Vaccine Delivery in Developing Countries Aakashi Kapoor, Caroline Krejci, Trond Nilsen
“Last-Mile” Vaccine Distribution: Current System Provincial Center District Center 1 District Center 2 District Center 3 Health Center 1 Health Center 2 Health Center 3 Health Center 4 Health Center 5 Health Center 6 Health Center 7 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
“Last-Mile” Vaccine Distribution: Proposed System Provincial Center Health Center 1 Health Center 2 Health Center 3 Health Center 4 Health Center 5 Health Center 6 Health Center 7 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Costs of Proposed System Vehicle purchase price Determined by vehicle type Vehicle type defined by carrying capacity Operating costs: Vehicle maintenance & repair costs Fuel costs Salaries 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Problem Statement Fleet mix varies Cost Capacity Fleet size varies Single depot Vehicles must return home Some routes penalized Danger Difficulty 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Formulation - I Vehicle types ordered by ascending capacity That is, a0 < a1 < ... < aK Only one vehicle visits each node Variable cost in fuel, personnel, maintenance, and penalty costs 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Formulation - II 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Formulation - III 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Variations of VRP Routing with time windows Vaccine must be delivered within a time window, anything besides that incurs cost. Multiple Depots Another vector for nodes introduced to keep track of each depot Deliveries in some days Generalization of VRP with Vaccines delivered over period of M days instead of 1. Split Delivery Routing More than one vehicle serving the same customer. Routing with time windows Time window associated with each customer. A solution becomes infeasible or adds penalty if a vaccine is supplied after the upper bound of its time window and vehicle arriving before the lower limit of the time window causes additional waiting time on the route. Also each route must start and end within the time window associated with the depot. Cost would now include cost of route , service cost and waiting cost. Multiple Depots Different fleet of vehicles at each depot. Cost would be same but the constraints would not expand according to the number of depots. Deliveries over a period of time Vaccines can be only delivered on some M days – generalized version of VRP where the delivery period is 1 day Split Delivery Routing More than one vehicle serving the same customer. Very difficult to get the optimal. Other variations which are not applicable on our models are Pick up and delivery routing Stochastic Vehicle routing Backhauls Routing problems 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Solution Techniques Exact Approaches Branch and bound (only up to 100 nodes) Branch and cut – combination of cutting plane and branch and bound. Heuristic Approaches Savings heuristics – Clark and Wright – most used algorithm for VRP Meta heuristics Ant algorithms Simulated annealing Tabu search 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen
Aakashi Kapoor, Caroline Krejci, Trond Nilsen Questions? 2/24/2019 Aakashi Kapoor, Caroline Krejci, Trond Nilsen