This work proposes a method to improve the flexibility of short sea shipping and to increase its competitiveness with other means of freight transport. A logistic model and a mathematical model are developed to manage a fleet of two or more vessels which transport cargo to and from several ports, bearing in mind the cargo distribution and delivery deadlines. At each port, the model determines which port to visit next, which containers to embark, disembark and to shift, as well as how to stow them on board. In fact, this formulation brings together the fleet management problem, the container stowage problem (CSP) and the vehicle routing problem (VRP). An example scenario is set up, using generated but realistic data. The problem is then solved, in a simplified version, using a Genetic Algorithm. The results show that introducing the possibility of route changes, the overall efficiency (and thus competitiveness) of short sea shipping can be improved

Andrade-Campos, António

Lobo, Lobo

Martins, Paulo

Moura, Ana

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Genetic algorithms approach for containerships fleet management dependent on cargo and their deadlines

Lobo,

Repositório Institucional da Universidade de Aveiro

Genetic Algorithms approach for containership fleet management dependent on cargo and their deadlines Paulo Triunfante Martins Portuguese Naval Academy (Escola Naval)  Ana Moura University of Aveiro  António Andrade-Campos University of Aveiro  Victor Lobo  Portuguese Naval Academy (Escola Naval)   IAME 2010 – 07/06/2010 • Introduction • Short Sea Shipping analysis • State of the art of the Optimization problems • Problem Definition • Mathematical formulation • Genetic Algorithm approach • Examples and Results • Conclusions • Future development Table of contents Advantages  Environmentally sound;  Contribution to road safety;  Low infrastructures cost (motorway is the sea);  Reaches “peripheral” regions.  Disadvantages  Customs bureaucracy;  Port costs and efficiency;  Dependency of environmental factors  Travel duration;  Inflexibility of routes.  Short Sea Shipping • Container stowage problem (CSP)  Avriel et al.  – binary programming (1993) – suspensory heuristics (2000)  Wilson and Roach  – two phase method (1999)   – branch and bound application (2000)  Several authors  – different implementation methods  • Ship routing and Scheduling   Christiansen and Nygreen (1998)  Agarwal and Ergun (2008)    • Vehicle routing problem with time windows - supply chains  Gendrau et al. (2006)  Moura and Oliveira (2009)   State of the art - optimization Scenario definition:  Five ports A , B , C , D,  E  Distances between ports < 1000 nm  - 10 possible arcs  Fleet of Two containerships    i. dimensions ii. deadweight  iii. speed  iv. fuel consumption  v. stability characteristics  Several containers   i. origin ii. destination  iii. weight  iv. deadline  Costs at each port  Problem definition (1) A C B D E Harbour fee € Berthing € Facilities € Pilot € Duration € ETC … 9 days 5 days 8 days 12 days 7 days 10 days 6 days 8 days 1 2  Problem definition (2) A C B D E 1 hypotesis a hypotesis b  9 days 5 days 8 days 12 days 7 days 10 days 6 days 8 days  Containers characteristics and deadlines  Containership characteristics  Containership operation cost What route for each ship? What containers to carry? Stage 1  2  Problem definition (3)  Containers characteristics and deadlines  Containership characteristics  Containership operation cost  Containerships routes  Containers carried in each journey How to stow the containers Stage 2  Altered from Wilson and Roach (1999)  Problem definition (4) A C B D E Possible solution  Removed   6          Added   4 Restack   0  Overstows   0  Total cost  €    Removed   3          Added   0 Restack   2  Overstows   0  Total cost  €    Removed   6          Added   3 Restack   0  Overstows   0  Total cost  €    Removed   4          Added   3 Restack   0  Overstows   0  Total cost  €   Stowage plan 2.1 Stowage plan 1.1 1 2 Stowage plan 2.3 Stowage plan 1.3 1 2 1 2 Stowage plan 2.2 Stowage plan 1.2 1 2 Input variables   - Ports and Scenario characteristics   - Vessels characteristics      - Containers characteristics   - Associated costs (money and time)  Decision variables      - Route selection    - Container distribution and stowage    Mathematical formulation (1) A C B D - distances; - port fees; - time to move each container  1 - dimensions - fuel consumption; - speed; - slots arrangement;  - operation costs; - weight - origin; - destination; - dimensions; - delivery deadline; - for each vessel - at each journey - what’s the port of origin - what’s the port of destination very large binary matrices - for each container - what vessel carries it - where is it embarked - what journeys is it onboard - where is it stowed  Objective function : • minimize cost; • deliver all cargo within the time limits (accepted loss?)        Mathematical formulation (2) ∑ ∑ ∑∑= ≠∧= = =+pipijjvkiijkijkkij fxxcdW1 1 1 11max)(φφφφ∑∑∑= = =pivkikikW1 1 12maxφφφφ µβ∑ ∑ ∑∑∑= ≠∧= = = =+pipijjvkcikjkjkik rCdestrCorigW1 1 1 1 13max)(φφ ααφφαφφOperation costs outside harbour Containers load/ unload costs at the ports of origin and destination Containers shift costs AM5AM6Diapositivo 10AM5 Para retirarAna Moura; 25-06-2010AM6 - Total cost minimization;Objective function composed of three componentesAna Moura; 25-06-2010Constraints: • route flow conservation - at each journey the vessel’s port of origin is the previous port of destination; • time sequence – the vessel service at each port does not begin before she arrives there; • containers’  deadline; • vessel’s capacity limit; • containers‘ exclusivity – only one ship can carry each container at the same time; • cargo attribution – the vessel that carries a container has to visit its port of destination (simplification);  • slots occupation – if a slot is occupied than the ones bellow are also occupied (cargo hatches not considered).     Mathematical formulation (3) AM2AM3AM4Diapositivo 11AM2 at each port, the time service does not begins untill the vessel arrivesAna Moura; 25-06-2010AM3 if a vessel arrives at a node then it has to leave from that node to another one.Ana Moura; 25-06-2010AM4 Each container is transported by one and only one vessel between ports.Ana Moura; 25-06-2010• Formulation of the problem into two different stages: a. Port sequence; b. Containers distribution by vessel; c. Container stowage problem.  • First stage chromosome construction:  [1 2 3 4 5   0 0 0 0   3 4 5 1 2   0 0 0 …. ]    • Matlab and University of Aveiro Operators used Genetic Algorithms Implementation Biological evolution 1st stage implemented 2nd stage not yet implemented Port Route for vessel 1 Route for vessel 2 Space to consider port repetition Implementation Results Example – scenario Ships Length (m) Beam (m) Draught (m) Speed (knots) N.º TEU Gross tonnage Fuel (t/h) 95 15.6 6.15 12.5 348 3814 0.378 132.2 20 7.7 16.5 641  8445 0.945 HEAVY AXE Scenario definition:  Five ports A , B , C , D,  E  Fleet of Two containerships    Several containers   Operation costs and port fees Example – Problem 1 MatLab Implementation:  Each square stands for 50 containers  No shift nor stowage constraints considered  Heavy departs from C and Axe departs from A  After 1 circular route – 100 not delivered  After 9 ports following a circular route – 300h, all delivered but 9 deadlines were surpassed   After 9 ports following a GA route – 271h, all delivered but 32 not in time, 5% cost reduction   Containers distribution: A – 200 B – 100 C – 200    D – 100 E – 100 Ship Route Travelled miles Time interval Deadlines surpassed Total cost  Circular routes Axe A – B – C – D – E  100 containers not delivered Heavy C – D – E – A – B  Axe A – B – C – D – E – A – B – C – D   3372 300 h 9 469500 Heavy C – D – E – A – B – C – D – E – A   3164 232 h GA Axe A – B – E – D – B – A – B – E – D   3083 271 h 32 446060 Heavy C – D – B – A – E – B – D – C  2693 209 h Example – Problem 2 MatLab Implementation:  Each square stands for 100 containers  No shift nor stowage constraints considered  Heavy departs from C and Axe departs from A  After 1 circular route – no solution was found  After 9 ports following a circular route – 100 containers not delivered   After 9 ports following a GA route – 315.5h, all delivered but 68 not in time Containers distribution: A – 400 B – 200 C – 400    D – 200 E – 200 Ship Route Travelled miles Time interval Deadlines surpassed Total cost  Circular routes Axe A – B – C – D – E  Not every container was embarked Heavy C – D – E – A – B  Axe A – B – C – D – E – A – B – C – D   100 containers not delivered Heavy C – D – E – A – B – C – D – E – A   GA Axe A – B – D – E – B – A – B – D – E  3134 315.5 h 68 634960 Heavy C – B – A – B – E – B – D – C  2653 236 h Example – Problem 3 University of Aveiro software:  No shift, deadlines, nor stowage constraints considered  Heavy departs from C and Axe departs from A;  Following a circular route it was found that 15 ports had to be visited by each ship  Two solutions better were found, with cost reductions of  7% and 14% 1313.213.413.613.81414.214.414.614.8150 1000 2000 3000GenerationsFitness function (x105)Conclusions • Conceptual and mathematical models have been built for the containership fleet management considering cargo deadlines, which included:  Route selection;  Cargo distribution per ship;  Container stowage problem solution. • A Genetic algorithm implementation for route selection and cargo distribution has been done; • Using a simple scenario of 2 containerships and 5 ports with distances between them smaller than  1000 nm, it was seen that:  There are routes better than circular pattern ones;  It is possible to manage a fleet considering the cargo deadlines and reducing time duration when necessary;  It is possible to turn the maritime transport more flexible with cost reductions.  Future development • Mathematical model improvement  • Implementation of the CSP in the GA model • Analysis of different methods efficiency to solve the model other than GA • Analysis of real scenarios with real data (collaboration required)  • Analysis of the impact of vessel characteristics in the results • Use the model to define owner requirements for new ship constructions based on known scenarios        

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Genetic algorithms approach for containerships fleet management dependent on cargo and their deadlines

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