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Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Executing Offshore Maintenance Activities Livia Stark, Toby Kingsman (Supervisor) September 1, 2017 Livia Stark, Toby
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary
Livia Stark, Toby Kingsman (Supervisor) September 1, 2017
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
◮ The UK generates the most
electricity from offshore wind in the world, 5.1GW per annum, 5% of demand
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
◮ The UK generates the most
electricity from offshore wind in the world, 5.1GW per annum, 5% of demand
◮ Fast growing, expected to rise
to 10% of demand by 2020
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
◮ The UK generates the most
electricity from offshore wind in the world, 5.1GW per annum, 5% of demand
◮ Fast growing, expected to rise
to 10% of demand by 2020
◮ Heavily subsidised
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
◮ The UK generates the most
electricity from offshore wind in the world, 5.1GW per annum, 5% of demand
◮ Fast growing, expected to rise
to 10% of demand by 2020
◮ Heavily subsidised ◮ Carrying out maintenance
activities more efficiently reduces need for subsidy
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
Maintenance is carried out at the wind turbines daily. Each task requires time and resources.
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
Maintenance is carried out at the wind turbines daily. Each task requires time and resources.
◮ The turbines where the tasks are located need to be visited
twice
◮ Maintenance personnel transported to the task ◮ Maintenance personnel collected from finished tasks Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
Maintenance is carried out at the wind turbines daily. Each task requires time and resources.
◮ The turbines where the tasks are located need to be visited
twice
◮ Maintenance personnel transported to the task ◮ Maintenance personnel collected from finished tasks
Ultimately, the aim is to maximise the value of completed tasks whilst minimising the cost
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Motivation The offshore maintenance problem
Maintenance is carried out at the wind turbines daily. Each task requires time and resources.
◮ The turbines where the tasks are located need to be visited
twice
◮ Maintenance personnel transported to the task ◮ Maintenance personnel collected from finished tasks
Ultimately, the aim is to maximise the value of completed tasks whilst minimising the cost
◮ To simplify the problem, we have assumed transportation costs
would dominate and be proportional to the distance travelled
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
◮ Applies to personnel transported to the tasks
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
◮ Applies to personnel transported to the tasks ◮ Generalisation of travelling salesman problem
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
◮ Applies to personnel transported to the tasks ◮ Generalisation of travelling salesman problem
◮ Locations need to be visited and a given amount of product
delivered
◮ There are multiple salesmen, but each have a limited capacity Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
◮ Applies to personnel transported to the tasks ◮ Generalisation of travelling salesman problem
◮ Locations need to be visited and a given amount of product
delivered
◮ There are multiple salesmen, but each have a limited capacity
◮ Two approaches considered, mathematical programming and
heuristics
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
The model
◮ V = {v0, v1, ..., vi, ..., vn} representing n locations with
demand qi
◮ A = {aij = ( vi, vj) | vi, vj ∈ V ; i = j} with cost matrix C ◮ m vessels of capacity Q available
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
The model
◮ V = {v0, v1, ..., vi, ..., vn} representing n locations with
demand qi
◮ A = {aij = ( vi, vj) | vi, vj ∈ V ; i = j} with cost matrix C ◮ m vessels of capacity Q available
Variables
◮ xij: xij = 1 if arc aij is used, xij = 0 if it is not ◮ ui: The amount delivered so far on the route that includes
vertex vi
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
The model
◮ V = {v0, v1, ..., vi, ..., vn} representing n locations with
demand qi
◮ A = {aij = ( vi, vj) | vi, vj ∈ V ; i = j} with cost matrix C ◮ m vessels of capacity Q available
Variables
◮ xij: xij = 1 if arc aij is used, xij = 0 if it is not ◮ ui: The amount delivered so far on the route that includes
vertex vi
Objective
◮ min i∈V
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Constraints
xi0 = m (1)
x0j = m (2)
xij = 1; ∀j ∈ V \ {0} (3)
xij = 1; ∀i ∈ V \ {0} (4) xij ∈ {0, 1}; ∀i, j ∈ V (5) uj ≤ Q + ( qj − Q) x0j; ∀j ∈ V (6) ui − uj + Qxij ≤ Q − qj; ∀i, j ∈ V (7) qi ≤ ui ≤ Q; ∀i ∈ V (8)
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Heuristics is used to find feasible, but not necessarily
The heuristic method written for CMVRP uses:
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Heuristics is used to find feasible, but not necessarily
The heuristic method written for CMVRP uses:
◮ Parallel routing
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Heuristics is used to find feasible, but not necessarily
The heuristic method written for CMVRP uses:
◮ Parallel routing ◮ The algorithm shown on
the right to determine the next task carried out
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Mathematical model Heuristic method
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Mathematical model
◮ Slow for large number of
turbines, while additional constraints would slow it further
Heuristic method
◮ Fast even for large number
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Mathematical model
◮ Slow for large number of
turbines, while additional constraints would slow it further
◮ Gives the optimal solution
Heuristic method
◮ Fast even for large number
◮ Large variations in the
relative gap between optimal and heursitic solution
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Description The two approaches
Mathematical model
◮ Slow for large number of
turbines, while additional constraints would slow it further
◮ Gives the optimal solution
Heuristic method
◮ Fast even for large number
◮ Large variations in the
relative gap between optimal and heursitic solution
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
A step towards finding a solution to the offshore maintenance scheduling problem is to pick up the personnel from the locations
completed
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
A step towards finding a solution to the offshore maintenance scheduling problem is to pick up the personnel from the locations
completed
◮ Discretised time with
increments of 0.05 and limit
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
A step towards finding a solution to the offshore maintenance scheduling problem is to pick up the personnel from the locations
completed
◮ Discretised time with
increments of 0.05 and limit
◮ Transfer of personnel out of
and into the vessel, travel, and completion of tasks takes time
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
A step towards finding a solution to the offshore maintenance scheduling problem is to pick up the personnel from the locations
completed
◮ Discretised time with
increments of 0.05 and limit
◮ Transfer of personnel out of
and into the vessel, travel, and completion of tasks takes time
◮ Once a task is finished it is
added back to the list of locations that need to be visited
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
To be able to pick up all personnel, in some cases the vessels need to wait at the turbines
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
To be able to pick up all personnel, in some cases the vessels need to wait at the turbines
◮ Before the vessels return to port, checks are carried out to see
if all tasks have been carried out and the personnel picked up
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
To be able to pick up all personnel, in some cases the vessels need to wait at the turbines
◮ Before the vessels return to port, checks are carried out to see
if all tasks have been carried out and the personnel picked up
◮ If all personnel have been picked up, the vessel returns to the
port
◮ If not all personnel have been picked up, the vessel is
instructed to wait at its current location for an hour
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
Project selection
◮ When fewer tasks are to be carried out than available ◮ Most valuable tasks chosen
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
Project selection
◮ When fewer tasks are to be carried out than available ◮ Most valuable tasks chosen
Vessel selection
◮ Multiple vessels of different types available
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
Project selection
◮ When fewer tasks are to be carried out than available ◮ Most valuable tasks chosen
Vessel selection
◮ Multiple vessels of different types available ◮ A solution is calculated for all number and permutation of
available vessels
◮ The solution chosen completed the most value in the shortest
distance
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
Small vessel: P01 T14 T15 T09 T14 T04 T09
T04 T03 T15 T03 P01
Medium vessel: P01 T12 T11 T06 T01 T11 T01
T12 T06 P01
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
◮ 9 tasks distributed
between 15 turbines
Small vessel: P01 T14 T15 T09 T14 T04 T09
T04 T03 T15 T03 P01
Medium vessel: P01 T12 T11 T06 T01 T11 T01
T12 T06 P01
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
◮ 9 tasks distributed
between 15 turbines
◮ 2 vessels chosen out
Small vessel: P01 T14 T15 T09 T14 T04 T09
T04 T03 T15 T03 P01
Medium vessel: P01 T12 T11 T06 T01 T11 T01
T12 T06 P01
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
◮ 9 tasks distributed
between 15 turbines
◮ 2 vessels chosen out
◮ Total distance
travelled: 76.93 units
Small vessel: P01 T14 T15 T09 T14 T04 T09
T04 T03 T15 T03 P01
Medium vessel: P01 T12 T11 T06 T01 T11 T01
T12 T06 P01
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary Extending the method The result
◮ 9 tasks distributed
between 15 turbines
◮ 2 vessels chosen out
◮ Total distance
travelled: 76.93 units
◮ Relative gap: 11.5%
Small vessel: P01 T14 T15 T09 T14 T04 T09
T04 T03 T15 T03 P01
Medium vessel: P01 T12 T11 T06 T01 T11 T01
T12 T06 P01
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary
◮ Improved project selection ◮ Accounting for costs not proportional to the distance travelled ◮ Comparison with other heuristic approaches ◮ More detailed comparison of performance of mathematical
model and heuristic approach
References
Paolo Toth, Daniele Vigo. Discrete Applied Mathematics, Volume 123, Issue 1, 2002, Pages 487-512. Models, relaxations and exact approaches for the capacitated vehicle routing problem The Crown Estate https://www.thecrownestate.co.uk/energy-minerals- and-infrastructure/offshore-wind-energy/. Offshore Wind Energy
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Capacitated Vehicle Routing with Delivery and Pick-up Summary
Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities