Lecture 8 Long-haul transport planning STUDENT€¦ · MTT045 Lecture 8: Long-Haul Transport...
Transcript of Lecture 8 Long-haul transport planning STUDENT€¦ · MTT045 Lecture 8: Long-Haul Transport...
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
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
Content
• Long-haul transport planning• The minimum cost flow problem• The minimum-cost flow problem• Time-expansion• Minimum cost spanning treep g
Lund University / Department of Industrial Management and Logistics
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
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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)
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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?
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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)
Lund University / Department of Industrial Management and Logistics
Example: Long-haul transport planning
NetworkTransport cost matrix
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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 41 6
2 3
4 5 1 N/A 0 2 N/A
5 N/A N/A 1 2 0 1
1 6
4 5
6 N/A N/A 4 N/A 1 0
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
Content
• Long-haul transport planning• The minimum cost flow problem• The minimum-cost flow problem• Time-expansion• Minimum cost spanning treep g
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
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
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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)
Lund University / Department of Industrial Management and Logistics
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)
Lund University / Department of Industrial Management and Logistics
Content
• Long-haul transport planning• The minimum cost flow problem• The minimum-cost flow problem• Time-expansion• Minimum cost spanning treep g
Lund University / Department of Industrial Management and Logistics
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?
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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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Lund University / Department of Industrial Management and Logistics
t = 1 2 3 4 5
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
Lund University / Department of Industrial Management and Logistics
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)
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
E l A i d d kExample: A time-expanded network
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Lund University / Department of Industrial Management and Logistics
t = 1 2 3 4 5
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
Lund University / Department of Industrial Management and Logistics
S h ld l hi i E l?So how could you solve this in Excel?
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Lund University / Department of Industrial Management and Logistics
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Content
• Long-haul transport planning• The minimum cost flow problem• The minimum-cost flow problem• Time-expansion• Minimum cost spanning treep g
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
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
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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.
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department of Industrial Management and Logistics
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
Lund University / Department 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
Lund University / Department of Industrial Management and Logistics
E l A i d d kExample: A time-expanded network
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Lund University / Department of Industrial Management and Logistics
t = 1 2 3 4 5