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 Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Motivation Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Motivation ◮ 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Motivation ◮ 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Motivation ◮ 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Motivation ◮ 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Introduction to the 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Introduction to the 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Introduction to the 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 Motivation Capacitated Vehicle Routing with Delivery and Pick-up The offshore maintenance problem Summary Introduction to the 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 Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary The Capacitated Multi-Vehicle Routing Problem ◮ Applies to personnel transported to the tasks Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary The Capacitated Multi-Vehicle Routing Problem ◮ 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 Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary The Capacitated Multi-Vehicle Routing Problem ◮ 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 Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary The Capacitated Multi-Vehicle Routing Problem ◮ 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 Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Mathematical programming I Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Mathematical programming I The model ◮ V = { v 0 , v 1 , ..., v i , ..., v n } representing n locations with demand q i ◮ A = { a ij = ( v i , v j ) | v i , v j ∈ 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 Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Mathematical programming I The model ◮ V = { v 0 , v 1 , ..., v i , ..., v n } representing n locations with demand q i ◮ A = { a ij = ( v i , v j ) | v i , v j ∈ V ; i � = j } with cost matrix C ◮ m vessels of capacity Q available Variables ◮ x ij : x ij = 1 if arc a ij is used, x ij = 0 if it is not ◮ u i : The amount delivered so far on the route that includes vertex v i Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Mathematical programming I The model ◮ V = { v 0 , v 1 , ..., v i , ..., v n } representing n locations with demand q i ◮ A = { a ij = ( v i , v j ) | v i , v j ∈ V ; i � = j } with cost matrix C ◮ m vessels of capacity Q available Variables ◮ x ij : x ij = 1 if arc a ij is used, x ij = 0 if it is not ◮ u i : The amount delivered so far on the route that includes vertex v i Objective ◮ min � � j ∈ V c ij x ij i ∈ V Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Mathematical programming II Constraints � x i 0 = m (1) i ∈ V � x 0 j = m (2) j ∈ V � x ij = 1; ∀ j ∈ V \ { 0 } (3) i ∈ V � x ij = 1; ∀ i ∈ V \ { 0 } (4) j ∈ V x ij ∈ { 0 , 1 } ; ∀ i , j ∈ V (5) u j ≤ Q + ( q j − Q ) x 0 j ; ∀ j ∈ V (6) u i − u j + Qx ij ≤ Q − q j ; ∀ i , j ∈ V (7) q i ≤ u i ≤ Q ; ∀ i ∈ V (8) Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
Introduction The Capacitated Multi-Vehicle Routing Problem Description Capacitated Vehicle Routing with Delivery and Pick-up The two approaches Summary Heuristic method Heuristics is used to find feasible, but not necessarily optimal solutions. The heuristic method written for CMVRP uses: Livia Stark, Toby Kingsman (Supervisor) Executing Offshore Maintenance Activities
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