Springer operational freight carrier planning basic concepts optimization models and advanced memetic algorithms 2005 ISBN3540253181

A transport department or a carrier company derives internal processes from the requests in order to satisfy the customer demands using the available resources in a n efficient manner..

GOR ■ Publications

Fleischmann, BernhardInderfurth, KarlMöhring, Rolf H.Voss, Stefan

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H.-O Günther and P v Beek (Eds.)

Advanced Planning and Scheduling Solutions in Process Industry

VI, 426 pages 2003 ISBN 3-540-00222-7

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This book represents the compilation of several research approaches on tional freight carrier planning carried out at the Chair of Logistics, University

opera-of Bremen It took nearly three years from the first ideas to the final version, now in your hands During this time, several persons helped me all the time

to keep on going and to re-start when I got stuck in a dead end or when I could not see the wood for the trees I am deeply indebted to them for their encouragement and comments

Prof Dr Herbert Kopfer, holder of the Chair of Logistics, introduced me into the field of operational transport planning He motivated and supervised

me Furthermore, he supported me constantly and allowed me to be as free

as possible in my research and encouraged me to be as creative as necessary

In addition, I have to thank Prof Dr Hans-Dietrich Haasis, Prof Dr Martin

G Mohrle and Prof Dr Thorsten Poddig

On behalf of all my colleagues, who supported me in numerous ways, I have

to say thank you to Prof Dr Dirk C Mattfeld, Prof Dr Christian Bierwirth, Henner Gratz, Prof Dr Elmar Erkens, Nadja Shigo and Katrin Dorow They all helped me even with my most obscure and dubious problems

My family supported me all the time They always showed me their trust and encouraged me continuously Special thanks are dedicated to my parents Monika and Heinz-Jiirgen

However, there is somebody who helped and supported me much more than any other person It's my beloved wife Ilka She believes in me more often than I beheve in myself But more importantly, she periodically rescues

me from the jungle of science and guides my attention to other wonderful

aspects of life Thank you very much

Bremen, Jorn Schonberger

January 2005

2.2 Hierarchical and Simultaneous Planning 22

2.2.1 Hierarchical Approach 22 2.2.2 Simultaneous Routing and Freight Optimization 23

2.3.3 Selection with Compulsory Requests 26

3.4.1 The PDSP with LSP Incorporation 38

8.2.2 Bundle Assignment by the Mediator 140

8.3 Computational Experiments 141

8.3.2 Collaborative Planning Approach 142

The division of labor among the continents, countries or regions over the world enables the production of goods in the most efficient manner Goods are produced a t different locations so that the overall costs are minimized The manufacture of a certain product often concentrates on few places in a region,

a country, a continent or even in the world However, the demand for the products manufactured a t certain locations in a n economic zone is typically scattered over the complete zone In order t o satisfy this demand with the centrally produced goods, extensive transport is needed Transport describes the spatial transformation of goods or persons with the goal of balancing supply and demand The increase of goods transport is accompanied by a significant extension of passenger transport The movement of manpower to the centralized production facilities becomes necessary and additionally, the enlarged incomes are used for private travel

In Sect 1.1 of this chapter, the economic importance of freight transport

is explored Some current trends, from which the demand for a reinforced planning arises, are shown by means of the examples European Union (EU) and United States (US) In Sect 1.2 the structure of a freight carrier net- work and the transport processes in such a network are analyzed Planning problems regarding the design, configuration and deployment of the transport system are discussed in Sect 1.3 The distribution and collection of freight from providers or suppliers t o a consolidation facility, and in the reverse di- rection, is identified as a very critical phase of the transport and the need for additional planning support is emphasized in Sect 1.4 The goals and the organization of this thesis are given in Sect 1.5

1.1 Recent Trends in Freight Transportation

The commonly used indicator for the performance of the goods transport sec- tor is the amount of realized ton-kilometers (tkm) expressing the product of

2 1 Transport in Freight Carrier Networks

the quantities moved and the sum of traveled distances For passenger trans- port the number of passenger-kilometers (pkm) gives an adequate measure for the quantity of passengers moved and the bridged distances

From 1990 t o 2000, the performance of the transport sector has grown significantly in the US as well as in the EU For the United States a growth of more than 20% (goods) and 24% (passengers) is reported (Fenn, 2004) The European rates show a n increase of 29% for goods and 17% more passengers (Eurostat, 2002)

At the same time, the Gross Domestic Product (GDP) of the US has expanded by 39% (Fenn, 2004) and the EU-GDP has improved by 21% in the observed decade(Eurostat, 2002) The absolute values of the performance indicators have increased from 5.76 billion tkm t o 6.93 billion tkm, from 6.23 billion pkm to 7.72 billion pkm (US), from 2.33 billion tkm t o 3.08 billion tkm and from 4.041 billion pkm t o 4.839 billion pkm (EU)

Different studies forecast a further significant increase in required trans- port (Eurostat, 2002; Arendt and Achermann, 2002; ICF, 2002) An annual growth of around 3.4% (US) and 3.0% (EU) is expected in the transport

of goods Relative to 2000, a growth of 40% (US) and 34% (EU) in goods transport will be achieved by 2010

This thesis is about problems in planning the transport of goods, often called freight transport (Crainic and Laporte, 1997) Freight transport is per- formed by different means of transport: road transport by trucks and vans, rail transport by trains, waterway transport by inland navigation (barges) and vessels and pipeline transport of fluid products The contributions of each mode (the modal split) have changed during the last decade In both economies, the contribution of pipeline transport remains on a approximately unchanged level Waterway transport's part has lost significantly in the US as well as in the EU Different directions are observed for rail transport: in the

US it has grown but in the EU it has declined

In both economic zones, the main share of the internal freight transport

is performed on the roads Trucks and vans make up 32% of the US-domestic freight transport (Moore, 2002) and 44% of the intra-EU transport of goods (Eurostat, 2002)

The domain of road transport mostly takes place in the short or medium size quantity field with shipments of less than 45 tons and distances of typically not more than 500 km (Eurostat, 2002; Moore, 2002)

Two modes of road transport are performed In the own account (AC)

mode, the owner of the vehicles and of the moved goods are identical Typi- cally, such a company requires transport in order t o manage the flow of their goods along their supply chain from the suppliers, through production stages and warehouses t o the customers The contribution of AC transports to the performance of the transport sector in the US has decreased slightly from 28% t o 24% (Moore, 2004) in the nineties A significant performance loss for

AC has been observed in the EU-zone For example, in Germany it has fallen from 42% down to 30%, and in France the value has dropped from 28% down

to 18% (Oberhausen, 2003) An increasing number of enterprises outsource their transport departments, basically to reduce their overhead costs They hire independent logistics service providers to execute the necessary trans- port Such a transport company is called a (freight) carrier: it operates in the so-called hire or reward (HR) mode This sector's contribution t o the overall performance varies from 50% (in Portugal) t o over 76% (in the US) and nearly 90% (in Spain) with an average value of nearly 70% In both modes, AC and

HR, short-distance (max 50km) and medium-distance transport operations (max 150km) are the most often demanded services (Oberhausen, 2003) in the EU In the United States the average haul distance is 730km, all other modes operate a t longer average haul lengths (Moore, 2002)

The environmental impacts of road transport are significant: 19% (US) and 24% (EU) of the annual carbon dioxide emission is produced by this mode of transport (Eurostat, 2002; Fenn, 2004) An increase of nearly 16% (US) and 20% (EU) during the nineties of the last century has been observed Besides the emissions, several other negative impacts to the environment are observed: intensified traffic congestion lowers the performance of the road transport, large surfaces are sealed by roads, parking lots and transshipment areas and noise emissions lower the quality of residential areas Regulations and laws have been announced in order to alleviate the pollution and t o maintain several standards of life quality (European Commission, 2001)

For the EU some additional current developments are observed which are expected t o have significant impacts on road transport and the companies involved

The transport enterprises in the current EU member countries expect the complete integration of the accession countries, e.g Poland or the Czech Re- public These new competitors can offer lower transport costs since their la- bor costs are low and the regulations are not as restrictive as the laws in the current full member countries of the EU The low cost structure in the pre- accession countries will lead to a new wave of competitors intruding onto the

EU transport market Therefore, the existing transport sector in the current

EU now has to improve the efficiency of their business

Roads are free of charge in most EU countries The construction and main- tenance of the expressways, highways and other roads is under the responsi- bility of public authorities For some special connections (typically including large bridges or tunnels) the payment of a toll is required Recently, several member countries like Germany, Austria and the Netherlands announced their intention to establish a toll system for using their national roads, and in most

of the pre-accession countries road pricing has been established for years The consideration of this additional kind of costs cannot be avoided in the future The public authorities are not able anymore to provide the necessary funding

in inter-urban transport infrastructure (roads, bridges, tunnels) Private in- vestors are sought for funding, constructing and maintaining these facilities They are allowed t o collect a toll from the users

4 1 Transport in Freight Carrier Networks

Several urban governments (e.g such as the municipality of the City of London, UK) have recently either introduced or plan t o introduce a toll for driving on the urban roads The urban-toll has been introduced mainly for the reason of preventing traffic congestion caused by private road transport with the goal of improving the speed of business transport in the urban areas (Nash and Niskanen, 2003)

As mentioned above, road transport is an important player in the US and European economy with a significant contribution t o the overall performance

of the economic zone However, it is faced with several challenges in the near future, which make it unconditionally necessary t o strive for an improvement

in the efficiency of the height transport operations on the roads Carrier com- panies, which only operate in HR-mode, will be most affected by the challenges due t o the increasing importance of road transport in the United States and

in the EU, and their unconditional need of external customers

1.2 Carrier Transport Networks

A customer request describes a single transport demand The location of the pickup and the location of the delivery are specified as well as the quantity to

be moved Typically, additional requirements like time limits for the loading

or unloading operation or special handling requirements are stipulated A transport department or a carrier company derives internal processes from the requests in order to satisfy the customer demands using the available resources in a n efficient manner Several independent requests with coinciding

or adjacent origins and coinciding or adjacent destinations are bundled t o shipments or truckloads of larger quantity A significant decrease of the relative price for the movement of one single request is achieved, because overhead costs are split into small amounts that are assigned t o each request The realization of maximum economies of scale requires consolidation processes, which both support as well as depend upon the operation mode of a transport company

Firstly, the AC-mode is analyzed This mode is typically selected for the distribution of finished goods in industrial productions From a small num- ber of factories, large quantities of different goods are moved over relatively long distances t o regional distribution centers (DCs) in order t o replenish the DCs with goods From a DC, the goods are distributed t o customers, who are situated relatively near to the DC Typically, the distance from a DC t o

a customer is less than 100 km, whereas the distance between a production facility and a DC is often more than several 100 km The links between the production facilities, DCs and the customers defines a distribution network

In a distribution network, the flow of goods is uni-directional from few sources (the production facilities) to many sinks (the customers) Since the quanti- ties moved for replenishment are large, this network topology supports the realization of economies of scale In Fig 1.1, a distribution network with two

production facilities Fl and Fz is shown These two factories produce goods that are used t o replenish the three distribution centers DC1, DCz and DC3 Each customer is assigned to one of the DC from which he is supplied The traveled distance and the moved quantities in the distribution are different from those observed in the replenishment In distribution tasks, the distances

to travel are significantly reduced and the quantities moved along a link are significantly smaller

Fig 1.1 Structure of a distribution network

The strict uni-directional flow of goods from the factories t o the DCs or customers leads t o a n inefficient use of the deployed vehicles They drive fully loaded from the production facilities t o the DCs, from a DC t o customers or directly from the factory t o a customer (if enough load is available) However, they have t o travel back t o the DC or production facilities If no back-freight

is available, which is carried on the way back to the DC or to the production facility, half of the traveled distance consists of empty miles

Often, the transport of finished goods cannot be combined with back- freights flowing in the reverse direction National laws in several countries (e.g Germany) do not allow vehicles operating in the AC-mode to trans- port goods that are owned by another company In order t o use the existing network and equipment also for moving goods of third parties, several man- ufacturing enterprises decided to outsource their distribution systems and let them operate (at own responsibility) as freight carriers in the HR-mode

A freight carrier transports goods for different customer companies Par- ticular batches of different customers are combined in one vehicle if the origins and the destinations match A vehicle of a carrier picks up goods of one cus- tomer a t a certain place and moves it either directly t o the final destination

or with intermediate loading, unloading or transshipment stops belonging t o other requests Afterwards, it continues t o a new pickup location situated

6 1 Transport in Freight Carrier Networks

near the destination of the former transport task and loads new goods that are then moved towards the specified destination

Typically, a carrier company operates for several customers The flow of the goods is not limited t o a small number of relations and it is not uni- directional, but rather bi-directional (Fleischmann, 1998) There are many sources and many sinks of flow spread over the whole operational area The quantity of goods associated to a certain pair of origin and destination is small, and the particular flows are numerous Long-distance transport demands and medium-distance demands must be satisfied as well as short-distance bridg- ing Exclusive origin-destination transport is typically not achievable (Trip and Bontekoning, 2002) Due to the small quantities of particular requests,

an efficient consolidation strategy is necessary in order to reduce the part

of the overhead costs that have to be assigned t o each single request The consolidation of small flows from a huge number of locations into large long- distance flows has to be supported as well as the deconsolidation into flows to the particular customer destinations

Therefore, the operations area of a carrier is hierarchically organized and the origin-to-destination transport process is partitioned in sub-processes ac- cording to the partition of the area Few large regions form the operations area, and each region is divided into several small zones A hierarchically organized network of transshipment facilities and connections between these facilities is maintained The network structure permits a successive aggregation of flows from customer origins into high quantity flows and a subsequent resolution from bundled flows into deliveries t o the several destinations Whenever a sin- gle transport demand requires the crossing of a n organizational border, the goods of a request are combined with goods of other requests or extracted from a large volume flow

Transport between different regions takes place only between hubs (H)

A hub is a transshipment facility where all inbound flows from other regions are received and where all outbound flows are released In each region, the hub receives the goods from different transshipment points (TP) situated in the zones and forwards incoming goods into the right destination zones In each zone, the goods are distributed from the TP t o the customer locations by vehicles within several tours The same vehicles are used to collect goods from customer locations These goods are delivered to the destinations in the same tour if the location is situated in the same zone Otherwise, they are brought

to the TP, where they are merged with other collected goods and forwarded

to the regional hub A typical layout of such a hierarchically structured freight transport network is given in Fig 1.2 The overall operations area is parti- tioned into four regions The thin continuous lines mark the borders In each region one hub (HI, Hz, H3 and H4) is available All extra-regional flows of goods out of a region are realized through this transshipment facility as well

as all inbound flows Each region is separated into several zones Their borders are given by the thin dotted lines In each zone one T P is maintained where the goods flowing out of the zone are bundled and forwarded and where the

s Hi = hub in region i Ti = transshipment point

Fig 1.2 Hierarchical network structure of a carrier network

flow of goods destined for this particular zone is received The distance from the customer location t o a T P in a zone is typically less than the distance between the T P and the corresponding regional hub However, the distance between the hubs often causes the main part of the distance necessary for moving a packet from its origin t o its destination

The hierarchically organization is typical for a freight transport network operated by a carrier It permits the economically reasonable service of ge- ographically scattered locations with averagely low flow between particular origins and destinations (Fleischmann, 1998) However, the described original structure is often modified adapted t o meet the special requirements (Wlcek, 1998) A hub serves as the T P for a zone or a complete region, if the quan- tity of the flow of goods does not require the strong tree structure in a region Direct origin-to-destination shipments among different regions or zones are of- fered in the event that the quantity of goods t o be moved and the associated revenues are sufficiently large

In the following, the transport process for carrying the less-than-truckload (LTL) packet p, of the request r is analyzed in detail Figure 1.3 shows the

five phases of the process from an origin C3 to the destination D

Initially, the packet p, is collected This phase is called collection Typi-

cally, a vehicle of small or medium capacity is deployed for the fulfilment of

1 Transport in Freight Carrier Networks

this task This vehicle collects packets from several requests with origins in one selected zone and carries them to the transshipment point (TP) of the zone A T P is a special facility, in which the packets of a zone, collected by several vehicles, are consolidated into larger quantities (truckloads) A truck- load consists of all quantities belonging to requests originating out of a zone with destinations in zones embedded in different regions Requests in which both the origin and the destination are included in the same zone are served without involving a TP

In the forward feeding phase, the truckload is carried from the T P of the origin zone to the regional hub All truckloads of a region arrive synchro- nized at this large and high-performance transshipment facility (Fleischmann, 1998) In contrast to a TP, incoming and outgoing goods are merged while passing a hub Bundled truckloads from different TPs are resolved before the packets are re-consolidated into shipments so that all packets in a shipment have to be carried to customer locations in the same destination region

hub hub TP destination 'l/

Fig 1.3 Process-chain of an origin-destination carrier transport

The complete shipment containing p, is now carried to the hub of the desti-

nation region, which includes the final customer location If the hubs are fully connected, then no intermediate stop at any other hub is necessary because there is a direct connection between each two hubs Otherwise the shipment

is moved to one or several intermediate hubs, reconsolidated if necessary, and then finally transferred to the hub of the destination region In this line haul phase (Daganzo, 1999), large distances are traveled The means of transport is often different to those in the previous phases Since the flow of goods is con- tinuous and of balanced quantity, the inter-hub connections are often served

in a regular way following a fixed schedule (Crainic, 2000) For this reason,

it is necessary that the feeder transport schedule be synchronized with the departures from the hub All feeder truckloads should arrive in time so that they can be considered for the inter-hub transport departures A synchronized arrival enables the most effective re-consolidation of the incoming truckloads from other hubs and from the TPs

At the destination hub, the shipment containing p, is resolved and merged

with other incoming shipments into truckloads, so that each truckload com- prises packets for different customers who are situated in the same distribution zone of the considered region Each truckload is transported t o the TP of the

corresponding zone This phase is denoted as backward feeding

At the T P of the zone, which contains the destination of r, the truckload is broken into the packets and the packets are distributed t o the customers that

are situated scattered over the destination zone Delivering p, t o the customer specified delivery location completes the request r

The first two phases of the transport process are subsumed under the name

pickup and the last two phases are referred to as delivery The pickup in a n

origin region is typically combined with the delivery of back-freight destined for this region Thereby, the flows of goods in both directions are combined

in an effective and efficient way

The correspondence of the five-phase transport process and the hierarchi- cally organized network is shown by means of a transport of a packet from a customer situated a t the small black point in the north-western zone t o the location marked by the small black point in the south-eastern zone in Fig 1.2

A vehicle following the route that visits all customer locations in the origin zone, shaded in grey, picks up the considered packet At TI, the TP of the origin zone, the packet is consolidated with all other packets originating from this zone into a truckload and it is fed t o the regional hub H I With a n in- termediate stop a t H3, the packet is carried to H4, the hub in the destination region There, it is transshipped and fed to T4, the T P in the destination zone F'rom T4 it is delivered on the route visiting all grey shaded locations, including the particular delivery site

1.3 Network Design, Configuration and Deployment

The construction, the management and the usage of a n effective and efficient freight carrier transport network require the solution of numerous often inter- dependent decision problems

Logistics System Design The design of a freight transportation net-

work affects several problems related to the location and the layout of the net- work components such as the TPs, hubs or traffic routes Three main classes

of design problems are distinguished (Crainic and Laporte, 1997):

0 How many hubs and T P s are needed? Where should they be installed?

How large should they be? (location and layout)

How should the hubs and T P s be linked? Which means of transport should

be used for the connections? How should the flow of goods be distributed

over the connections between the hubs? (network design)

0 How can the network be protected against disadvantageous external influ- ences and evolutions arising from infrastructure modifications, the evolu-

10 1 Transport in Freight Carrier Networks

tion of demand and from new governmental or industrial policies? (regional multi modal planning)

Network design problems are strategic The necessary funding and the nec- essary time for the construction or modification of a n existing infrastructure

do not allow short or medium-time changes Design problems are solved using estimated data expressing the expected flows of goods The decision for a cer- tain network architecture is based upon the costs for installing, maintaining and using the facilities and the traffic links between them

Logistics System Configuration comprises three main mid-term plan-

ning categories (Crainic, 2000): service selection, traffic distribution and ter- minal policies A service describes a repeated transport operation connecting hubs or hubs and TPs In a service selection problem, the offered services in a network are determined Typically, the repetition of a service follows a regular schedule The departure and the arrival times a t the first, the last and the intermediate stops are defined and announced The necessary work power and transport capacity to offer the intended services is procured

Several services are compiled into closed routes (itineraries) For each itinerary, a vehicle is allocated and the corresponding necessary terminal op- erations are fixed Services are determined only for connections of hubs with

T P s or other hubs The derived schedule is valid for up to several months in the future, but exact long-term planning data are not available The quanti- ties of goods have to be estimated, e.g based on observations from the past However, reliable estimates need reliable input data, which is typically avail- able only for the feeder or line haul connections The consolidation of packets from the customers ensures a predictable and balanced flow of goods between the hubs

A terminal policy describes the offered activities a t a given hub or TP The type of performed consolidation tasks a t a certain hub or T P is specified and defines the available throughput that can be handled Additional resources have to be maintained in order to compensate for peaks in the demanded services

Logistics System Configuration aims at establishing services that allow ef- ficient operations t o answer customer demands and t o ensure the profitability

of the operations (Crainic, 2003) Efficiency is typically measured in terms of costs for fulfilling the customer demands a t a predicted quality that allows the customers t o maintain complex and reliable production systems (Rodrigue, 1999)

Logistics System Deployment comprises short-term planning problems

in a freight carrier network In contrast to the design and configuration of the network, deployment decisions are mainly based on known problem data These data are derived from the known or declared flows of goods extracted from the customer demands The goal is to allocate labor and capacities in order to support the efficient fulfilment of known customer demands with respect to the policies and services determined in the configuration step These

planning problems are solved following the rolling horizon planning paradigm

in order to handle the continuously updated information about additional, cancelled or modified customer requests The necessary operations for the next period are definitively determined together with a tentative determination of the operations planned for the subsequent planning periods The following short-term planning problems occur (Crainic and Laporte, 1997):

Assignment of crews, reserve crews or maintenance teams t o vehicles or transshipment facilities in order t o support the planned operations (crew scheduling)

0 Preparation of the operations for the next planning period (empty balanc- ing)

0 Scheduling of the services for the pickup and the delivery phases (vehicle routing and scheduling)

Logistics System Deployment mainly impacts the short-term planning of pickup and delivery operations The operations during the long haul phase are determined by the valid regular schedules For two reasons the determination

of a long-term schedule for the pickup and the delivery operations is not achievable:

1 The locations that have to be visited are typically not known in advance

2 There is no balanced flow of goods that permits the prediction of necessary services and/or necessary capacities in a zone

The costs for the operations in the first and in the last phase of the carrier transport process are, expressed in terms of money units per tkm, the most expensive part in the complete transport from the pickup location to the final delivery location Herry (2001) states that the costs per tkm in short- distance transport are a t least three times larger than the costs per tkm in the middle or long distance case The reason for this extreme increase of the costs can be seen in the relatively small quantities that are delivered or picked

up a t a customer site stop, and in the lack of consolidation options due t o the scattered locations of customer sites that requires a visit Furthermore, the unconditional need for the consideration of tight time windows for the pickup and the delivery visits confines the realization of economies of scale that are otherwise achieved by the bundling of several requests (Punakivi et al., 2001) The consideration of time windows is necessary in order t o synchronize the transport processes performed by the carrier company with the internal processes of the customers

Each customer request is split into five internal requests according t o the subprocesses described in Sect 1.2 A collection task is necessary t o carry the

12 1 Transport in Freight Carrier Networks

demanded quantity from the customer specified origin t o the next TP Within the forward feeding task, this quantity has to be carried t o the regional hub, typically together with quantities from other customer requests The line haul tasks expresses the necessity to transport the quantity to the destination hub, the backward feeding task requires the movement of the quantity t o the TP

in the destination region and the distribution task describes the final carriage

to the destination In the remainder of this thesis, the term request is used as

a synonym for task or internal request

Each line haul task is assigned t o one of the regular services, which ensures the execution of the task The remaining tasks cannot be assigned t o such a regular service, because there are no regular services for tasks within one region It is necessary t o allocate resources for the remaining four tasks in each planning period To fulfil the required tasks associated with different requests, company-owned vehicles can be used or, for the payment of a fee, other carriers can be instructed to complete selected tasks

Pickup and delivery planning problems comprise the allocation of the re- sources for fulfilling the tasks within a region for a given planning period

A solution of a pickup and delivery planning problem is the transportation plan (Crainic and Laporte, 1997) and the necessary costs are called fuZjilment

which comprises just a day or often even only several hours For subsequent periods, the transportation plan is renewed considering the recently released information of additional, cancelled or modified requests and the currently available transport resources

Altogether, the following issues characterize pickup and delivery planning problems

The request portfolio cannot be modified In some cases a postponement

of some of these requests is allowed

The consideration of a large number of low-quantity packets instead of bundled shipments requires a large number of stops a t customer sites The composition of several requests into routes is necessary in order t o achieve profitability (Trip and Bontekoning, 2002)

Compared t o the line haul tasks, the costs for fulfilling a (regional) pickup task or delivery task are tripled (Herry, 2001)

No regular services are available For each planning period, a new transport plan has t o be determined (logistics system deployment problems) The flow in both directions t o and from the TP/hub is typically not syn- chronized A time gap between freight and back freight has t o be managed Several time constraints have to be taken into account: earliest departure times from the TP/hub (availability), latest arrival times a t the TP/hub and customer site time windows

The routes are determined following a rolling horizon planning, the period length depends upon the frequency of incoming feeder or long haul services

a t the TP/hub and upon the portfolio of released, but so far unconsidered, customer requests

0 The demanded transport capacity is not balanced: it varies from planning period t o planning period

0 Other carrier companies are allowed to be ordered t o fulfil tasks (subcon- tractor incorporating, externalization)

Pickup and delivery planning aims a t finding a reasonable trade-off be- tween necessary costs (resulting in reasonable offered prices) and service qual- ity Mathematical optimization models are proposed in which the costs are expressed in a cost function that is minimized In order t o ensure customer satisfaction, several constraints have t o be considered, especially time windows that restrict the delivery or collection time

Existing models for pickup and delivery problems typically refrain from involving external carriers However, their consideration can be profitable if the charges are below the costs for using a n own vehicle Additionally, the occasional involvement of external carriers for a fixed charge allows a quick and temporary capacity expansion when the available resources do not suffice

to serve all tasks

1.5 Aims of this Book and Used Methods

Systems for freight transport require an exact and efficient coordination of the different processes in order to offer a reliable service to customers and t o keep the necessary costs within an acceptable budget

The setup of regular services in a particular zone or region is generally not targeted because the local flow of goods is unpredictable Neither the demanded quantities nor the locations to be visited can be estimated in a sufficient manner Since the costs for each performed tkm are significantly enlarged compared t o the long-haul operations the determination of efficient long valid schedules is hardly possible The determination of the necessary tasks to fulfill the demand for transport in a particular region is furthermore compromised by a significant reduction of available and maintained transport resources due t o the current poor market conditions and due t o the intrusion

of low-cost carriers from the EU candidate countries into the market

The involvement of carrier companies t o fulfill requests for a fixed charge becomes more and more attractive for freight carrier companies who offer and manage wide-area transport networks Instead of maintaining own equipment

in all regions (with often severe costs for employment, depreciation, main- tenance and insurance), subcontractors are involved for a previously known charge whenever it is possible (due t o lower costs) or necessary (due to a short-term capacity bottleneck)

The planning of the regional collection and distribution traffic of a freight carrier company is a very sophisticated challenge, since it is impossible t o

14 1 Transport in Freight Carrier Networks

establish regular services between customer locations and transshipment fa- cilities Planning support for the incorporation of external carriers has received only minor attention so far, although it is extensively required in practice Ad- equate planning models are rarely proposed but they are becoming more and more necessary t o support freight carrier planning The intention of this thesis

is to contribute new ideas to close this gap between real world requirements and available planning support

The first goal of this thesis is to derive general modeling approaches for incorporating external logistics service providers in the fulfillment planning of

a freight carrier network Chapter 2 provides a n introduction t o operational carrier planning problems The corresponding scientific literature is surveyed and four main modeling approaches with special consideration of the external request fulfillment are derived

As the second goal, the extension of existing pure routing models by the incorporation of a carrier incorporation feature is performed One of the most general routing problems which represents a variety of different planning sit- uations, the pickup and delivery problem with time windows, is generalized Therefore, the possibility of the usage of a n external carrier for unprofitable requests is added Four different problem variants representing several special planning environments are set up For each single variant, adequate test prob- lems are generated Chapter 3 comprises all these investigations of so-called

pickup and delivery selection problems A pickup and delivery selection prob- lem can be modeled as a multi-constraint mathematical optimization problem The solving of instances of such a problem requires massive computational ef- fort even for small number of incorporated requests and vehicles Optimality guaranteeing algorithms are not available

The third goal of this thesis is the derivation of adequate algorithms t o solve instances of pickup and delivery selection problems The configuration

of Memetic Algorithms is proposed Memetic Algorithms combine the proven exploration capability of Genetic Algorithms for restricted combinatorial op- timization problems with the exploitation capabilities of problem-specific al- gorithms General concepts of the memetic search are presented in Chap 4 This class of algorithms has been successively applied to routing problems for vehicles The general configurations of a memetic search algorithm for routing

problems are surveyed in Chap 5 The configuration of a Memetic Algorithm

for solving pickup and delivery selection problem instances is presented in the Chapters 6 and 7 Its applicability is assessed within extensive computa- tional experiments It is shown, how it might possibly be incorporated into and exploited by a carrier service The presented framework can be used for problems based on any of the four carrier incorporation approaches

The applicability of the derived models and algorithms is investigated for

a cooperative planning scenario described in Chap 8

This thesis concludes with a summary of the core findings of the investiga- tions and formulates topics for future research in the field of planning models for freight transportation with the possibility of incorporating a paid carrier

This chapter is about operational (short-time) planning problems that must be resolved in order to determine the transportation plan of a carrier company for the next planning period The focus of the investigations is on the coordination

of the operations t o realize the outer legs of the freight carrier transport process described in the first chapter The aim is t o determine the necessary operations t o fulfill the demand for transport between customer locations and the next transshipment facility in a particular region

A carrier has t o solve different decision problems in order to setup the transportation plan for a certain planning period The first decision concerns the question as t o whether the responsibility for a request fulfilment is taken

on Each accepted customer request is resolved into several internal tasks (internal requests) distinguishing between pickup, line-haul and delivery re- quests Line-haul tasks are assigned to the designated regular and scheduled services

The second decision problem comprises the selection of the fulfilment mode

of the pickup and the delivery requests Mode selection means to decide whether a request is fulfilled with own vehicles (carrier controlled vehicles)

or whether it is externalized and fulfilled by another carrier for a charge (ex- ternal order processing)

To utilize the own fleet in a most efficient manner it is necessary to solve

a routing problem in which the requests are assigned to different vehicles and execution orders are setup (third decision problem) In order to reduce the overall sum of charges t o be paid t o other carriers, a freight charge mini- mization problem has to be solved (fourth decision problem) These decision problems are analyzed in Sect 2.1

The four decision problems are interdependent In a hierarchical solving approach, the problems are solved successively: Initially, the mode of execu- tion is selected for each accepted request and afterwards the resulting routing and the resulting freight minimization problem are solved In a simultaneous approach, the decisions upon the selected mode, the routing and the freight charge minimization are derived simultaneously within one closed optimiza-

16 2 Operational Freight Transport Planning

tion problem Hierarchical and simultaneous approaches are described in Sect 2.2

The simultaneous approach has received only minor attention so far al- though it is most promising and required in many real-world applications Adequate decision models or problem representations are required In Sect 2.3, four generic frameworks for combined mode selection, routing and freight charge minimization problems are introduced Each one represents a simulta- neous problem for a special environment

If a carrier accepts a customer request then it takes over the responsibility for the reliable completion of the customer specified transport demand The carrier company receives a certain revenue for each satisfactorily completed request If a request is not completed to the customer's satisfaction, the carrier

is sanctioned The agreed revenues and the agreed penalties are typically codified in a contract between the carrier and the customer

Solving the request acceptance problem for a request r means t o decide

whether r can be fulfilled in a profitable manner or not Therefore, the request

acceptance problem is a binary decision problem

A carrier company is faced with different request acceptance problems

Tactical request acceptance problems require a general decision about the future acceptance of different request types Such a type comprises typ- ically all the requests of a certain customer This acceptance problem is a management problem, because the general acceptance of all requests of a cus- tomer requires medium- or long-term investments for additional transport

or transshipment resources The general acceptance is fixed in medium- or long-term contracts In such a contract, the expected quality of the request fulfilment is codified Furthermore, the revenues achieved for the request ful- filment are determined The general acceptance is recommended if, and only

if, the agreed revenues cover the sum of necessary investment and operation costs A reasonable contribution t o the profit has t o be achieved

In a n o p e r a t i o n a l a c c e p t a n c e problem, the carrier company has to decide about the acceptance of particular requests whose fulfilment is not enforced by long-lasting contracts Such a request is accepted if the expected revenues cover the expected additional costs caused by the consideration of this additional request Negotiations with the customer are often necessary

in order t o commit the customer to pay larger revenues If the negotiations lead t o sufficiently large revenues then the request is accepted otherwise its completion is refused In contrast to tactical acceptance problems, investment costs are not considered in the profitability calculations (Meier-Sieden, 1978) Two additional aspects compromise calculation based solution approaches for operational acceptance decisions In the current market situation, several carriers compete for few customer requests If a carrier refuses a customer demand then it can be expected that also all other requests of this customer are lost for this carrier These lost revenues cannot be adequately incorporated into the calculation of the profitability of a request (Schmidt, 1989)

A carrier company receives demands for transport successively during the whole working day As soon as a new demand is expressed and submitted to the carrier company, a decision immediately becomes necessary, whether the responsibility for the request completion is overtaken or not So far unknown requests cannot be considered while evaluating the worth of the current re- quest (Riebel, 1986)

Each accepted customer request is resolved into several internal tasks or internal requests according to the differentiation of a pickup, a delivery or a line-haul operation These operations are coupled and have t o be synchronized

A line-haul task is assigned to one of the established regular and scheduled services This is not possible for a pickup or a delivery task because there are

no regular services to fulfill the operations within a region

In the remainder of this thesis, it is assumed that all available requests are internal requests derived from customer requests It is aimed a t determining a most profitable transportation plan for fulfilling all requests within one region

In the following three subsections the necessary decision problems t o setup the corresponding transportation plan for a given set of internal requests are discussed

2.1.2 M o d e Selection

A carrier company has two possibilities t o complete a request It can use an own vehicle for the execution of the necessary tasks or it pays another carrier for fulfilling the corresponding tasks Such a carrier is called a logistics service provider (LSP) In the following, the term 'carrier' is used for the company for which the vehicles have t o be routed The term 'LSP' is dedicated t o each company that offers the fulfilment of requests for a previously known freight charge

Two reasons for the incorporation of an LSP are possible:

18 2 Operational Freight Transport Planning

1 The considered carrier company does not maintain enough transport re- sources t o fulfill all requests as contracted

2 The external processing costs (freight charge paid t o the LSP) lie below the additional costs for the utilization of carrier-owned equipment The decision whether an LSP is incorporated or not is based upon the relevant variable costs In the case of LSP incorporation these costs are the freight charge and in the case of the usage of own resources, the relevant costs are determined by the additional travel costs of the own used vehicle

If the available transport resources of the considered carrier are not scarce then a request r is assigned t o an LSP if and only if its claimed freight charge

is less than the additional (travel) costs caused by the incorporation of r

The situation is different in the case where the transport resources of the carrier company are scarce and some requests with travel costs below LSP- charges cannot be served with own equipment The fleet of the considered carrier company serves those requests that utilize the bottleneck resource(s)

in the most efficient manner All remaining requests are assigned t o a n LSP The set R+ comprises all requests served by own equipment and R- in- cludes the requests served by an LSP The ordered pair (R+, R-) is denoted

as request selection A request selection is feasible if

1 All requests contained in R+ can be served with carrier-owned and -

controlled vehicles without violating any desired restrictions and

2 If a n LSP is available for each request assigned to R -

The goal of mode selection is to determine a most beneficial request se- lection It is aimed a t maximizing the profit contribution achieved from the selection ( R + , R - ) This is the difference between gained revenues and ex- pended costs The selection is evaluated by the sum of paid LSP charges for the requests assigned to R- and costs that are caused by the own-equipment- service of the requests in R+ This sum is denoted as fulfilment costs The goal is t o minimize this amount It is assumed that the sum of achieved rev- enues does not depend on a particular selection so that the fulfilment cost minimization is equivalent to the maximization of the profit contribution Schmidt (1989) proposes a calculation model for long-distance operations

in which the costs for the execution of a request r with own equipment are compared to the LSP-charges for r The requests with the highest difference between the costs for the LSP and the own travel expenses are assigned t o the available own vehicles until their capacity is exhausted All other requests should be assigned t o an LSP Initially, each request is considered separately Cost savings that arise from the coupled fulfilment of two or more requests within one itinerary of a vehicle (coupling savings) are rarely considered The large number of possible combinations of requests for an itinerary does not allow the identification of the most advantageous request compositions Erkens (1998) proposes a refined calculation model However, requests are calculated

in isolation The consideration of coupling savings is not incorporated

There may appear situations in which special contracts between the car- rier company and a customer prohibit the fulfilment of requests by an LSP Furthermore, several requests cannot be served by LSPs because the LSPs are not equipped with the necessary vehicles like cooling tanks or special security containers

Mode selection problems are mainly treated with comparative calculation approaches in order to solve the question whether the LSP incorporation is cheaper than the usage of own equipment However, in many situations the desideration of savings from request compositions and consolidations reduces the quality of the proposals derived from the solutions of the calculation mod- els

An LSP can be incorporated whenever it becomes necessary, but the charges may increase if a request requires an urgent completion or if the specifications of the request do not match with the remaining request stock

of the LSP

Routing describes the problem of determining the routes for the vehicles of

a carrier company These routes are used as the instructions for the drivers and describe the way in which the customer requests are served A request is completed after the necessary customer locations have been visited and the specified quantities have been transferred between the right locations Two concatenated decision problems have t o be solved First, it has to be decided for each request which vehicle is used t o serve this request Therefore, each request is assigned t o exactly one vehicle The set of requests assigned

t o a certain vehicle v is called the tour of vehicle v In order t o determine the route for this vehicle, all customer locations requiring a visit of v, are arranged in a sequence that defines a visiting order, called the route The set

of the routes of all vehicles of the carrier company represents a solution of the routing problem

Typically, several solutions are available for one particular routing prob- lem In order t o maximize the contribution to the profit gained for the consid- ered carrier company through the completion of the requests within R , the aim should be to minimize the travel costs connected with the implementation

of a solution Therefore, several requests are composed into the same route in order to realize maximum coupling savings

Routing problems are typically modeled as mathematical optimization problems consisting of a set of feasible solutions and a n objective function that represents the profit contribution of a particular solution These models combine the assignment subproblem and the sequencing subproblem in one model

Since the routing problems usually appear in practical applications, several complicated additional conditions compromise the determination of the most advantageous routes In a capacitated routing problem, the maximal allowed

20 2 Operational F'reight Transport Planning

load of the available vehicles is limited so that maximum coupling savings cannot be achieved If the visit t o one or more customer locations is restricted

to a certain time interval (time window) then profitable sequences are often not realizable This type of routing problem is called time constrained If

several precedence relations in the routes have t o be kept then a precedence- constrained routing problem has to be solved Models for practical routing

problems typically involve combinations of these generic problem variants The most extensively studied vehicle routing problem is the Traveling Salesman Problem (TSP) The goal of the TSP is to determine the shortest

length route for one vehicle in which all specified customer locations are visited exactly once (E.L Lawler et al., 1990), hence solving a pure sequencing prob- lem Capacity, time restrictions or precedence constraints are not given In the

multiple TSP the request portfolio has to be partitioned into routes for two or

more vehicles, an assignment problem and several sequencing problem have t o

be solved in parallel (Domschke, 1985) In the Capacitated (time constrained) Vehicle Routing Problem (VRP), a knapsack constraint hinders the imple-

mentation of the most promising routes (Christofides, 1990) This constraint represents a maximum capacity of the used vehicles, a maximum route length

or maximum trip duration If visits to (customer) locations are restricted to well-defined time intervals (time windows) then the VRP is denoted as the

Vehicle Routing Problem with Time Windows (VRPTW) (Solomon, 1987)

Precedence constraints are typically imposed if the considered portfolio com- prises both internal collection and internal distribution requests associated to the same customer request This type of problems will be discussed in more details in the following chapters of this thesis

Routing models are solved by automatic solution approaches following different search paradigms Optimal (exact) approaches guarantee the iden- tification of a solution that is provable not to be dominated by other so far unconsidered solutions However, their performance is often insufficient be- cause the models a t hand are very complex and the algorithm's running times are excessively long Heuristic algorithms (heuristics) try t o identify suffi- ciently good solutions, but they cannot guarantee that the optimal solution

is found Nevertheless, heuristics are often able t o find solutions whose qual- ity is close t o the (unknown) optimum Specialized heuristics exploit special problem structures or features Their applicability is typically restricted t o a closely defined problem family Meta-heuristic search algorithms follow gener- alized search paradigms that are problem independent For this reason their applicability is not restricted to some special well-defined applications (Aarts and Lenstra, 1997; Reeves, 1993)

The carrier company wants to minimize the costs for the fulfilment of the requests for which LSP incorporation has been selected Each LSP uses a freight charge function in order to determine the price for the fulfilment of

a request Typically, the charge depends upon the starting position and the destination of the requests, the kind of goods t o be moved, their weight and their size as described in the request The charge function is degressive so that the average cost of each transported weight or size unit decreases with each additional unit assigned to a particular relation between a n origin and a destination (Kopfer, 1992)

Every request r E R- is split up into a sequence of partial requests

Fl, , Fny according to the subprocesses described for freight carriers in the previous chapter The goods q, have to be move from o to d f l describes the request to move q, from o t o a location where q, is consolidated with goods from other requests For the combined quantity the request F2 is specified in order t o transport the quantities to another location where additional quanti- ties are added The last partial request f n T expresses the demand for delivering

q, from the final consolidation or resolving point to its final destination d

Fig 2.1 Assignment of partial requests t o relations

Figure 2.1 illustrates this approach Four requests R1, R2, R3 and R4 have

to be fulfilled by a n LSP Instead of instructing an LSP to carry the quantity

of R1 directly from A t o F, it is split into the concatenated requests A t o B,

B t o Dl D to E and E to F R3 is resolved into the two partial requests B t o

D and D to E The request R4 is defined as the concatenation of C t o B, B to

D, D to E and E t o F Five requests are defined and assigned t o LSPs: from

A to B with the quantity of R1, from C to B with the quantity of R4 The request for the connection B to D comprises of the quantities from all four requests, whereas the request from D t o E comprises the quantities of R1, R3 and R4 The quantities belonging t o R1 and R4 are bundled into one request from E t o F The number of necessary requests is enlarged from four t o five,

22 2 Operational Freight Transport Planning

but the quantities for the relation B to D, D to E and E to F are large, so that the part of the costs assigned to each request is reduced

The search for a least cost partition of the outsourced requests and their

assignment t o different relations is called freight charge optimization Mathe-

matical optimization models and solution approaches for this type of carrier planning problem are investigated in Pankratz (2002) and Kopfer (1989,1984)

The four decision problems (request acceptance, mode selection, routing and freight optimization) have to be solved in order t o minimize the costs for the completion of all requests in the current portfolio As discussed, the company's management typically decides about acceptance or refusals of requests For this reason it is assumed that the completion of all requests in the portfolio

R must be achieved The decisions for the selected mode, the routing and the freight optimization remain the subject of pickup and delivery planning 2.2.1 Hierarchical Approach

In a hierarchical planning approach the mode selection decision is the first decision made For each request r in the portfolio R it is determined whether

r is completed by a vehicle of the considered carrier company or by a vehicle

of a n LSP This decision is irreversible and determines the request selection (R+, R - ) The marker x, is set t o 1 if, and only if, x, is served by a n own vehicle of the carrier company If an LSP is incorporated for the completion

of r then x, is set t o 0

After the mode of completion has been determined for all requests in R , a routing problem is solved for all requests contained in R + The vehicle v,- that serves a certain request f E R+ is chosen and the position p, in the visiting sequence of v, is set Therefore, the ordered pair (v,,pF) is irrevocably fixed for each request f E R+

If r is assigned to R- it has to be decided by which shipment sequence 1, this request is served

After r has passed the different planning stages, its attributes can be

expressed in the quadruple (x,, v,, p,, 1,) If x, = 1 then the information in the fourth component is ignored, otherwise the second and the third component remain unconsidered

In the hierarchical planning approach mentioned above, the set R of ac- cepted customer requests is separated into two the disjoint sets R+ and R-

A set of routes has to be determined in order to serve all requests in R+ The requests in R- are distributed among different LSPs so that the overall sum

of paid charge is minimized If the mode of a request has been determined

it cannot be modified anymore so that the assignment of the requests to the sub-portfolios R+ and R- is unalterable This hierarchical planning approach

is illustrated in Fig 2.2

request r

mode selection

fulfilment of r fulfilment of r

Fig 2.2 Hierarchical solution of the decision problems

2.2.2 Simultaneous Routing and Freight Optimization

In general, it is not possible to identify the subset of the request portfolio that leads t o positive profit contributions if they are served by own equipment It depends on the routes of the vehicles whether a certain request enlarges the profit contribution (joint-product production) For this reason the profitability

of a request served by an own vehicle of a carrier company, can only be esti- mated roughly in the mode selection step If, during the solving of the routing problem, it turns out that a certain request is unprofitable and compromises the generation of profitable routes it should be given to an LSP for completion

On the other hand, the change of the execution mode is advantageous, if the self-service of a tentatively externalized request with a carrier-controlled ve- hicle leads t o considerable additional profit contributions because the request fits appropriately into the routes

In simultaneous pickup and delivery planning problems, the changes of the execution modes of requests are allowed For each request, a mode is deter- mined tentatively As soon as it turns out that a change of the execution mode

of requests leads to additional profit contributions, the necessary changes are performed

In the model for a simultaneous pickup and delivery-planning problem,

x, is decidable for each request r As a consequence, the two other decisions (routing and freight minimization) have to be coded in such a model a t the same time in order to allow for the evaluation of the mode selection A model for the planning of the pickup and delivery operations, in which all three decisions can be modified, is called simultaneous pickup and delivery selection model

Simultaneous planning approaches work as follows Initially, a tentative separation of the request portfolio into R+ and R- is determined by selecting

0 or 1 for x, for each request r For the requests in R+, tentative routes are

24 2 Operational Freight Transport Planning

generated and the requests in R- are tentatively assigned t o different LSPs The execution modes of some requests are altered and this new separation is evaluated by solving a routing problem for the requests in R+ and a freight optimization problem for the requests in R - If no additional profit contribu- tions are detected the mode alternations are canceled and other requests are selected for a tentative mode alteration The exchange is repeated until it can

be guaranteed that the fulfilment costs (travel costs plus LSP charges) are minimized, which is equivalent to the maximization of the profit contribution

Fig 2.3 Simultaneous solution of the decision problems

The information flow between the three decision problems mode selection, routing and freight optimization is shown in Fig 2.3 Different modes are

tentatively assigned t o each request r until the optimal mode for each request with respect t o the fulfilment costs is identified

In the following, different generic frameworks for simultaneous planning mod- els are derived It is assumed, that a request portfolio R is given The request selection ( R + , R - ) is evaluated by means of the corresponding revenues and costs R ( R + ) represents the revenues obtained for the requests fulfilled with own equipment In some applications, the LSP incorporation is not prohib- ited, but is sanctioned by a reduction of the paid revenues However, in the remainder of this thesis it is assumed that the utilization of an LSP does not lead to revenue decreases Therefore, the sum of achieved revenues remains unchanged as long as all requests are completed by own or LSP equipment The cost evaluation of a request selection requires the determination of an explicit transportation plan (cf Subsection 1.4) and therefore the solving of a

routing and a freight optimization problem The transportation plan describes the determined routes of the own vehicles to serve the requests in R+ and the

selected assignment of the request collected in R- Let T(R+) be a least cost routing plan for serving the requests in R+ The costs for executing T(R+)

are given by C(T(R+)) Let B(R-) be a cost minimal distribution of the

requests in R- among the available LSPs and let F(B(R-)) represent the summarized charges for the LSP incorporation

2.3.1 Maximal-Profit Selection

A carrier company aims t o achieve maximum or a t least non-negative contri- butions t o the overall profit of the company Therefore, it tries t o minimize the costs for fulfilling the given request portfolio Since the sum of achievable revenues is fixed, the minimization of the fulfilment costs leads to a maximum difference between the gained revenues and the spent costs

In order to achieve maximum savings by LSP incorporation, it is uncondi- tionally necessary that the most promising request selection can be generated Therefore, all requests are allowed t o be served by an LSP This allowance is typically available as long as the LSP can provide a n equivalent performance, reliability and service quality

The costs for a transportation plan are determined by the chosen request selection This means, that a cost reduction can be achieved only by modifying the current request selection Therefore, the fulfilment cost minimization of the carrier company can be represented as the following optimal selection problem

s.th (R+, R-) is a feasible request selection of R (a.2]

Diaby and Ramesh (1995) and Pankratz (2002) investigate problems, in

which costs are minimized by distributing the requests among the own vehicles and vehicles of LSPs

2.3.2 Bottleneck Selection

The fulfilment of a request consumes resources like fuel, load capacity or time The transport costs typically comprise fuel because this is the only resource whose consumption can be determined exactly Load capacity or time consumption cannot be measured in terms of monetary units in order to distribute these costs among the requests in a fair manner However, there is only a fixed amount of such a resource available

The quantities to be transported within a zone are not balanced; they vary significantly from planning period to planning period In order to operate a vehicle continuously in the most efficient manner, an averagely high usage level

26 2 Operational Freight Transport Planning

of this vehicle is aimed at The available capacity is therefore adjusted t o the average flow (Erkens, 1998) Highest peaks in the flow cannot be served with this capacity and require the incorporation of a n LSP t o fulfill all requests The collection and the pickup routes have to incorporate strict duration constraints The collection has to be terminated in time, so that the picked up packets can be brought to the next consolidation center in time t o perform a consolidation before the feeder operation departs from the consolidation facil- ity On the other hand, the frequency of deliveries from the T P s is not allowed

to fall below a certain value If the time between two adjacent deliveries from such a transshipment facility is too long then the on-site storage capacities are exceeded and the on-site handling efficiency decreases Therefore, strict duration limits have to be considered and the execution of all required pickup and delivery tasks often becomes impossible

In general, assume that the utilization of own vehicles consumes a resource The consumption is given by Res(T(R+)) The amount Resmax is available This constraints the generation of a feasible request selection because several sets R+ require more than Resmax capacity units In this situation, the set

of feasible and implementable request selections is pruned by the bottleneck resource The resource constraint has t o be added t o the selection model (2.1)- (2.2)

(Rf , R - ) is a feasible request selection of R (2.5)

If the knapsack-type restriction (2.4) in model (2.3)-(2.5) is tight due to a low availability of the resource then it is no longer possible t o serve all prof- itable requests with own equipment Requests are sorted by increasing costs for one unit of the scare resource Those requests which cause the least costs per bottleneck resource unit (most efficient bottleneck usage) are composed into the routes of the own vehicles The remaining requests are assigned t o the available LSPs

Problems in which a t least one scarce resource requires a selection of re- quests are investigated by Pekny and Miller (1990), Laporte and Martello (1990), Gendreau et al (1998), Millar and Kiragu (1997), Feillet et al (2001), Gensch (1978), Cloonan (1966), Golden et al (1981) and Verweij and Aardal (2000) for problems with one own vehicle Erkut and Zhang (1996), Chao

et al (1996), Millar (1996), Butt and Ryan (1999), Butt and Cavalier (1994) and Schonberger and Kopfer (2003) investigate similar problems with more than one vehicle owned by the considered carrier company

In the two selection models introduced just above, it is possible to decide for each request whether it is fulfilled by a vehicle of the considered carrier

company or by equipment of an LSP However, these two frameworks do not cover several practical situations

Existing contracts prohibit the outsourcing of some requests to a n LSP The corresponding customers claim a request fulfilment with vehicles owned

by the carrier itself (Schmidt, 1989) Such a request is called compulsory request An LSP is not permitted to fulfill a compulsory request

The satisfaction of the compulsory condition requires the implementation

of another restriction t o the base model (2.1)-(2.2) This restriction ensures that only request selections are considered in which the set of compulsory requests is completely contained in the set R+ of carrier-served requests The model (2.6)-(2.8) describes the general selection problem with consideration

of compulsory requests The set Rcomp comprises all requests whose fulfilment

is allowed only for vehicles of the considered carrier company No request in this set can be assigned t o an LSP for completion

min C(T(R+)) + F ( B ( R - ) ) (2.6) s.th R+ > Rcomp (2.7) (R+, R-) is a feasible request selection of R (2.8)

If it is not allowed for any request to be fulfilled by an LSP, which means that the set Rcomp is equal to R then the problem is reduced t o a pure routing problem

The on-site storage capacity of a transshipment facility is typically constrained (Grunert and Sebastian, 2000) In order to prevent exceeding this capacity,

it sometimes becomes necessary t o desist from carrying the packets of all available requests t o the terminal If possible, requests should be postponed

in order t o release facility capacity to the most urgent customer demands Long lasting contracts or customer satisfaction issues often forbid the ac- ceptance refusal of unprofitable requests for which no adequate LSP can be found because the claimed charge is too expensive In these cases it is often a remedy to postpone those requests into the future, expecting that currently unprofitable requests will be able t o be combined with other so far unknown but expected requests so that the expected sum of revenues will lead to posi- tive profit contributions

Rolling planning horizon approaches determine transportation plans for the next T planning periods P I , , PT Only the transportation plan for the period PI is mandatory Transportation plans for subsequent periods can be modified until the relevant period is reached After one planning period has been passed, a mandatory transportation plan is determined for the immediate next period Modifications of the planning data are considered as known so far

28 2 Operational Freight Transport Planning

However, it is not necessary in pickup and delivery planning problems

to determine a sequence of transportation plans for the periods P I , , PT including all so far known demands Requests are only scheduled if their ful- filment leads to positive profit contributions It is allowed for the fulfilment time to be assigned to a later planning period so that the corresponding pickup and delivery time windows are met In such a case, the determined fulfilment time can be updated in later planning runs

If the start of a request fulfilment cannot be postponed into periods later than PI (urgent request) then this request is scheduled in the recent trans- portation plan regardless of whether their fulfilment leads t o positive profit contributions or not The execution mode is determined for all urgent requests The remaining requests are left temporarily unconsidered If their fulfil- ment becomes necessary in future planning periods, they are combined with other so far unreleased and unknown requests or they are assigned to a n LSP

It is expected, that the changes of the request portfolio during the sequence

of planning periods allow the realization of additional positive contributions

to the profit in later periods

Such a myopic planning approach is adequate only in the case where the problem data for the periods Pz, , PT are highly unsure In this case, the saving of the profits gain-able from the current request portfolio is preferable Request selection with postponement means to solve a static profit con- tribution maximization problem before PI is opened In contrast t o the so far considered situations, one of three different modes can be selected for each re- quest: the completion with carrier equipment, the completion by a n LSP and the postponement To take this trinity into account, a third mode is offered in the mode selection for each request Each postponed request is inserted into the set RPP A pd-request can only be postponed if the customer specified time windows allow a delay of execution, e.g if both the pickup and the deliv- ery task can be executed after P I The execution of a n urgent request cannot

be delayed, because either the pickup or the delivery task or both of them have to be completed in P I

Let Rurgent denote the set of all urgent requests To ensure that all urgent requests are routed in time, the urgent requests have to be routed or assigned

to a n LSP preferentially The objective function (2.9) guarantees the consid- eration of the most profitable remaining requests Constraint (2.10) ensures that all urgent requests are included in the generated transportation plan The profit contribution is targeted directly since the sum of revenues varies with respect to the requests selected for fulfilment next Revenues for postponed requests remain unconsidered

max R ( R + U R-) - C ( T ( R + ) ) - F(B(R-)) (2.9) s.th R+ U R- > RUrgent (2.10) ( R + , R- , R p p ) is a feasible request partition of R (2.11)

Golden et al (1984) investigates a problem of oil replenishment Within this distribution problem, a fleet of gas tankers is available t o delivery fuel

to consumers Following a push-strategy, customers whose oil reserve is near empty should be visited within the next period Since the period duration does not allow for visiting each customer, the most urgent customer deliveries have

to be selected for fulfilment within the next period Requests with the highest urgency are served immediately in the next period whereas customers with larger reserves are served only if time is still available within the considered period

The determination of a transportation plan requires the solving of several well- defined, but interdependent decision problems These problems comprise the mode selection for each request: does a carrier-owned and controlled vehicle serve a certain request or is a n LSP ordered? Furthermore, the composition of maximum profit routes for the own vehicles is targeted Finally, a n adequate assignment of externally fulfilled partial requests t o several LSP in order to minimize the costs for the LSP incorporation is determined

To realize the maximum success it is necessary to consider all three prob- lems simultaneously The resulting decision problems are combined selection (of modes), assignment (of requests to vehicles or LSPs) and sequencing (op- erations) problems Several additional customer or managerial requirements and recommendations compromise the generation of optimal transportation plans Four generic base models have been proposed t o model the simultaneous decision problems

The incorporation of the mode selection decision into the operational transport planning of a carrier company has received only minor scientific interest so far However, it is of high practical relevance because carrier com- panies often need to incorporate LSPs if the usage of their own equipment is unprofitable or if additional transport capacity is required immediately

Pickup and Delivery Selection Problems

This chapter is about mathematical optimization models for the generation

of transportation plans It is aimed at allocating resources for the fulfilment

of the transport demands in a particular and restricted region Decisions con- cerning the mode selection for the available requests, routing of the controlled vehicles and freight charge optimization for LSP-served requests are simulta- neously considered in these models

A literature review about problems and models associated with the allo- cation of transport resources of freight carrier companies reveals that these kinds of transport planning problems have received only minor attention so far The main results from this review are reported in Sect 3.1

The General Pickup and Delivery Selection Problem is introduced in Sect 3.2 It represents the problem of determining a transportation plan from a given portfolio of transportation requests between pairs of pickup and delivery locations A mathematical model is proposed

Four special variants of the General Pickup and Delivery Selection Problem are described in Sect 3.4 An explicit problem is described for each of the four generic simultaneous problems introduced in Sect 2.3 A profit maximization problem (Subsect 3.4.1), a bottleneck selection problem (Subsect 3.4.2), a problem with compulsory requests (Subsect 3.4.3) and a problem with post- ponement (Subsect 3.4.4) are presented All variants can be described by a modification of the mathematical model proposed for the General Pickup and Delivery Selection Problem These models represent combinatorial optimiza- tion problems with several intricating constraints

The generation of artificial test instances for each of the proposed problems

is described in Sect 3.5

3.1 Problems with Pickup and Delivery Requests

A pickup and delivery request (pd-request) r expresses a n indivisible transport demand between a n origin location (pickup location) p$ and a destination

location (delivery location) p; Goods of the quantity q, have to be moved Loading the goods a t the pickup location is often allowed only during the pickup time window T,?, determined as the interval between an earliest and

a latest allowed operations time The unloading a t the destination location is allowed only during the delivery time window T,-

It is distinguished between three types of a pd-request r within a region If

r is a collection request then p- coincides with a transshipment facility in the considered region that receives the quantity q, In the case of a distribution request the location p+ coincides with a transshipment facility that releases

q, A direct delivery request describes the transport demand between two customer locations p+ and p-, the quantity q, is not transshipped during request fulfilment

Figure 3.1 illustrates the different pd-request types in a region The request from p: to p l is a distribution request because p; coincides with the depot (transshipment facility) of the region The second request from p; to p; is

a collection request, since the delivery location p z coincides with the depot The third request from p$ to pq is a direct delivery request The carriage

of the corresponding goods to the depot is not necessary and typically not allowed

outbound flclw

collection request

P3 direct delivery request

Fig 3.1 Types of pd-requests in a region