bypassing the hubs. This research is interested in the performance of non-overlapping and overlapping hinterland configurations, adopted from emergency vehicle location literature. The idea is that the productivity of flexible trailers is increased as more servers are able to respond to emergencies. Consequently, flexible trailers cover smaller areas and therefore less empty kilometres are driven. In this overlapping hinterland configuration, an additional hinterland covers all ### hubs in the PNP hub-and-spoke system because a large part of the demand trips occurs between hubs. These demand trips could be served by a dedicated flexible trailer in the overlapping hinterland, allowing the flexible trailers in the remaining hinterlands to fulfil remaining demand trips.
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This thesis is structured as follows. The next chapter describes how parcels are generally routed through the PNP network and addresses the problems of the current planning approach. This process is vital to understand why flexible trailers exist and how the current planning process is designed. Chapter three discusses the relevant literature for this research. Parcel transportation systems, hub-and-spoke distribution systems and emergency vehicle location problems are the three main fields of research for this study. Chapter three concludes with the identified gap in literature which is addressed in this research. The fourth chapter explains and supports the methodologies which are used to design the simulation model and associated algorithm. Relevant assumptions and parameters help to explain how the model is designed. The results of several hinterland configurations are shown in chapter five and consequently compared to PNP’s current planning approach. Chapter six provides an in-depth discussion and addresses the limitations of this research. The answer on the main research question is provided in chapter 7, where future research on several aspects of this problem is suggested.
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Problem description
Flexible trailers are used to transport parcels through the hybrid hub-and-spoke network if regular trailers are not able to perform this transport. In order to understand why some parcels have to be transported with flexible trailers, we have to understand how a parcel is routed through the PNP network. The succeeding chapter elaborates how the PNP line-haul transportation system is designed, how flexible trailers are currently allocated and a research question is formulated.
2.1 System overview
Parcel Service Delivery (PSD) providers have designed an overnight line-haul transportation system with the purpose to route parcels between depots within a predetermined time-frame (Grünert & Sebastian, 2000). The system basically entails depots, hubs, sorting machines, trucks with trailers, parcels and a routing schedule which determines the efficiency and capacity of the line-haul transportation system.
The current PNP network # ## ## ## ## # consists of # depots where sorting and distribution activities are performed. Due to the significant volume growths, the network is recently extended to connect # ## # depots to # ## ## #. Parcels originating from a depot’s region are collected at the depot and consequently sorted on their destination in a roll cage (RC). These RCs contain parcels which have their destination depot in common. The next step is to transport every RC to the correct destination depot by using trailers with a capacity of # RCs. Since the total daily parcel volumes are not sufficient to route full-truck-loads (FTL) from every depot to every depot, an extension to the hub-and-spoke network has been designed to allow both direct shipments between depots and economies of scale by consolidating less-than-truckload (LTL) quantities between depots. This extension is called a hybrid hub-and-spoke network (Lee & Moon, 2014). ### of the centrally located depots perform additional cross-docking activities where transhipments are performed to allow more efficient trailer usage (Wasner & Zäpfel, 2004).
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Figure 1: Schematic overview of a hybrid hub-and-spoke system. Hubs C and D perform additional cross-docking activities.
Not all depots have the same processing times in which the previously described process takes place. Also, the processing times vary depending on the total parcel volume of that day. Most depots have scheduled their operations between # # and # #, which means that retailers are allowed to offer their parcels to PNP before # # to be transported by regular trailers.
PostNL uses flexible trailers to anticipate on unexpected disruptions during a delivery night. Beukeboom (2016, p. 3) defined a flexible trailer as “a stand-by trailer that can flexibly be allocated to a specific route on the delivery night where needed”. In contrast to regular trailers, the flexible trailers can be allocated to any route at any time and are therefore capable to respond to unexpected disruptions. Regular and flexible trailers are in terms of capacity, speed and sustainability exactly identical. Examples of disruptions are equipment breakdown, IT failure, traffic jams or high unforeseen demand at a depot, causing congestions of parcels in the network. Such congestions result in high inventories of unsorted parcels at one or more depots and some of these parcels can not be transported with regular trailers. For example, a # ## # downtime of the sorting system in # ## # at # # causes a backlog of # # ## parcels that have to be sorted and transported before # #. When the sorting system resumes its operations, it has to process the backlog in addition to the incoming parcels between # ## #. and # ## #. As the sorting system has a certain capacity per hour, some parcels in the backlog can not be sorted before # # ## and are consequently not loaded in the latest regular trailers. Those parcels have to be transported since PostNL promises a service level of at least # # and customers expect to receive their parcels the next day.
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backlogs caused by disruptions early in the evening could be caught up during the rest of the evening. The disruptions can not be completely prevented nor foreseen, which is why PNP orders multiple flexible trailers in advance. The required flexible trailers are ordered # ## # in advance and cost €# # per # # shift regardless of its usage, which is significantly more expensive compared to regular trailers. Depending on the moment of ordering, regular trailers cost €# # to €# # per route. Therefore, flexible trailers become economical viable if # # or # # trips are made during a night (Beukeboom, 2016). The starting location of the flexible trailers is an important factor for the response time when a disruption occurs at a depot. If a flexible trailer is already present at that depot, it does not need to travel to the disruption first, avoiding waste of time and LTL distance travelled (Lin & Chen, 2008).
2.2 Current planning approach
Simply adding an additional regular truck on every route at the end of the night is too expensive. With over # # routes in the network, this would approximately costs €# # per day. Also, on most routes no disruptions occur and an additional regular trailer would therefore be unnecessary. Flexible trailers are not limited to a specific route and are able to perform several trips during an # ## # shift. # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. Depending on the day of the week, # # to # # flexible trailers are ordered and located at different depots, as shown in Table 1. More parcels are generally routed through the system on Mondays than other weekdays # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. Weekday Average Daily volume Current Flexible Trailer quantity Ordering costs Monday # # # # # # Tuesday # # # # # # Wednesday # # # # # # Thursday # # # # # # Friday # # # # # # Saturday # # # # # # Sunday # # # # # #
Table 1: Current planning approach for flexible trailers
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1. Flexible trailers often need to travel to the depot where the flexible trailer is needed. This causes a direct waste of time and negatively influences the flexible trailer’s productivity. 2. Too many flexible trailers are ordered for a night which causes some flexible trailers to stay
at its starting point during the entire night.
3. Traveling between a pair of depots without RCs is environmental unsustainable.
2.3 Research Question
The following research question has been developed in order to address the problems involved with the current planning approach.
How can backup trailers in a hub-and-spoke distribution network be allocated more efficiently?
First, the relation between the required backup capacity and the total parcel volume routed through the network is analyzed. Next, a decision on the quantity of flexible trailers and the starting location of each trailer has to be made. Three sub questions are formulated to support the main research question:
1. What is the relation between the number of demand trips and the total daily parcel volume
that is routed through the PNP distribution network?
2. How many flexible trailers are required to fulfil a number of demand trips in a delivery night? 3. Where should the flexible trailers be located in the PNP distribution network?
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3
Theoretical background
Chapter three discusses the relevant literature for this research. Parcel transportation systems, hub-and-spoke networks and emergency vehicle location are the three main fields of research for this study. The identified gap in literature is defined as a result of a literature review of these three fields of research.
3.1 Parcel transportation systems
When the parcel volumes were significantly lower than the current volumes, both parcels and letters were routed through the same distribution network. Nowadays, many parcel transportation systems in several countries are designed on the principles of the postal network design but are separated from each other due to significant parcel volume increase. For example, Grünert and Sebastian (2000) have described how the German postal network is organized from the sender to the receiver. PNP’s network shows fundamental similarities except that the German network entails the use of aircrafts to cover long distances within the country. Grünert and Sebastian (2000) divided the postal transportation process in five phases. The collection phase (i) comprises the collection at customers, collection points and mailboxes before it is transported to a nearby depot. Input sorting (ii) entails the pooling of items which have the same destination in RCs. The sorting process at depots is basically a production process where a sorting machine has a capacity to process a number of items per hour. The outputs of the sorting process are several RCs containing items destined for the same region. Global area transportation (iii) includes the physical transportation of RCs between depots, domestically or internationally located. Wasner and Zäpfel (2004) define the transportation movements between depots or hubs as line-haul operations and is generally the most efficient process in the complete transportation network due to a high degree of pooling parcel streams as well as the associated possibility to utilize larger and more efficient vehicles. The output sorting (iv) phase embraces the unpacking of RCs and sorting the individual parcels for the delivery, generally based on the receiver’s postal code. The final phase, the distribution (v), is the actual delivery of the parcels to the receivers. A schematic overview of the postal transportation process is shown in Figure 2 (Grünert & Sebastian, 2000). This research is concerned with phase (iii) since the transportation of pooled RCs between depots are line-haul operations (Lin & Chen, 2008).
The rough costs structure of the complete network is divided in three components. The pickup and delivery costs, relevant in phase (i) and (v), are the most expensive operations as 35% to 60% of the total operating costs occur here (Salhi & Rand, 1989; Wasner & Zäpfel, 2004). Approximately 25% to 45% of the costs are derived from depot and hub operations in phase (ii) and (iv). The line-hail transportation process in phase (iii) is responsible for 15% to 25% of the operations costs (Wasner & Zäpfel, 2004).
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Figure 2: Configuration of a postal transportation network. Adopted from Grünert and Sebastian
(2000).
Wasner and Zäpfel (2004) researched how the previous described system should be configured from scratch in Austria. Their decision variables were the number of hubs and depots and the positioning of those locations in the country. The objective of the developed mathematical model was to minimize the total system costs, based on the previously described costs distribution, without violating service level requirements. This trade-off is in line with (Grünert & Sebastian, 2000, p. 289), who argue that PSD providers have to “balance the requirements of short service times with the needs of low cost operations”. Important parameters for such models are the daily parcel volumes between postal code, operational costs, and geographical factors such as mountains that influence the driving times of transport vehicles (Wasner & Zäpfel, 2004). The optimal system design in Austria, based representative data on that time, was a pure hub-and-spoke system with one centrally located hub.
While the design of the complete system is typically a strategic one, some aspects of the actual configuration of the network are tactical and operational (Crainic & Laporte, 1997; Wasner & Zäpfel, 2004). The locations of hubs, their corresponding capacities, the fleet composition, long-term scenario analysis and type of provided services are identified as the most important strategic choices (Crainic & Laporte, 1997; Grünert & Sebastian, 2000). Main aspects of the tactical level are concerned with the transportation in line-haul operations phase, such as developing a set of vehicle routes and hub policies for unloading and loading which is capable of economically efficient handling all requests (Grünert & Sebastian, 2000).
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depot. Also, managers and decision makers tend to have difficulties to analyse enormous amounts of available data and appropriately adjust their schedule, mainly because those schedules involve hundreds of vehicles (Lee & Moon, 2014). To make the process even more complex, PSD providers generally use external freight haulers for line-haul transportation. Such freight haulers compute their bills based on driven mileage and driver wages but also medium to long term agreements between the hauler and the PSD provider play an important role. In general, scheduling freight hailers a few weeks in advance is less expensive compared to last-minute ordering (Wasner & Zäpfel, 2004).
3.2 Hub-and-spoke networks
The pure hub-and-spoke is a network of connections in which all transportation movements between depots or nodes occur along spokes connected to the hub at the centre (Lin & Chen, 2008). A depot is a consolidation centre in a distribution network that bundles the LTL quantities or volumes of several demand points to achieve economies of scale. A hub is a consolidation centre that bundles the consolidated LTL quantities or volumes between depots to achieve economies of scale for transports between depots (Kuby & Gray, 1993; Lin & Chen, 2008; Liu et al., 2003; Wasner & Zäpfel, 2004). This approach has been widely used in in logistics, telecommunications, freight, and distributed computing and air transportation (O'Kelly, 1998). Hubs are implemented in such networks to decrease the number of links between origin and destination nodes since movements only occur from and to the hubs (Kuby & Gray, 1993; Lin & Chen, 2008). For example, a network without a hub and with 𝑘 nodes has 𝑘(𝑘 − 1) links. However, if one hub is implemented to connect all other nodes with each other only 2(𝑘 − 1) links exist (Farahani et al., 2013). This paradigm is frequently applied in logistics due to consolidation advantages related to the hub-and-spoke structure. Since significantly less links exists in a hub-and-spoke network compared to a network without a hub, transport volumes have to be consolidated during transportation.
Especially when demand volumes between depots are not sufficient to achieve FTL transport, the consolidation of several LTLs enables FTL transport movements (Grünert & Sebastian, 2000; Lin & Chen, 2008). There it is combined with other LTL volumes to be transported to its destination node or to an intermediate hub until it eventually reaches its destination. This more efficient mode of transportation enables high costs reductions because vehicles are more efficiently scheduled and larger vehicles tend to be more efficient (Wasner & Zäpfel, 2004). Extensive research shows that the hub-and-spoke networks can lower total transportation costs, and are consequently applied to many geographical areas and industries. A disadvantage of this approach is that the reduction of links causes detours which is consequently negative for the transportation time (Grünert & Sebastian, 2000; Liu et al., 2003).
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called a multiple-hub network and is often used when a system consists of a large number of nodes and the transported volumes between every node are not sufficiently high to allow FTL transports. In such networks, all hubs are interconnected, and every other node is only directly connected to one or more hubs (Lee & Moon, 2014). The set of nodes which are directly connected to a hub form a hinterland of that corresponding hub (O'Kelly, 1998). As mentioned earlier, the design of a transportation network is dependent on the daily volumes routed through the network (Lee & Moon, 2014; Liu et al., 2003; Wasner & Zäpfel, 2004). Another extension is the hybrid hub-and-spoke network where nodes are allowed to bypass hubs in case FTL transportation is possible between these nodes (Farahani et al., 2013; Lee & Moon, 2014).
3.3 Emergency vehicle location
Lee and Moon (2014) performed a comparable study as Wasner and Zäpfel (2004) and designed a postal logistics network in South Korea by simultaneously considering the allocation of depots and their locations. They made the noteworthy discovery that managers seem to have significant difficulties to analyse the enormous amounts data to design and adjust the network. This makes it challenging to adjust routing schedules, both pickup, delivery and line-haul operations, when even small volume changes occur in the system. Lee and Moon (2014) argue that if a predetermined transportation schedule is not capable of transporting every item through the network, temporary vehicles are used. This brief remark is, to my best knowledge, the only literature available for flexible trailers, backup transport or temporary vehicles in hub-and-spoke distribution systems.
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One of the most frequently used mathematical approach in location literature is the set covering problem (Alsalloum & Rand, 2006). The aim of this problem is to minimize the total location costs while satisfying a predetermined level of coverage (Farahani et al., 2012). Numerous applications in practice have determined the location of telecommunication towers, public buildings, hospitals, police stations, mailboxes and so on, in order to serve every demand point within a radius or timeframe. Many extensions to the set covering problem have been proposed, each emphasising different characteristics of different problems (Alsalloum & Rand, 2006). Determining the location of a telecommunication tower involves different mechanisms than the location of an ambulance dispatching centre. While such characteristics of different applications seem significantly different, the underlying objective is to serve or cover all demand at least location costs.
In contrast to mathematical models, queueing models are frequently used to incorporate the interaction of several servers in a model (Marianov & Revelle, 1994). When a vehicle is dispatched to an emergency, it is not available to respond on other emergencies (Goldberg et al., 1990b). In case multiple emergencies occur simultaneously when limited servers are available, a queue of emergencies arises. Queueing models aim to determine how many servers are required to reduce these queues because these are undesirable in case of potentially life threatening emergencies (Iannoni & Morabito, 2007). The most frequently used queueing model is the hypercube model, where each server has, at any given time, one of two states (Marianov & Revelle, 1994). Either a server is idle (0) or busy (1) and these two states determine if a server is able to respond on emergencies. One of the extensions of the centralized hypercube model, where all servers have the same centralized starting location, is the partial backup model (Iannoni & Morabito, 2007). If an emergencies occurs in a region, servers from neighbouring regions are also able to respond to the call. Whilst the respond time of the servers may increase, the average time an emergency is queued is significantly reduced (Iannoni & Morabito, 2007; Iannoni, Morabito, & Saydam, 2008, 2011).
3.4 Research Novelty
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allowed to respond on demand trips that either have an origin or a destination inside its service area. An additional hinterland, overlapping the # # hubs in the hybrid hub-and-spoke network, provides the system with more server candidates, possibly resulting in more efficient flexible trailer schedules. This configuration shall be defined as an overlapping hinterland configuration. Figure 3 presents a schematic overview of the two discusses hinterland configurations. Consider a demand trip from the hub in hinterland 4 to a depot in hinterland 1, shown as the blue arrow. In a non overlapping hinterland configuration (left), the demand trip can be fulfilled by a flexible trailers located in hinterland 4 or 1. In case an additional overlapping hinterland is configured (right), it has an additional flexible trailer candidate in hinterland 5.
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4
Methodology
The aim of this research is to determine how flexible trailers can be allocated more efficiently to fulfil demand trips that occur as a result of unforeseen disruptions. This chapter describes the used research method in order to test the differences between several hinterland configurations and to determine the most efficient configuration for PNP. First, the decision to model the PNP problem in a Monte Carlo simulation is elaborated and the key assumptions in this research are explained. The relationship between the number of demand trips and the total daily parcel volume that is routed through the PNP distribution network is examined in section 4.3, providing an answer to the first research question. An algorithm containing several planning procedures determines the quantity and location of the flexible trailers. The design of the algorithm is discussed in section 4.4.
4.1 Why a simulation study is chosen
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These downsides can be resolved in a simulation study. A Monte Carlo simulation is capable to use demand distributions of several historical datasets, each representing different system configurations, to generate a significantly large dataset representing the current system design to achieve reliable results (Landau & Binder, 2014; Shardt, 2015). Next, an algorithm containing several planning procedures determines how many flexible trailers are required on a day to achieve a predetermined service level. Also, the planning procedures used in the algorithm can be applied to a user friendly decision tool for the PNP control room to achieve this research’s results in practice.
4.2 Assumptions
Several assumptions have been made to decrease the model’s complexity. How many demand trips a flexible trailer is able to fulfil during its # ## # shift is dependent on multiple variables. Trip duration, connection between trips and time of arrival are the three main variables and have to be incorporated in the model in order to achieve reliable results.
4.2.1 Trip duration
The distance between two depots determines the transportation time of a flexible trailer. While the average trip transportation time is around # # minutes, shorter or longer trips do occur often. In order to know how many trips a flexible trailer can do within an # ## ## ## shift, the transport duration of each demand trip should be known. Transportation times in logistics are subject to variability because several reasons can cause unforeseen delays. PostNL has gathered the average transportation time between every combination of two depots. Mainly due to the fact that traffic jams are exceptional during the night, the assumption has been made that every demand trip between depots takes exactly the average time that PostNL has determined over time. The transportation times matrix is shown in appendix B.
4.2.2 Connection between demand trips
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4.2.3 Time of arrival
Generally, the demand trips become available for transportation between # # and # #. In the current situation the flexible trailers are available between # # and # #. The latest moment at which a flexible trailer is allowed to arrive at the destination depot is between # # and # #, depending on the time the delivery process starts. Consequently, there is sufficient time to satisfy every demand trip in # ## ## ## #. This makes the time that a demand trip becomes available for transportation less important. For modelling simplicity, the assumption has been made that every demand trip appears at # #, the beginning of the flexible trailer shift.
4.2.4 Miscellaneous trips from or to retailers
Demand trips do not occur exclusively between depots because flexible trailers have occasionally been used to collect large parcel volumes at retailers and deliver those to a nearby PostNL depot. While such trips have not occurred frequently, it has to be incorporated in the model to simulation model to achieve reliable results. The difficulty is to incorporate every retailer’s warehouse in the hinterland parameter set. These demand trips from or to a retailer are classified as miscellaneous sending or receiving locations in order to simplify the model. Depending on the hinterland of the retailer’s warehouse, the miscellaneous trip is allocated to a hinterland # ## ## #.
4.3 Monte Carlo simulation to construct data
PostNL is continuously gathering data of flexible trailer demands in their # ## ## ## ## ## ## ## # (# #). The main properties of every demand entry are the starting location, destination location, date, time and transported volume. Although plenty of data is available in # #, it is challenging to find a dataset which is representative for the current PostNL system. A new cross-dock facility in # ## # has been implemented late August in the PNP network # ## ## ## ## ## ## ## ## ## ## ## ## #. Flexible trailers are required to serve # ## ## ## ## ## ## # but sufficient data since the implementation of # ## ## ## ## ## # not yet available. Although the historical datasets are not representative for the current system, their statistical distributions have not been changed. The Monte Carlo method uses repeated random sampling to generate simulated data which can be used for mathematical models (Landau & Binder, 2014). In this research, the Monte Carlo method is first used to determine how many demand trips occur on a day with a given forecasted total parcel volume. When the number of demand trips for a day is established, the starting and destination locations of each demand trip is determined. This simulation will perform many runs and subsequently generates a large representative dataset of this research. An algorithm uses this dataset to calculate how many flexible trailers are required to fulfil each demand trip on every day and determines the starting location of each flexible trailer.
4.3.1 Correlation between daily parcel volume and number of demand trips
# ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. Figure 4 illustrates the correlation between the independent variable Daily
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between the two variables is 0.690, indicating a strong relationship between the two (Hinkle, Wiersma, & Jurs, 2003). In other words, more disruptions occur on a busy day.
Figure 4: Correlation (𝒓 = 𝟎. 𝟔𝟗𝟎) between the number of demand trips that have to be fulfilled by
flexible trailers and the daily parcel volume.
The Monte Carlo method is able to generate the number of demand trips on a day by using the probability density function (Shardt, 2015):
𝑓 𝑥 = 1
𝜎 2𝜋𝑒
−(𝑥−𝜇)2
2𝜎2 (1)
Where 𝜇 is the mean or the expected value, 𝜎 is the standard deviation of the distribution and 𝑥 is a random number as sampled by the Monte Carlo simulation. The 𝜇 and 𝜎 associated with the total daily parcel volume variable are calculated by two trend lines which are based on the data presented in Figure 4. A trend line function, equation 2, is used to determine the expected number of demand trips for a given daily parcel volume. The output of this equation is the 𝜇 in the probability density function in equation 1.
𝑦 =# ## ## ## ## # (2)
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𝑦 =# ## ## ## # (3)
Since it is theoretically possible to generate a negative or an unrealistically large amount of demand trips, an upper bound and a lower bound has been defined. Equation 4 prevents any number of demand trips on a day to be less than half of the expected value 𝜇. Equation 5 sets the upper bound to # times the expected value but has a minimum value of ## demand trips. Even with small daily parcel volumes, # demand trips may occur, since this has occurred in the past, as shown in Figure 4.
𝐿𝑜𝑤𝑒𝑟 𝐵𝑜𝑢𝑛𝑑 = # #𝜇 (4)
𝑈𝑝𝑝𝑒𝑟 𝐵𝑜𝑢𝑛𝑑 = 𝑚𝑖𝑛
(5)
Now that the 𝜇, 𝜎, lower bound and upper bound are known for every demand volume, the Monte Carlo simulation is able to determine how many demand trips occur on a day. Figure 5 summarizes the described input parameters of the simulation. This process is repeated for a large number of simulation runs, resulting in a vast amount of simulated input data for the algorithm to be processed.
Figure 5: Calculated expected value, bounds and standard deviation per daily parcel volume. St an da rd d evi at io n Nu m be r o f D em an d Tr ip s p er d ay Total daily parcel volume
Main parameters of the Monte Carlo simulation
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4.3.2 Probability matrix
As previously explained, the Monte Carlo simulation has determined how many demand trips occur on a day. Consequently, this aspect of the simulation defines the starting depot and destination depot of each demand trip. The transportation network has changed significantly since the implementation of # ## ## # and a suitable dataset for this research is therefore not available. In order to work around this difficulty, the decision has been made to generate demand data based on the probability of occurrence. A probability matrix of demand trips occurring from a starting depot to a destination depot has been established. This matrix has been constructed on data from ### ## to # # #, which represents the system # ## ## ## ## ## ## ## ## #, and data from # ## # and # ## # # #, representing the current state of the PNP system with. The relative weighting of the old dataset to the new dataset is # # since the old dataset contains # # times more data than the new dataset. As a result, a probability matrix followed that contains representative data of the current PNP system and is therefore able to generate representative days for the simulation model. The probability matrix is shown in appendix C. A random number is chosen by the simulation model which determines the sending depot. For example, Depot # ## # has a # #% change in the probability matrix of being selected as a sending depot. A new randomly chosen number determines the receiving depot of the demand trip. In case of the Depot # # example, the probability is # #% that Depot # ## # is the receiving depot. Therefore, the probability that a demand trip from Depot # ## # to Depot # ## # occurs is # #%. Any duplicate demand trips in a day are deleted and substituted with a distinctive demand trip for that particular day. For example, it is not possible to have two entries from # ## # to # ## # since this would never happen in practice. The result of this step in the simulation is a generated day with a representative number of unique demand trips, sending depot and receiving depot.
4.4 Algorithm to process the constructed data
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4.4.1 Assignment of demand trips to hinterlands
The current PNP system for regular line-haul transport is designed according to the hub-and-spoke paradigm, where each of the # ## # hubs are connected to their hinterland. These regions form the first # # hinterlands and the # # hinterland is the crossdocking location in # ## # with the ## # # depots. This configuration is initially adopted for this study regarding the flexible trailer allocation. As a result, we have # # non overlapping hinterlands covering all # # and # # depots exactly once. The algorithm is designed to assign every demand trip to a flexible trailer which is present in a hinterland. In other words, a flexible trailer is only allowed to fulfil a demand trip if this trip occurs in the service area of the flexible trailer. The difficulty in the allocation process is that the sending depot and receiving depot could be located in different hinterlands, which requires the algorithm to choose between multiple flexible trailers to fulfil the demand trip. Which depot lies in which hinterland is a parameter set in the model. Since we are interested what the effect is on the required flexible trailers in an overlapping hinterland hub-and-spoke system, the algorithm is designed accordingly. The effects on the model is that a demand trip between two depots could be served by two, three or four flexible trailers, depending on both depots’ hinterlands. The decision procedures of the algorithm are explained below.
4.4.1.1 Demand within one hinterland
The algorithm’s first procedure is to index every sending and receiving depot and their associated hinterlands. Demand trips that have both sending and receiving depots in the same hinterland can only be allocated to a flexible trailer in that hinterland. These relatively easy demand trips are allocated first and all other demand trips are marked as ‘unassigned’. Before the remaining demand trips are assigned, the number of required flexible trailers (𝑓𝑟) in hinterland 𝑟 is calculated, see
equation 6, by summing all trip durations of every demand trip assigned to hinterland 𝑟. Next, that number is divided by the effective driving time parameter 𝑇 and rounded up to its nearest integer, as explained in section 4.2.2.
𝑓𝑟= 𝑡𝑟
𝑇 (6)
Now we know how many flexible trailers are required per hinterland to fulfil only the easy demand
trips. However, those flexible trailers are not evenly busy. The remaining available driving time (𝑠𝑟)
in hinterland 𝑟 is determined, which will be used to allocate the unassigned demand trips to flexible trailers.
𝑠𝑟= 𝑓𝑟𝑇 − 𝑡𝑟 (7)
4.4.1.2 Demand between multiple hinterlands
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algorithm selects an unassigned trip and determines the hinterlands of both sending and receiving depot. Only the flexible trailers located in these possible hinterlands are allowed to fulfil the selected
unassigned demand trip. Since the remaining available driving time (𝑠𝑟) per hinterland is known, the
algorithm allocates the selected demand trip to the possible hinterland with the highest 𝑠𝑟 in order to
reduce the idle time of the flexible trailers in that hinterland. If none of the possible hinterlands have sufficient idle time to fulfil the selected unassigned demand trip, an additional flexible trailer is
assigned to the hinterland with the highest 𝑠𝑟. As soon as the demand trip is assigned to a region,
equations 6 and 7 calculate the number of required flexible trailers (𝑓𝑟) and the remaining available
driving time (𝑠𝑟) of every hinterland. The algorithm restarts the loop if any ‘unassigned’ trips are
still present, which means that this described procedure is repeated until every demand trip is assigned to a hinterland. When all demand trips for a day are allocated to hinterlands and the
number of required flexible trailers (𝑓𝑟) per hinterland 𝑟 are calculated, the results for that day are
exported to a database. The last step of the algorithm is to initiate one new Monte Carlo simulation run to generate a new day by using equation 1.
4.4.2 Determine starting location
A flexible trailer is most effectively located is the trailer is present at a depot where a disruption occurs. If not located appropriately, the flexible trailer is required to travel empty to a depot. The problem description in chapter 2 revealed that empty trailer movements are a waste in terms of time, costs and environmental sustainability (Lin & Chen, 2008). The location of each flexible trailer is therefore determined on the probability of occurrence. However, to prevent all flexible trailers to be allocated in one hinterland, the algorithm locates each newly allocated flexible trailer to a consecutive hinterland. Where the flexible trailer consequently is located within this hinterland is determined by the probability that a demand trip occurs at one of these hinterland depots.
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5
Results
This chapter presents the results of several performed simulation runs. How the results should be interpreted is explained first. Two different hinterland configurations are tested and compared with the current PNP flexible trailer ordering policy. The costs reductions for PNP as a result of the proposed planning approach are calculated and presented. Also, the effect of the effective driving time parameter 𝑇 on the results is revealed in an additional experiment. This chapter concludes with the determination of the starting locations of each ordered flexible trailer.
5.1 Interpretation
Every simulation has performed 5,000 iterations since the variability of the results on simulations with less iterations was too high and therefore less reliable. The algorithm prints the main results of each simulated night on a results page. An example of the results page is shown in appendix E, where only the first 40 iterations are shown. Figure 6 presents a histogram based on the results of one simulation run with a daily parcel volume of # ## # and an effective driving time parameter
𝑇 =# # 𝑚𝑖𝑛𝑢𝑡𝑒𝑠. The frequency that a number of flexible trailers was sufficient to fulfil all demand
trips on a day is shown in the histogram. For more than ## ## of the # # # generated days it appeared to be sufficient to allocate # # flexible trailers in the PNP network. However, for some days even # # flexible trailers were necessary to fulfil all demand trips on that day. PostNL attempts to deliver # % of all sent parcels the next day. Such service levels point out that approximately # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. The number of required flexible trailers is therefore determined by calculating the service level per quantity of allocated flexible trailers. For example, allocating # # flexible trailers achieves a service level of # # #%, significantly less than the targeted # %. As shown in Figure 6, a # % service level, at a daily demand volume of # ## # is achieved with # ## #flexible trailers.
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This chapter presents the results of several configurations. For each demand volume in each configuration, the number of required flexible trailers to achieve a service level larger than # % is highlighted. Since was proven that the number of demand trips is a function of the daily parcel volume, it is expected that the number of required flexible trailers increases as the daily parcel volume variable increases, which can be observed in the results tables in the following sections.
5.2 Hinterland configurations
The first experiment calculates the difference between a system with # # or # # hinterlands. In a system without overlapping hinterlands, every depot is allocated to exactly one hinterland. The # # and # ## # have their hinterlands as currently designed by PNP. The second system has an additional ### hinterland which covers the #############.
Table 2 shows the results of a non-overlapping hinterland structure. The algorithm has determined for # daily parcel volumes (### to #####) how many flexible trailers should be ordered to achieve a service level of at least # %. Every simulation per daily parcel volume consists of 5,000 iterations, meaning that # # # simulations were performed to determine the service levels in Table 2. Results show that # # flexible trailers achieve a # # % service level at a daily parcel volume of # # # parcels. Such volumes are averagely routed through the PNP network on a ####. Table 7 shows how many flexible trailers are currently ordered for each parcel volume. Calculations show that reductions in the number of required flexible trailers are small for low daily parcel volumes.
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Se rvi ce Le ve l Fr eq ue nc y Number of required Flexible Trailers
Service Level per Flexible Trailer
Frequency Cumulative Service Level28 However, # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #.
Daily Parcel Volume
Nu m be r of F le xi bl e Tr ai le rs Required:
Table 2: Service levels in a non-overlapping hinterland configuration. T = # # minutes
The results of a configuration with an additional overlapping hinterland are shown in Table 3. With the exception of a daily demand of # ## # parcels, every parcel volume requires an additional flexible trailer compared to a non-overlapping hinterland structure.
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Daily Parcel Volume
Nu m be r of F le xi bl e Tr ai le rs Required:
Table 3: Service levels in an overlapping hinterland configuration. T = # # minutes
5.3 Location of flexible trailers
The starting location at the beginning of the flexible trailer’s shift influences the effective working hours. If a flexible trailer first has to travel empty from its starting location to the location where it is required to fulfil a demand trip, the flexible trailer is less effective compared to a situation where the flexible trailer is stationed at a location where the demand trip occurs. Figure 7 shows how often a depot is either the sending location or the receiving location in a simulation. The decision has been made to allocate at least one flexible trailer to every region. If only # # flexible trailers are required, every hinterland has # ## ## ## #. Every additional flexible trailer is alternately allocated to a another hinterland. Table 4 shows the starting locations per number of required flexible trailers. Results show that the first flexible trailers are allocated to # ## ## ## ## ## ## ## ## ## ## ## ## # is most likely. Starting from the # # flexible trailer, # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #.
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Figure 7: How often a depot is either a sending or a receiving location in a generated demand trip
Hinterland Starting Depot
Table 4: Starting points of the Flexible trailers for several quantities
5.4 Driving time parameter
One of the assumptions in this research is that a flexible trailer is able to perform # # demand trips in an # ## # shift. This assumption is supported by historical data and experience by PNP’s planners. As an average demand trip has a duration of # # minutes, the default effective driving time parameter 𝑇 = # ## ## # 𝑚𝑖𝑛𝑢𝑡𝑒𝑠. This section shows the results if the effective driving time parameter 𝑇 is changed. The base case for this experiment are the results of the overlapping hinterland structure shown in Table 3. Table 5 shows that a reduction of effective driving time causes an additional required flexible trailer compared to the base case of # # minutes.
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Daily Parcel Volume
Nu m be r of F le xi bl e Tr ai le rs Required:
Table 5: Service levels in an overlapping hinterland configuration. T = # # minutes
Table 6 shows that an increase in parameter 𝑇 results a reduction of required flexible trailers, providing comparable results as the non-overlapping hinterland configuration shown in Table 2.
Daily Parcel Volume
Nu m be r of F le xi bl e Tr ai le rs Required:
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5.5 Comparison with PNP’s current approach.
Table 7 summarizes how many flexible trailers were ordered by PNP # ## ## ## ## ## ## ## ## . On average, # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. The calculated results show that the targeted service level exceeding # #% can be achieved with less flexible trailers, except # ## #. # ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## # by applying a non-overlapping hinterland structure.
Weekday Average Daily volume Current Flexible Trailer quantity Calculated results Absolute difference Relative variation Costs reduction Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Table 7: Comparison between current PNP planning approach and calculated results for one week
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6
Discussion and Limitations
This chapter discusses how this research supports current literature as well as the limitations of this research. The aim of this research is both practical and academic. While the practical objective is to allocate flexible trailers more efficiently in the PNP distribution system, the academic objective is to create a planning framework to achieve this costs reduction. Also, an experiment with two hinterland configurations is tested and compared.
Results of this study are generalizable for other organizations with a hub-and-spoke distribution system, such as parcel delivery service providers, freight transporters and even airliners. This problem is applicable to other industries if a certain volume is routed through a hub-and-spoke network, and a small share of that volume is not able to be routed by regular transportation means. In order to prevent those small volumes from reaching their destination, backup transportation capacity can be allocated in the hub-and-spoke network to ensure on-time delivery. This provided framework might be especially useful when representative data of the distribution system is lacking. A Monte Carlo simulation is able to generate reliable datasets according to known probability distribution, on which an algorithm with planning procedures can be applied. Demand trips are allocated to the backup vehicle, or any means of transportation, which is (i) a candidate to fulfil the demand trip and (ii) has the most idle time in its shift. Since time is usually more crucial for backup transportations, it is argued that hubs are bypassed to achieve time savings compared to regular hub-and-spoke routing. The calculation of the minimal required backup vehicles is determined by the predetermined service level of the distribution system. The achieved costs savings in this study might not be realisable in other industries or even other parcel service providers because the current planning approach of the case study organization was based # ## ## ## ## ## ## ## ## ## ## ## ## #.
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The time of which a demand trip occurs is neglected in this research, as sufficient time remains available during the night to fulfil every demand trip in the current PNP system. For this research it sufficient to allocate demand trips to flexible trailers with planning procedures neglecting the time of occurrence. However, this assumption is not likely to withstand if demand volumes increase. If the absolute number of demand trips increases, the opportunity emerges to connect demand trips without traveling empty to the next unfulfilled demand trip. A mathematical model that determines the optimal routing path per flexible trailer on a delivery night may result in more efficient allocation of flexible trailers.
Against expectations, an additional hinterland which covers mainly the hubs in a hub-and-spoke network is not resulting in less required flexible trailers to fulfil all demand trips. It was expected that an overlapping hinterland configuration resulted in less required trailers because the planners had more possibilities to allocate demand trips to flexible trailers. More possibilities were expected to result in more efficient scheduling of demand trips. The calculated results show that an overlapping hinterland configuration requires an additional flexible trailer compared to a non-overlapping configuration. However, these results are based on a constant effective driving time parameter 𝑇 , which is arguable in an overlapping configuration. Flexible trailers are less often required to travel from the centre of the hinterland to the hubs located at the edge, which is likely to increase the parameter 𝑇 as flexible trailers have to spend less time traveling empty to a starting point of a demand trip.
Possibly, the calculated service levels are negatively biased because the calculations are based on the number of days a quantity of flexible trailers was sufficient to fulfil all demand trips. When a quantity of flexible trailers is not able to fulfil all demand trips, it does not mean that none of the demand trips is fulfilled during that night. A more accurate service level calculation would also incorporate the number of fulfilled demand trips on days that not all demand trips are fulfilled. However, the impact on the results are not likely to be significant and the used calculation method is therefore appropriate for this research.
Another limitation to take into consideration is the use of an upper bound in the Monte Carlo simulation, preventing the model to generate an exceptionally disrupted day. It is imaginable that such a day could occur, even considering the minimal associated probability. The upper bound in this research is especially required to bound the number of demand trips at small daily parcel volumes. As a very small portion of the generated days has been capped by the upper bound, the accuracy of the model is not expected to be greatly altered by the upper bound.
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7
Conclusions
This chapter explains the main conclusions of this research which attempts to answer the following main research question:
How can backup trailers in a hub-and-spoke distribution network be allocated more efficiently?
To answer the main research question, three research questions have been formulated in chapter 2. The first research question researched if any relationship existed between the number of demand trips and the total daily parcel volume that is routed through the PNP distribution network. A strong linear correlation of 𝑟 = 0.690 has been found, which means that the required backup capacity is a function of the daily parcel volume variable.
Due to a recent design change in PNP´s distribution system, a representative dataset was not available for this research. A Monte Carlo simulation model was able to generate a large representative dataset by merging historical datasets. These datasets were used to answer the second research question, which covers the quantity of required flexible trailers. A set of planning procedures are implemented in an algorithm. The objective of the algorithm is to allocate every demand trip on a day to a minimum number of flexible trailers. Two hinterland configurations were tested to measure the impact of an overlapping hinterland configuration on the required flexible trailers. Flexible trailers are assigned to the hinterlands in a hub-and-spoke distribution network. Consequently, the algorithm assigns demand trips to one of the candidate flexible trailers. The flexible trailer with the most idle time is selected in case multiple candidates are available to transport one demand trip. Many simulation runs have been performed in order to achieve reliable results. The aim of this research is to determine how the flexible trailers could be allocated more efficiently, which means that the same service level has to be achieved with less resources. Calculated results show that a non-overlapping hinterland structure achieves a costs reduction of # ## ## ## ## ## ## ## ## ## ## ## ## ## #, without negatively affecting the service level. Based on the probability of occurrence, the location of each flexible trailer is determined. The chances that a demand trip starts at # ## ## ## ## ## ## ## ## ## ## ## ## ## ## #. Therefore, locating flexible trailers at # ## ## ## ## ## ## ## ## ## ## # to travel empty to a starting point of a demand first. # ## ## # or more flexible trailers are required on a day, additional trailers are also # ## ## ## ## ## ## ## #. This answers the last research question of this research, concerning the starting points of the flexible trailers.
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trailers per demand volume. It is also recommended to update the probability matrix every time when new significant disruptions have occurred. This will lead to a rich database which more complete data to perform the calculations on.
7.1 Further research
This study tries to provide a framework to determine the quantity and location of flexible trailers in distribution systems, which has not been extensively studied in current literature. Several future research opportunities have been identified to extend this provided framework. As already mentioned, a mathematical routing model is likely to be more appropriate when the absolute number of demand trips is sufficiently large to reduce empty trailer movements to unfulfilled demand trips. At which parcel volumes a mathematical methodology is more appropriate and the corresponding expected benefits need to be calculated.
The data analysis revealed that the number of RCs in a demand trip varies significantly. This research assumed that the flexible trailer fleet is homogeneous since every RC has a capacity of # # RCs. Smaller vehicles can be ordered at lower costs compared to regular flexible trailers which could result in more effective resource allocation. Also, a mixed fleet is potentially more environmental sustainable if the quantity and location is appropriately determined.
An extension to the proposed planning procedures in the designed algorithm could be further researched. This algorithm allocates a demand trip to the flexible trailer with the most idle time, but other approaches may achieve different results. For example, allocating the longest demand trips on a day before the shorter trips could lead to less idle time and consequently higher flexible trailer productivity. A bin packing problem may be applicable to the allocation of demand trips to flexible trailers.
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