A Greedy Construction Heuristic for the Liner Shipping ... · The Liner shipping network design problem Given a complete graph G0between a set of ports P, a ﬂeet divided into vessel

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A Greedy Construction Heuristic for the Liner Shipping Network Design Problem

Brouer, Berit Dangaard

Publication date:2010

Document VersionEarly version, also known as pre-print

Link back to DTU Orbit

Citation (APA):Løfstedt, B. (2010). A Greedy Construction Heuristic for the Liner Shipping Network Design Problem[Sound/Visual production (digital)]. Optimization Days 2010, Montréal, Canada, 10/05/2010

http://orbit.dtu.dk/en/publications/a-greedy-construction-heuristic-for-the-liner-shipping-network-design-problem(c3fc10b9-59f3-4aac-851b-f3e440c1b626).html

A greedy construction heuristic for the LinerService Network Design Problem

Berit Løfstedt

Operations ResearchDepartment of Management Engineering

Technical University of Denmark

May 5, 2010

Outline(jg

1 The Liner Service Network Design Problem (LS-NDP)2 Methods based on integer and linear programming relaxations3 LS-NDP as a multilayered Multiple Quadratic Knapsack Problem4 The greedy construction heuristic5 Critique of model and method6 Future work

Berit Løfstedt (DTU Management) LS-NDP May 5, 2010 2/22

Outline(jg



Outline(jg



Outline(jg



Outline(jg



Outline(jg



Outline(jg



Problem definition(jg

The Liner shipping network design problemGiven a complete graph G′ between a set of ports P, a fleet dividedinto vessel classes A and a set of commodities K determine aminimum cost network G = (V ,E) consisting of disjoint non-simplecyclic vessel routes to transport the most profitable subset of thecommodities.


Characteristics of a service(jg

Figure: Example of a single service

CyclicNon-simpleInbound vs. outbound direction


Characteristics of a network(jg

Figure: Network design

Transhipment of cargo at transhipment hubs and main portsCapacity classes: feeder, panamax, super panamaxFixed schedule -mainly based on weekly port visits


Selection of previous work(jg

Figure: Transhipment of cargo

Focus:Multiple routings (i.e.network design)Multiple hubs

Relevant literature:#models = #articlesMain difference:transhipment


Previous work(jg

Article Method Optimal Transhipment vessels/ports[1] Lagrange, Benders No No 3v, 20p[2] Branch-&-Cut Yes Yes, handling cost per container 6v, 20p[3] greedy, column generation, Benders No Yes, no cost 50v, 10p[4] tabu search, LP solver No Yes, individual cost per container 100v, 120p

Table: Overview of main articles with multiple route construction

[1]: Rana & Vickson 1991[2]: Reinhardt & Kallehauge 2007[3]: Agarwal & Ergun 2008[4]: Alvarez 2009


Going global....(jg

Challenges

Scaling to a global liner shipping network200+ ports, 200+ vessels

Scalability Issues:

Symmetry:Cyclic RoutingVessel Specs

Large scalemulticommodity flow

problem


Motivation(jg

Good solutions to the liner shipping network design problem

Competitive networkLow cost networkInclusion of dynamic non-linear bunker cost calculationNo optimality guarantee

Sheet1

Page 1

14 16 18 20 22 24 26 28

0

100

200

300

400

500

600

Bunker curve

non linear function

Mton/day

Knots

MTons

/day

Figure: Fictious example of non linear bunker curve


Work in progress...(jg

Create a good model including bunker costBuild a local search framework (ALNS)

Combining sets of:

1 Construction Heuristics2 Destruction Heuristics

Topic of this talk:First building block:

1 Greedy construction heuristic2 Based on a simplified LS-NDP model with simplified cost structures



Create a good model including bunker costBuild a local search framework (ALNS)Combining sets of:








Topic of this talk:

First building block:







1 Greedy construction heuristic

2 Based on a simplified LS-NDP model with simplified cost structures






1 Greedy construction heuristic

2 Based on a simplified LS-NDP model with simplified cost structures








Model simplifications(jg

Rephrase the problem:

1 A set of routes2 Place port calls on

routes

Avoid evaluatinga large scale

multicommodity flowproblem

Multiple QuadraticKnapsack Problem

(MQKP)Routes=Knapsacks

Port calls=items

Profit function, f :f (distance,

demand ,

transhipment)




1 A set of routes

2 Place port calls onroutes





Port calls=items


demand ,

transhipment)





routes





Port calls=items


demand ,

transhipment)





routes





Port calls=items


demand ,

transhipment)





routes





Port calls=items


demand ,

transhipment)





routes





Port calls=items


demand ,

transhipment)


Layer characteristics(jg

Layer Port types Distances Direct Transportto Hub

Weeks

FeederSpokes Short secondary primary 1-3

Main portsHubs

Panamax Main ports Medium primary secondary 3-8Hubs

Super Main ports Long secondary primary 6-12panamax Hubs

Table: Layer classification




Weeks


Main portsHubs







Weeks


Main portsHubs







Weeks


Main portsHubs





Multilayered algorithm(jg

Figure: Multi layered knapsack interpretation of the LS-NDP

Three layers: feeder, panamax and super panamaxPort items: Scheduled port visitsEach layer may have multiple visits to a port


Solve an MQKP for each layer(jg

i 0 1 20 0 287 3061 -25 42 7422 14 513 0

Table: Profit matrix

Vlayer :items (scheduled port calls with the capacity class of thislayer)Rlayer : knapsacks (Services)Services are assigned a standard number of vesselsNumber of vessels = Duration in weeks


Specialised MQKP - Mathematical model(jg

maximize(MQKP) = ∑r∈R

∑i∈V

∑j∈V

pij xri x r

j + ∑r∈R

∑j∈V

pj xrj

subject to: ∑r∈R

x ri = 1 ∀i ∈ V (Mutually exclusive)

x ri x r

j ≥ y rij ∀i ∈ V , j ∈ V , r ∈R (Activate edge variable)

∑j∈V

y rij − ∑

j∈Vy r

ji = 0 ∀i ∈ V , r ∈R (Cyclic)

∑j∈V

y rij ≤ 1 ∀i ∈ V , r ∈R (Simple)

uri −ur

j +y rij ∑

i∈Vx r

i ≤ ∑i∈V

x ri −1 ∀i ∈ V , j ∈ V , r ∈R (Connected)

∑i∈V

∑j∈V

y rij (tij + ti )≤ σ(Ca) ∀r ∈Ra ,a ∈A (Duration)

x ri ∈ {0,1} ∀i ∈ V , r ∈R

y rij ∈ {0,1} ∀i ∈ V , j ∈ V , r ∈R

uri ∈Z + ∀i ∈ V , r ∈R

Quadratic objective function - heuristic solution method


Greedy parallel insertion(jg

The football teaming principleThe knapsacks take turn at choosing the most profitable item amongthe remaining items

Principle: parallel insertionMotivation: Distribution of difficult items


Algorithm(jg

GREEDYCONSTRUCTION (instance)

1 layers← FLEETTOLAYERS(instance)2 SCHEDULETOITEMS(instance, layers)3 profitIncrease← TRUE4 for each layer ∈ layers5 do MAKEKNAPSACKS()6 while (Vlayer 6= /0∪profitIncrease )7 do profitIncrease← FALSE8 for each r ∈ Rlayer9 best ← NULL

10 bestValue← 011 for each i ∈ Vlayer12 deltaValue← ∑j∈r pij13 if (deltaValue > bestValue)

then14 bestValue← deltaValue15 best ← i16 if (bestValue > 0)

then17 profitIncrease← TRUE18 UPDATEDEMANDMATRICES(knapsack , best )19 r ← best20 Vlayer ← Vlayer \best


Results(jg

Solve an instance of 234 ports and roughly 14000 demands in 33secondsEvaluated by Network specialists at Maersk Line

1 The routings are overall realistic2 Emphasis on direct transportation3 Transhipment fascilities are weak4 Good basis for a local search

Conclusion:Good construction heuristic as initial solution for further local search


Critique of the approach(jg

Not based on the true objective i.e. the MCF problemLittle interaction between layersOnly tested on a single instance of the Maerskline networkNo transhipment cost, bunker cost or vessel deployment costNote: Integration in ALNS will provide evaluation of true cost


Future work for MQKP heuristic(jg

Interaction between layersMore realistic goal function

1 Solve uncapacitated MCF2 Evaluate the transit times and the potential throughput

Test on real life data (Benchmark suite in progress)Compare results to the network cost of the initial schedule


Future work for ALNS framework(jg

Fast delta evaluation of multi commodity flow problemDestruction/ construction heuristicsBenchmark suite for Liner shipping


Bibliography(jg

[K. Rana and R.G. Vickson]“Routing container Ships Using Lagrangian Relaxation and Decomposition”Transportation Science 25, 201-214 (1991)

[L. B. Reinhardt and B. Kallehauge]“Network Design for Container Shipping Using Cutting Planes”Conference on Maritime & Intermodal Logistics, Singapore, December 2007

[R. Agarwal and O. Ergun]”Ship Scheduling and Network Design for Cargo routing in Liner Shipping”Transportation Science 42, 175-196 (2008).

[J.F. Alvarez]“ Joint Routing and Deployment of a Fleet of Container Vessels”Maritime Economics and Logistics 11, 186-208 (2009)

[S. Røpke and D. Pisinger],“A general heuristic for vehicle routing problems”,Computers and Operations Research 34, 2403-2435 (2007)

[I. Akio and K. Shintani and S.Papadimitriou]”Multi-port vs. Hub-and-Spoke port calls by containerships”Transportation Research Part E 42 , 740-757 (2009)

[D. Pisinger, S. Ropke]”Large Neighborhood Search”

Book Chapter, http://www.diku.dk/hjemmesider/ansatte/sropke/Papers/lns.pdf


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A Greedy Construction Heuristic for the Liner Shipping ... · The Liner shipping network design problem Given a complete graph G0between a set of ports P, a ﬂeet divided into vessel