Lecture 8 Long-haul transport planning STUDENT€¦ · MTT045 Lecture 8: Long-Haul Transport Planning Fredrik Eng Larsson Lund University / Department of Industrial Management and

MTT045 Lecture 8: Long-Haul Transport PlanningPlanning

Fredrik Eng Larsson

Lund University / Department of Industrial Management and Logistics

International Physical Distribution: The ’Red Thread’ of the Course

Vehicle routing

Shipment size & modal choice

Network design & planning

Operations

& modal choice & planning

Road Airconsignees

Performance objectives

Logistics service providersRail Sea

Modes Security/risk issuesSustainability challengesInternational trade issuesHumanitarian aid distribution

MarketsInfrastructure

Intermodality Terminalsconsignors


Learning objectives

• Understand the concept of planning long-haul transports• Understand what network flow modeling is and how it can be appliedUnderstand what network flow modeling is and how it can be applied• Understand the minimum cost flow problem• Learn how to plan flows in a transport network and how it can be

modeled/solvedmodeled/solved• Understand what time-expanded network flow modeling is and how it can

be applied• Understand the minimum cost spanning tree problem and how it can be

applied to transport network flow planning


Content

• Long-haul transport planning• The minimum cost flow problem• The minimum-cost flow problem• Time-expansion• Minimum cost spanning treep g


Th i bi diff i l h l d hThere is a big different in long-haul and short-haul transportation

Long-haul (truckload, TL)

Full truckloadsLonger deliveriesDirect deliveries or between terminals (hubs)

Short haul (less than truckload LTL)Short-haul (less-than-truckload, LTL)

Pallets/cartons/pieces/etc.Last-mile deliveriesBetween terminals (hubs) and producers/consumers


Th bl h l i f dThe problem concerns the planning of goodsmovement in distribution networks

• Underlying network (of terminals) exists

• All nodes must not be visited

• Vehicles are loaded and unloaded and dispatched at different frequenciesb t dbetween nodes

• Transport costs are per unit and link(must not be linear)

Lund University / Department of Industrial Management and Logistics 6

E l A id N i d HiPP b b f dExample: Arvid Norquist and HiPP baby food distribution The situation

• Arvid Nordquist HB is a large Swedish q gdistributor of food and wine

• Arvid Nordquist imports HiPP babyfoodfrom Pfaffenhofen in so thern Germanfrom Pfaffenhofen in southern Germanyfor further distribution

• When they reviewed their transport y pcontracts in 2007, they had several routing options through their network

How should they plan their long-haul transports?How should they plan their long-haul transports?


L h l l i h h f ll iLong-haul transport planning has the following properties

• Goal: Freight routing decision

• Focus: Total cost minimization– Purchase– Transportation– Inventory (pipeline, warehouse)

• Limitations:– Deterministic with finite horizon– All parameters (including demands) are assumed

known– Limited “look-ahead” for planning (e.g. 6 months, 2 months, 3 weeks)


Example: Long-haul transport planning

NetworkTransport cost matrix

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1 0 2 N/A 5 N/A N/A

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3 N/A 4 0 N/A 1 41 6

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4 5 1 N/A 0 2 N/A

5 N/A N/A 1 2 0 1

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Beehive

• Discuss what route to use in order to minimize the transport costs (1 = origin, 6 = destination)g , )

• Groups of 2• 5 minutes• Prepare to give an answer• Prepare to give an answer


Content



Minimum cost flow problem

• Determine a least cost shipment of a commodity through a network in order to satisfy demands at certain nodes form available supplies at other nodes

• Applications:

Application Supply nodes Transshipment nodes Demand nodes

Distribution network Sources of goods Intermediate storagefacilities

Customersfacilities

Solid waste management Sources of solid waste Processing facilties Landfill locations

Supply network Suppliers Intermediate warehouses Processing facilities

Cash flow management Sources of cash at a specific Short-term investment Needs for cash at a specificg ptime options

ptime


I h k fl d l hIn the network flow models we use the following notationNetwork flow notation

• G = (N,A)– N, set of n nodes– A, set of m arcs (directed links)

• Each node i in N is associated with:– bi, its supply or demand (bi > 0 supply node, bi < 0 demand node, and bi = 0

transshipment node)

• Each arc ij in A is associated with:– cij, transportation cost per unit flow

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– xij, arc flow variable (unit flow on each arc)– uij, upper bound on the flow

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Example: A network

• Nodes, N– 1,2,3,4,5,6

• Arcs, A• (1,2) (1,4) (2,3) (2,4) (3,5)

(3 6) (4 5) (5 6)• Demand/supply, b(i)– b(1) b(2) b(3) b(4) b(5) b(6)

(3,6) (4,5) (5,6)• Flow variables, xij

• x12 x14x24 x23 x45 x35x36 x56

U b d

2 3c23

• Upper bounds, uij

• u12 u14 u24 u23 u45 u35 u36u56

1 6

2 3c12

c24 c35

c36

4 5c14

c45

c56


Formulation: Minimum cost flow problem

• Objective: Minimize shipment costs for flows• Constraint1: Mass balance constraints (what goes in comes out)• Constraint2: Flow bound constraints (upper bound)


pp

E l Th A id N d i bl i hExample: The Arvid Nordquist problem with capacity constraints

2 32 (70)

4 (100)

4 (60)

1 6

2 (70)

1 (100) 1 (80)

4 (60)

4 580 pallets -80 pallets

5 (80)

2 (50)

1 (100)


Content



Wh i i i h k dWhen time is important the network may need time-expansionTime-expansion

• Oftentimes, transit times is a crucial d i i i bldecision variable

• Applications:R il i h l i– Railways with slot-times

– Logistics networks with lean control– Manufacturing lines

• How do we include a time-dimension?


E l A i d d kExample: A time-expanded network

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E l A i d d k (2)Example: A time-expanded network (2)

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What is a time-expanded network?Time-expanded network flow notation

• G = (V,E)V set of n timed copied nodes in N– V, set of n timed copied nodes in N

– E, set of m arcs of both holding and transportation• T, set of time periods

• Each node i in V is associated with:– bt

i, its supply or demand at time t (bti > 0 supply node, bt

i < 0 demand node, and bt 0 transshipment node)and bt

i = 0 transshipment node)

• Each arc ij in E is associated with:ct transportation cost per unit flow– ct

ij, transportation cost per unit flow– xt

ij, arc flow variable (unit flow on each arc)– ut

ij, upper bound on the flow


F l i Ti d d i iFormulation: Time-expanded minimum cost flow problem

• Objective: Minimize shipment costs for flows• Constraint1: Mass balance constraints (what goes in comes out)• Constraint2: Flow bound constraints (upper bound)


Example: Time-expanded freight routing decision

• Supply occur in t=1 at node 1 of 1 unit Transport cost matrix (for all t)

• Demand occur in t=5 at node 6 of 1unit 1 2 3 4 5 6

1 0 2 N/A 5 N/A N/A

2 2 0 4 1 N/A N/A

3 N/A 4 0 N/A 1 4

4 5 1 N/A 0 2 N/A

5 N/A N/A 1 2 0 1

6 N/A N/A 4 N/A 1 0



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Beehive

• Discuss what route we should use in order to minimize the transport costs– From node 1 t=1From node 1, t 1…– …to node 6, t=6

• Groups of 25 i• 5 minutes

• Prepare to give an answer


S h ld l hi i E l?So how could you solve this in Excel?

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Content



Minimum cost spanning tree problem

• The objective is to define the network in a way that minimizes the total length of links inserted into a networkg

• Starting with only the nodes for a network, the problem now is to design the network by deciding which links it should havethe network by deciding which links it should have

• Potential applications:– Road and rail infrastructure– Telecommunications networks– Electrical networks– Pipelines


For the problem we use a similar denotationThe minimum cost spanning tree problem

• G (N A)• G = (N,A)– N, set of n nodes– A, set of m arcs

• Each node j in N is needs to be connected to the network

• Each arc ij in A is associated with:– cij, traversing cost


W l h bl i l i h hWe solve the problem using an algorithm that provides the optimal solution

1. Choice of the first link: Select the cheapest potential link.

2. Choice of the next link: Select the cheapest potential link between a node that already is touched by a link and a node that does not yet have such a link.

3. Repeat step 2 over and over until every node is touched by a link (perhaps more than one). At that point, an optimal solution (a minimum spanning tree) has been obtained.


Example: TSPCo

• TSPCo has seven hubs in different cities that needs to be connected. TSPCo wants to have line transports between the hubs, and cross-docking facilities in each hub handling transshipments to other hubs How should they design the network?

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transshipments to other hubs. How should they design the network?

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5 3Total cost: 1+2+3+3+3+4=16


Learning objectives revisited

• Understand the concept of planning long-haul transports• Understand what network flow modeling is and how it can be appliedUnderstand what network flow modeling is and how it can be applied• Understand the minimum cost flow problem• Learn how to plan flows in a transport network and how it can be

modeled/solvedmodeled/solved• Understand what time-expanded network flow modeling is and how it can

be applied• Understand the minimum cost spanning tree problem and how it can be

applied to transport network flow planning


Thank you for today!

Box 118, SE-221 00 LUND, SwedenVisiting address Ole Römers väg 1, Lund

Phone +46 46 222 81 72Fax +4 46 222 46 15

E-mail [email protected]

Fredrik Eng LarssonPhD Candidate

Department of Industrial Management and LogisticsDepartment of Industrial Management and Logistics


Example: Long-haul transport planning

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Solution:c + c + c + c 2 + 1 + 2 + 1 6

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c12 + c24 + c45 + c56 = 2 + 1 + 2 + 1 = 6



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Documents

Lecture 8 Long-haul transport planning STUDENT€¦ · MTT045 Lecture 8: Long-Haul Transport Planning Fredrik Eng Larsson Lund University / Department of Industrial Management and