Int J Adv Manuf Technol (2014) 70:1053–1061 DOI 10.1007/s00170-013-5349-3
ORIGINAL ARTICLE
Hierarchical modelling of Last Mile logistic distribution system Tauseef Aized & Jagjit Singh Srai
Received: 13 January 2011 / Accepted: 25 September 2013 / Published online: 10 October 2013 # Springer-Verlag London 2013
Abstract Last Mile logistic distribution system is the final step in business-to-customer supply chain which needs careful investigation in order to efficiently and economically deliver goods to customers. This study is aimed at providing a conceptual planning approach of modelling a Last Mile system based on hierarchy which is particularly useful in routing planning of the system. The hierarchical modelling is implemented using the Petri net method which is suitable to the needs of the system being a discrete event dynamical system. Keywords Supply chain . Last Mile logistic system . Modelling
1 Introduction A supply chain is as an integrated process in which a number of various business entities like suppliers, manufacturers, distributors and retailers work together in an effort to acquire raw materials, convert materials into final products and deliver them to retailers and customers. The concept of supply chain emerged from a number of changes in the manufacturing environment, including the rising costs of manufacturing, the shrinking resources of manufacturing bases, the shortened product life cycles and the globalization of market economies T. Aized Department of Mechanical, Mechatronics and Manufacturing Engineering, UET, KSK Campus, Lahore, Pakistan T. Aized (*) Institute for Manufacturing (IFM), University of Cambridge, Cambridge, UK e-mail:
[email protected] J. S. Srai Centre for International Manufacturing, Institute for Manufacturing (IFM), University of Cambridge, Cambridge, UK
[1]. During the last three decades, supply chain management has gained much attention because by coordinating the production, shipment and delivery of the goods required to meet their business needs, organizations have been able to more easily meet the demands of their customers. In most supply chain operations, raw materials after passing through the processing industry and attaining the shape of finished goods are stored in warehouses or distribution centres from where two main options of distributing the goods are possible: firstly, the traditional system with supermarkets and retail shops and secondly, a system with direct-to-consumer deliveries. The Last Mile in the supply chain is considered as the last part of the supply chain for the direct-to-consumer market. In supply chain logistic operations, Last Mile refers to the last part of physical goods delivery process which involves a set of activities that are necessary for the delivery process from the last transit point to the final drop point of the delivery chain. The Last Mile is critical because it is responsible for the final delivery of products to customers and is typically a source of high amount of costs of delivery chains. This paper focuses on the Last Mile logistic distribution process and is organized in such a way that Section 2 gives details of related work and contribution of this paper. Section 3 explains Last Mile modelling, system configuration and hierarchical and Petri net-based modelling scheme, and conclusion is drawn in Section 4.
2 Related work and contribution In order to effectively design, coordinate and manage supply chain systems, many methods and models have been developed which mainly consist of deterministic, stochastic, economic and simulation modelling paradigms [1]. Among supply chain management activities, one important concern is logistics and freight management. A review of urban freight studies that have taken place in the UK over approximately a
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30-year period from the early 1970s to the present has been presented in [3] which covered both goods collection and delivery and service vehicle activities. The significance of electronic commerce for freight transport, logistics and physical distribution has been discussed in [9]. Russo and Comi [18] analysed existing studies relative to freight policies implemented at urban scale and proposed a general classification of measures adopted at an urban scale with empirical analysis of results of proposed measures. The freight pipelines discussed in [6] presented a novel way for the movement of freight transport and offered an alternative to conventional transport modes. Cidell [4] examined the suburbanization of warehousing and trucking activity in metropolitan areas using Gini indices as a measure of concentration. An analysis of the evolution of logistics pertaining to the core dimensions of transport geography (flows, nodes/locations and networks) is presented in [10], and the concept of logistical friction is also introduced to illustrate the inclusion of the multidimensional notion of impedance in integrated freight transport. A comprehensive discussion on operational research-based dynamic modelling is given in [15] and that on stochastic programming in transportation and logistics is in [16]. A general modelling and algorithmic framework, based on mathematical programming techniques for the tactical planning of freight transportation, was developed in [5] which generated, evaluated and selected operating strategies by globally considering the service network of the company and the routing of the freight under the double criteria of economic efficiency and service quality. A review of operational research models regarding intermodal freight transportation is given in [12] which emphasized intermodal over unimodal transport modes. A marginal-cost-based framework was developed in [14] to analyse the resulting trade-offs between travel distance and vehicle capacity utilization in the context of freight carrier operations. Soehodho and Nahry [19] focussed on traffic flow dependency within a freight distribution network with the mathematical formulation of a minimum cost multicommodity flow (MCMF) problem. Traffic flow dependency was incorporated into the model by introducing a coefficient of speed, which was derived from the traffic assignment of ordinary traffic associated with the transportation of the type of freight under consideration. A compilation of the solutions and initiatives that can be implemented by local administrations in order to improve freight deliveries in urban environments is discussed in [13] from the point of view of urban communities and the relation between freight transport and general urban traffic. Russo and Comi [17] developed a model system in order to support ex ante assessment of city logistic measures which allowed to simulate the choices of each decision-maker involved in the urban freight transport and logistics and to investigate how the policies and measures can influence different choices.
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Around the world, interest in urban and metropolitan goods movements is increasing since they account for a substantial share of traffic in urban/metropolitan areas but there have been only few studies that considered the behaviour of the stakeholders in the Last Mile logistic area [20]. Although the Last Mile system has different environmental, social and technological issues, this study is aimed to examine routing planning of distribution system. This paper is focused on the Last Mile distribution system using hierarchical modelling concept implemented through Petri net. Previous work on the subject does not deal the Last Mile logistic distribution network as a discrete event hierarchical modelling paradigm. The advantage of dealing the Last Mile network as a discrete event problem, modelled through Petri net, is that it can effectively handle routing planning of logistic network. Also, the Petri net method has the merit to accommodate any changes in modelling network which usually arise from time to time, a feature commonly known as scalability in discrete event modelling approach. As discrete event systems grow, the modelling becomes complex but Petri net has an ability to model growing changes, that is, Petri nets especially higher classes of Petri net like coloured Petri net are characteristically scalable models. Additionally, when models grow and become computationally complex and expensive, they need more and more time to reach solutions. Coloured Petri net approach, being an advanced class of Petri net, has constructs like place, arc and transitions which can have mathematical functions and hence can solve computationally complex problems in relatively shorter time; if coupled with modern computational computer process, more and more complex problems can be solved easily in shorter periods of time. This paper discusses the downstream end of a single channel supply chain. Due to the involvement of customers, this end of supply chains is difficult to handle and therefore should be carefully modelled. As the preferences, choices and demand patterns vary with the passage of time, hence the downstream side of supply chains causes a lot of uncertainties and variations which may propagate towards the upstream side of the chain. Consequently, modelling the downstream side of supply chain due to the presence of uncertainties is a challenging task.
3 Last Mile modelling Last Mile focuses on the period when parcels leave the transportation system, that is, the last step in the delivery process. Usually, a parcel is bought to the recipient’s home/office or it can also be stored until the recipient picks it up or forwarded to another address. It is the link between an online ordering process and physical product delivery [7]. It involves a set of activities that are necessary for the delivery process from the last transit point to the final drop point of the delivery chain. The Last Mile is the last stretch of a business-to-
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consumer parcel delivery to the final consignee who has to take reception of the goods at home or at a cluster/collection point. The Last Mile is considered one of the most expensive parts of the supply chains and accounts for 13 % up to 75 % of the total supply chain costs [8]. Among the problems encountered in designing Last Mile are the high degree of failed deliveries which yields extra costs, a high degree of empty running of vehicles and a low volume of delivery goods. These problems call for an efficient routing planning in order to generate reasonable profit margins necessary to run the system smoothly. 3.1 System configuration The Last Mile system configuration in relation to a partial supply chain considered in this study is shown in Fig. 1. In order to focus the Last Mile operations, the components of supply chain before production facility, that is factory, are not shown. In this system, the customer places an order to the retailer or a “parcel source” (e.g. friends, relatives, etc.). While the parcel is being processed, there can be also an information exchange between the transportation service provider and the customer (e.g. parcel tracking, notice of expected arrival, etc.). The shipping unit is getting processed (e.g. factory, warehouses, cross-docking hubs, sorting, different types of transportation, etc.) till it arrives at the defined urban area. Crossdocking is the process of rehandling freight from inbound trucks and loading it to outbound vehicles [2] . The information and material flow among different components of the system are shown in Fig. 1. The Last Mile system comprising of transit point, drop point and customer is further elaborated in Fig. 2. The transit point is the last cross-docking point within the supply chain which may be a consolidation centre, distribution hub or a retailer outlet. Consolidation, in the context of freight
transport, refers to the reduction in the number of vehicles operating with part or full load. This is achieved by combining delivery orders for the same or similar location for at least part of the journey. Urban consolidation centres (UCCs) are operated by a single, major logistic operator who is responsible for running the centre and making the final deliveries. Freight consolidation centres (FCCs) are distribution warehouses, situated close to town centre, shopping or construction site, at which loads are consolidated and delivered to the target area resulting in fewer journeys. The important characteristic of consolidation centres is that shipping units are cross-docking processes to fulfil the last mile in the way it satisfies the involved stakeholders (e.g. increase load factor, reduce traffic in urban area, etc.). Hubs commonly serve as consolidation, switching and sorting centres and allow for the replacement of direct connections between all nodes with fewer, indirect connections. However, the main difference from consolidation centres is that distribution hubs are, in general, only distributing the goods from one or a few defined origins. The retailer outlet is a good supply facility that directly delivers to the customer. The retailer outlet is also placed in the urban area and provides in general the possibility of in-store shopping for the customer. The roll-out logistics providers are responsible for delivery from the last transit point to the specific drop point. In general, the roll-out logistics operates from one specific hub and delivers the parcels to the assigned urban area. The drop point is the place where the roll-out logistics service provider drops the parcel and the customer receives or picks up the shipping unit. There can be different possibilities for drop points like collection point, neighbour, etc. All delivery options that are designated to ship the freight units not to the customer’s home are grouped into a term called “collection point”. This also involves that the customer needs to go to the collection point to pick up the parcel. The term “neighbour” summarizes all the events when the parcel is
Simplified flow model (one layer model) Retailer
Hub 1 Factory
Defined urban area of the last mile system
Warehouse Hub n
Or Parcel source
Information management
Material flow
Information flow
Fig. 1 Last Mile operations in partial supply chain
Transit point
Drop point
Customer
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Fig. 2 Last Mile logistic system
Defined urban area Transit point Consolidation centre
Distribution hub
Retailer outlet
Drop point
Roll-out logistics
Inbound logistics
Collection point
Customer home
Private customer
Neighbor
Express delivery logistics
not delivered to its set destination and be handed over to a third party that is close to the customer. In home delivery, the goods are being delivered to the home of the customer. This includes home delivery service with/without time window as well as home delivery service to the home-unattended reception box. 3.2 Hierarchical modelling of the Last Mile system The Last Mile system is confined to a specific geographical location in which transit point, drop point and customers are present. In order to define a specific Last Mile region, many factors are taken into consideration which include distance between transit points of adjacent regions, local infrastructure and regulations, road network, traffic intensity, parking space, congestion, tolls and taxes, etc. There are certain indicators related to residents which need careful consideration when defining a Last Mile region. These indicators are quantitative like number of customers and number of houses in the region, socio-economic which includes purchasing power of residents and socio-demographic like age of householders and type, variability and prediction of demand pattern. Based on these factors, the customer density ratio, defined as the expected customers in a specific area, can be calculated, which is one of critical factors in designing a Last Mile system. A three-layered hierarchical model is developed in this study for planning the Last Mile region. These are institutional, industrial and customer layers. The top layer called institutional layer gives the total perspective of the system in which four transit points have been assumed, although the numbers of transit points may vary from case to case depending on the design considerations of the Last Mile system. The trucks deliver goods to these transit points and return. The next layer is called industrial layer, and transit points are
available in both institutional and industrial layers as both layers are actually connected to each other at these points. From the transit points, vans pick up the goods and stuff and move into the industrial layer of the Last Mile region. The van has to serve attended points, unattended points and consumer’s house which is available in the lowest hierarchical layer called consumer layer. The house in the consumer layer is the destination point of the stuff, but the consumer may have to visit attended and unattended drop points if he/she wishes to have his stuff dropped there. This three-layered hierarchical model is shown in Fig. 3. 3.3 Petri net modelling of the Last Mile system The Last Mile transport system is a discrete event dynamical (DEDS) system, which is asynchronous, parallel and eventdriven in nature. The routing planning of the Last Mile system can be carried out with the Petri net method which is a generic method for DEDS modelling. A DEDS can be characterized by events and conditions. A Petri net consists of places, transitions and directed arcs represented by circles, rectangular bars and arrows, respectively. Arcs run between places and transitions. Places may carry a number of tokens, and a distribution of tokens over the places of a net is called a marking. Transitions act on input tokens by a process known as firing or occurring. A transition can fire or occur if it is enabled, i.e. there are tokens in every input place. When a transition fires or occurs, it consumes the tokens from its input places, performs some activity and places a specified number of tokens which may vary from zero to any definite number into each of its output places. The conditions of a Last Mile system, being a DEDS, may be described by places, events by transitions, relations between events and conditions by arcs and holding of conditions by tokens in places. The occurrences of events are described by
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The granularity off low (three layer model) 1
Defined Urban Area
Institutional Layer
2
1
Industrial Layer
Truck
Transit point arrival
3
Key Drop point (Consumer home) Drop point (attendant)
Consumer Layer
Transit point outwards
Van
Drop point OR
Drop point (unattendant) Transit point
Customer home
Transportation vehicle
Fig. 3 Hierarchical modelling of the Last Mile system
firing of transitions which remove tokens from input places and add tokens to output places, and the behaviour of a system is described by firing of transitions and movements of tokens. Places, transitions and tokens must be assigned a meaning for proper interpretation of a model. In the Last Mile systems, places may represent resources like transportation means, that is, trucks/vans, etc., and the existence of one or more tokens in a place represents the availability of a particular resource, while no token indicates that the resource is unavailable. A transition firing represents an activity or process execution, for instance, a transportation process. Places and transitions together represent conditions and precedence relationships in the Last Mile system’s operation. Due to a large number of resources, conditions and activities, the Petri net model can be of a big size with a lot of places, transitions, arcs and their allied constructs in a practical Last Mile system, and it becomes extremely tedious to handle and comprehend such a big modelling net. This problem can be solved using a higher class of Petri net called coloured Petri net (CPN) which can compactly handle bigger modelling nets. This study uses the formal definition of CPN given in [11]. A hierarchical CPN is a tuple HCPN=(S, SN, SA, PN, PT, PA, FS, FT, PP) satisfying the following requirements: 1. S is a finite set of pages such that: Each page s∈S is a non-hierarchical CPN: CPN ¼ ð∑s; Ps; Ts; As; Ns; Cs; Gs; Es; IsÞ
(The non-hierarchical CPN is defined in [11].) The sets of net elements are pairwise disjoint: ∀s1; s2∈S : ½s1≠s2⇒ðPs1∪Ts1∪As1Þ∩ðPs2∪Ts2∪As2Þ ¼ :
2. SN⊆T is a set of substitution nodes. 3. SA is a page assignment function. It is defined from SN into S such that: No page is a sub page of itself: n
o s0 s1 …sn ∈S* n∈N þ ∧s0 ¼ sn ∧∀k∈1…n : sk ∈SAðSNsk −1Þ ¼ :
4. PN⊆P is a set of port nodes. 5. PT is a port-type function. It is defined from PN into {in, out, i/o, general}. PA is a port assignment function, FS⊆Ps is a finite set of fusion sets, FT is a fusion-type function and PP∈SMs is a multiset of prime pages. For details of PA, FS and FT, we refer to [13]. The model is developed using CPN Tools which is a CPNbased program developed on the basis of CPN ML language. The CPN ML language is derived from Standard ML which is a general-purpose language. The Last Mile logistic distribution system has been modelled by CPN Tools which is capable to simulate and validate the system. Figures 4, 5 and 6 show the snapshots of models taken from CPN Tools.
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Int J Adv Manuf Technol (2014) 70:1053–1061 Stuff_1_ available Fusion 1
(t,tc)
Stuff_1 Stuff (t,tc)
stuff(1)
(t,tc)
Ready to return 1
stuff(2)
unloading1
(t,unloaded)
Transit_Point
Stuff
[t=Truck(1) andalso tc=loaded]
ready to return 3
(t,tc)
(t,tc)
Point 1
(t,unloaded)
(t,tc) (t,tc)
moving to 3
Point 3
Transit_Point
Transit_Point [t=Truck(3) andalso tc=loaded]
(t,tc)
(t,tc)
1`(Truck(1), loaded)++ 1`(Truck(2),loaded)++ 1`(Truck(3), loaded)++ 1`(Truck(4), loaded)
[t=Truck(3) andalso tc=loaded]
unloading 3 (t,tc)
returning [ tc=unloaded] from 3
(t,tc)
[tc=unloaded] returning from 1
(t,tc)
stuff 3
Stuff_2_ available Fusion 2
Transit_Point (t,tc)
[(t=Truck(1) orelse t=Truck(3)) andalso (tc=loaded)]
(t,tc) Trucks moving to Institutional Layer (t,tc) Transit_Point
[(t=Truck(2) orelse t=Truck(4)) andalso (tc=loaded)]
(t,tc)
[t=Truck(4) andalso tc=loaded]
(t,tc) [tc=unloaded] (t,tc)
returning from 2
(t,tc)
moving to 4
Point 2 (t,tc)
Transit_Point
Point 4 Transit_Point
(t,tc) (t,tc) (t,unloaded)
(t,unloaded) stuff(4)
(t,tc)
Ready to return 2
(t,tc) ready to return 4
[ tc=unloaded] [t=Truck(2) andalso tc=loaded]
(t,tc) stuff_4_ available Fusion 4
returning from 4
unloading 2
stuff(3)
[ tc=loaded]
(t,tc)
Stuff_3_ available Fusion 3
(t,tc)
stuff_2 Stuff
unloading 4
Transit_Point
(t,tc)
stuff_4 Transit_Point
Stuff
Fig. 4 Institutional layer of the coloured Petri net model
Stuff_condition Stuff_1 available Fusion 1
Stuff
attended point 1 Fusion 5 Stuff_condition
unattended point 1
(s,v)
s
Stuff for House1 Fusion 7
Fusion 6
Stuff_condition
(s,v) (s,v)
stuff loading 1
(s,v)
(s,v) stuff loaded 1
(s,v)
moving1
approaching1
(s,v)
moving2
(s,v)
approaching2
(s,v)
reached point 3
moving3 v
Vans
Stuff_condition v
Stuff_condition
Stuff_condition
v
1`van(1) empty
van1 v
stuff loading 3
Van3 Vans
s
Vans
stuff_3_ available Fusion 2
Stuff
(s,v) (s,v) House 2 Fusion 16
Stuff_condition
moving11
stuff loaded 3 (s,v)
(s,v)
Stuff_condition
approaching8
unattended point 2 Fusion 15
moving10
Stuff_condition
approaching3
Stuff_condition
(s,v)
(s,v)
Stuff_condition
attended point 3
Fusion 8 (s,v)
(s,v) (s,v)
(s,v)
moving4
Stuff_condition
(s,v)
moving5
Stuff_condition
approaching7
unattended point 3
Fusion 9
Stuff_condition
(s,v) (s,v) (s,v)
attended point 2 Fusion 14
Stuff_condition
approaching4
moving9 (s,v)
Stuff_condition
(s,v) moving6
(s,v)
stuff loaded 2 v
Stuff_condition (s,v)
Stuff_2_ available Fusion 4
s
stuff loading 2
empty
van4
van2
Stuff
Vans
Vans
empty
v v reached point 2
(s,v) moving8
(s,v) approaching6
(s,v)
moving7
(s,v) approaching5
(s,v)
moving 6
Vans
(s,v) stuff loaded 4
v stuff laoding 4
Stuff_condition
Stuff_condition
(s,v)
House 4 Fusion 13
(s,v)
Stuff_condition
unattended point 4 Fusion 12 Stuff_condition
Fig. 5 Industrial layer of the coloured Petri net model
s
(s,v)
attended point 4 Fusion 11
Stuff_4_ avaialable Fusion 3 Stuff_condition
reached 4 Vans
Stuff_condition
Stuff
Stuff for House 3 Fusion 10
Stuff_condition
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Stuff_condition
(s,v) delivering 1 Packet(1) Packet delivered to house 1 Packet Packet(1)
Packet(1) 1`person(1) Unattended Point 1
(s,v)
Fusion 6
for unattended point 1
p p
p p
House 1 person
for attended point 1
(s,v)
Person
Stuff_condition
Attended point 1 Fusion 5
Stuff_condition
Unattended Point 2 Fusion 15 Stuff_condition (s,v) Attended Point 3 Fusion 8
for unattended point 2
Stuff_condition
(s,v) pp Stuff for (s,v) House 2 Fusion 16 Stuff_condition
delivering 2
Packet(2)
Packet(2) Packet delivered to house 2
1`person(2) for attended point 3
House 2 person Person
Packet(2)
House 3 person
p p
Unattended Point 4 Fusion 12 Stuff_condition
(s,v)
for unattended point 4
1`person(4)
p House 4 person p
p
Attended for attended point 4 (s,v) Point 4 Stuff_condition
p
Person
Packet(4)
Packet(4)
delivering 3
(s,v)
Stuff for House 3 Fusion 10
Packet(3)
for unattended point 3
Fusion 11
Stuff_condition
Packet delivered to house 3 Packet
Person
(s,v)
Stuff_condition Packet(3)
1`person(3)
for attended point 2
Attended Point 2 Fusion 14
Packet(3)
p p
pp Packet
(s,v) Unattended Point 3 Fusion 9 Stuff_condition
Packet delivered to house 4 Packet Packet(4) delivering 4 (s,v) stuff for House 4 Fusion 13
Stuff_condition
Fig. 6 Customer layer of the coloured Petri net model
All three layers of the model, that is, institutional, industrial and consumer, are connected through hierarchical relationships using a construct of CPN Tools called fusion place set [11]. The model developed is conceptual in nature as the aim of this study is to elaborate a methodology based on Petri net for hierarchical modelling of the Last Mile system. This model assumes four transit points in a defined geographical region where trucks arrive, offload and return. The stuff offloaded is loaded on a van which visits one attended and unattended drop point to deliver goods and then approaches a house for a house delivery. After serving one drop point, the van moves to serve the next drop points in a similar way, and after completing all four drop points, it returns to its original location, that is, the first drop point in the industrial layer. This scheme of picking and dropping material is hypothetical but can be used to add specific conditions and constraints required in any particular Last Mile system. The requirements of the system may include time and capacity specifications of trucks delivering goods in the Last Mile system; scheduling, routing and number of vans aimed at delivering the goods in the region; the scheme of delivering goods; and other related conditions. The conceptual hierarchical modelling of the Last Mile system and its implementation using Petri net is a convenient method for analysing the system under consideration. Such a modelling method can accommodate any changes which may arise anytime in the Last Mile logistic distribution system; hence, the coloured Petri net modelling method is scalable in its format and is a suitable technique to incorporate any changes in the system.
Places and transitions in Figs. 4, 5 and 6, that is, institutional, industrial and customers layers, are named descriptively. Table 1 shows the places/transitions and their description in the institutional layer where similar explanation is assumed for the industrial and customer layers. The conceptual modelling results generated by the coloured Petri net method using CPN Tools presented in this paper have been validated using another class of Petri net called high-level Petri net which has been modelled and simulated using ALPHA/Sim tools. The use of high-level Petri net through ALPHA/Sim for validation purpose has
Table 1 Institutional layer places and transitions description Place
Description
Trucks moving to the institutional layer Points 1, 2, 3 and 4 Stuff 1, 2, 3 and 4 Stuff 1, 2, 3 and 4 available
Trucks are approaching the institutional layer of the Last Mile system Geographical distribution of four points Unloaded stuff at points 1, 2, 3 and 4 Stuff 1, 2, 3 and 4 available for transportation to the industrial layer
Transition Descriptions Unloadings 1, 2, 3 and 4 Trucks are being unloaded at points 1, 2, 3 and 4 Ready to return 1, 2, 3 Trucks are ready after unloading at points 1, and 4 2, 3 and 4 Returning from 1, 2, 3 Trucks are returning from points 1, 2, 3 and 4 and 4 and moving out of the institutional layer
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revealed that coloured Petri net is more compact and scalable, hence more suitable for the Last Mile logistic distribution system. 3.4 Case example A case example has been developed to demonstrate the coloured Petri net-based modelling of the Last Mile distribution system. The number of vans in the customer layer has been increased from 1 to 4. In the first case, there is only one van which is serving the entire customer layer. T1, T2, T3 and T4 are the times which are required when the delivery stuff is distributed in customer 1, 2, 3 and 4 regions. The van moves from customer region 1 to region 3, from where it moves to region 4 and finally to region 2. The stuff numbers 1, 2 and 3 denote stuff delivered at the attended point, the unattended point and the customer house point, respectively. Time is measured in dimensionless time units while simulating the model. In case #1, the stuff delivery time is increasing as the van moves from the first to the last customer region. The number of vans has been increased to 2 in case #2 in such a way that the first van serves customer regions 1 and 3 and the second van serves regions 4 and 2. The stuff delivery times have improved as T1 and T4 and also T3 and T2 become equal. The delivery time can further be improved by adding another van in the system as is shown in case #3 where there are independent vans for regions 1 and 3 but one van for regions 4 and 2 which first serves region 4 and then region 2. In the last case (case #4), all customer regions have separate vans, and hence, stuff delivery time becomes equal. The key performance metrics for the Last Mile logistic distribution system is the time required to deliver stuff to its specified destination in this study. Another associated measure with overall time required to deliver stuff is resource (vans in this study) utilization which can be measured by calculating the
time for which each van is in working (loading, unloading, moving, etc.) condition compared with the overall time period for which the logistic distribution system is studied. Although stuff delivery time is improved by adding more vans in the system, it should be noted that van utilization times are bound to decrease along with an increase in capital and overall logistic distribution system expenses. Van utilization times can be measured by adding coloured Petri net modelling constructs in CPN Tools. Table 2 shows a decrease in time to deliver stuff with an increase in the number of vans, but this time decrease is directly linked with poor utilization of vans, and hence, the Last Mile logistic distribution system must be further explored using CPN Tools in order to achieve a tradeoff between delivery times and van utilization times.
4 Conclusion Last Mile is considered one important step in supply chain and business-to-customer paradigms and is responsible for efficient and economical final delivery of goods to customers. This study has addressed the modelling issue of the Last Mile system through the development of a hierarchical modelling implemented through the Petri net method. The proposed scheme is suitable for routing and congestion planning of delivery goods in a defined geographical location. The study can be furthered according to particular requirements of a particular Last Mile logistic system. This research will be extended to incorporate other related technological, environmental and social issues encountered in the logistic distribution system.
References Table 2 Last Mile simulation results
Case #1 (number of vans=1)
Case #2 (number of vans=2)
Case #3 (number of vans=3)
Case #4 (number of vans=4)
Stuff number
T1
T3
T4
T2
1 2 3 1 2 3 1 2 3 1 2 3
5 7 9 5 7 9 5 7 9 5 7 9
12 14 16 12 14 16 5 7 9 5 7 9
19 21 23 5 7 9 5 7 9 5 7 9
26 28 30 12 14 16 12 14 16 5 7 9
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