Routing and Planning for the Last Mile Mobility System

Transcription

1 Routing and Planning for the Last Mile Mobility System Nguyen Viet Anh 30 October 2012 Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

2 Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

3 Introduction Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

4 Introduction The Last Mile Problem? From wikipedia: The Last mile refers to the final leg of the telecommunications networks delivering communications connectivity to retail customers; the part that actually reaches the customer The last mile is typically the speed bottleneck in communication networks; its bandwidth limits the bandwidth of data that can be delivered to the customer Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

5 Introduction Motivation The problem is similar in urban transportation The motivation from the Last (and First) Mile Problem: The hardest and most time consuming part of a passenger s trajectory is his last (and first) mile Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

6 Introduction Motivation The challenges of urban transportation Unscalable infrastructure Burden of aging societies Carbon footprint The importance of Transportation On Demand (TOD) Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

7 Introduction Motivation We consider a small scale Transportation On Demand system which connects passengers from a transportation hub to their desired destinations using a fleet of vehicles Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

8 Scenario Introduction 1 Passengers send requests 2 IT system analyzes and assign requests to vehicles 3 Reply service detail to passengers 4 Passengers proceed to take the service Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

9 Major challenges Introduction Practical constraints of implementation of a mobility system: 1 Profitability, Viability 2 Routing constraints: low computational time, good solution quality 3 Fluctuating demand along the day 4 Service quality, passengers comfort 5 Exceptions (bad weather, bus breakdown, traffic jams) Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

10 Introduction Objective of research Develop a routing platform which can assists the service provider in: 1 Strategic planning Profitability test Fleet size selection (capacities and number of buses) 2 Operational planning Daily routing 3 Contingency planning Handle exception (bad weather, bus breakdown, traffic jams) Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

11 Introduction Criteria when designing the algorithm These criteria are taken into account when we design our algorithm: 1 Stability: Performing well with limited number of vehicles 2 Robustness: Giving good results on a large number of test cases 3 Accuracy 4 Speed 5 Simplicity 6 Flexibility 7 Reproducibility Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

12 Routing Algorithm Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

13 Tabu search Routing Algorithm We use tabu search algorithm to find a sub-optimal solution to this problem Our objective is: 1 Maximize the number of customers served 2 Minimize the number of vehicles used 3 Minimize the total distance traveled by the fleet Several neighborhood moves are used to explore neighbor solutions: Insertion, Deletion Exchange, Flip Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

14 Routing Algorithm The heterogeneous fleet algorithm In order to handle the real life demand, the service provider may 1 Buy vehicles of different capacity (internal vehicles) 2 Sign contract with taxis, school bus fleet etc (external vehicles) The vehicles may have different fixed cost and variable cost We propose a modified tabu search routine which incorporates the different in fixed and variable cost of the vehicles Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

15 Result Routing Algorithm Pr Brandao (2011) LMP Total cost Time(s) Total cost Time(s) Avg Very good computational time with small deterioration in the quality of solution Note: Brandao s algorithm is probabilistic and the result reported is the best result found Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

16 The Fleet Sizing Problem Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

17 The Fleet Sizing Problem Clementi feeder services Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

18 The Fleet Sizing Problem The morning rush hour demand We consider the morning rush hour from 645am until 10am, which is decomposed into 40 periods of 5 minutes We solve the fleet sizing problem to determine different fleet setup for the service provider Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

19 The Fleet Sizing Problem Fleet sizing result Fleet 1 Fleet 2 Fleet 3 Fleet 4 Capacity No Veh Capacity No Veh Capacity No Veh Capacity No Veh Internal External External External Based on the number of vehicles required, the service provider may choose a good fleet composition to invest in Sign external fleet contract (school bus etc) Routing with heterogeneous fleet Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

20 The Fleet Sizing Problem Fleet sizing result Fleet planning for Fleet 4 Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

21 Contingency planning Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

22 Contingency planning Contingency planning Establish rules to handle exceptions 1 Bus breakdown Send new bus(es) to recover Alter existing routes 2 Traffic jams / Bad weather Modify distance matrix, update time Send new bus(es) if required Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

23 The Last Mile problem under uncertain travelling time Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

24 The Last Mile problem under uncertain travelling time LMP under uncertain travelling time Given uncertain travelling time, the service provider wants to maximize the probability of meeting the customer s time windows However, calculating the probability is computationally intensive We may not know the true probability distribution Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

25 The Last Mile problem under uncertain travelling time The satisficing measure Let T be the set of possible travelling time Definition Given a time target, τ R, the lateness index (LI), ρ τ : T [0, + ) is defined by ρ τ ( t) = sup{a > 0 : C a ( t) τ} where the function C a ( t) : T R is defined by ( ) 1 C a ( t) = sup P F a log E P[exp(a t)] = 1 log sup (E P [exp(a t)]) a P F This is also the satisficing measure proposed by Brown and Sim (2009) Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

26 The Last Mile problem under uncertain travelling time Properties of the lateness index C a ( t) is a non-decreasing function of a > 0 Thus we can use binary search to find ρ τ t Analytic expression of C a ( t) available when t follows: Normal distribution Uniform distribution Gamma distribution Distribution with bounded support and bounded mean support Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

27 The Last Mile problem under uncertain travelling time Tabu search with lateness index Definition For a routing plan of N customers, for each customers i, i = 1,, N, there is a time target τ i, the overall lateness index of the routing plan is defined as: ϱ = N ρ τi ( t i ) i=1 where t i denotes the travelling time to customer i The overall lateness index is used as an objective function for the vehicle routing problem Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

28 The Last Mile problem under uncertain travelling time Experimental result We compare 3 solutions: mean, 90th-percentile and the LI solution Normal distribution Gamma distribution Test case Mean 90th-percentile Lateness index Mean 90th-percentile Lateness index Table: Distance results by each algorithm Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

29 The Last Mile problem under uncertain travelling time Experimental result 1 Normal distribution travelling time, Test case Cumulative probability Mean solution 90 percentile solution Lateness Index solution Natural logarithm of violation probability Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

30 The Last Mile problem under uncertain travelling time Experimental result 1 Gamma distribution travelling time, Test case Cumulative probability Mean solution 90 percentile solution Lateness Index solution Natural logarithm of violation probability Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

31 The Last Mile problem under uncertain travelling time Experimental result The 90-percentile solution is better than the lateness index solution However, we cannot find the 90-percentile solution for cases such as The travelling time for each arc is a sum of different random variables (eg normal plus gamma) The travelling time is uncertain Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

32 Insights Outline 1 Introduction 2 Routing Algorithm 3 The Fleet Sizing Problem 4 Contingency planning 5 The Last Mile problem under uncertain travelling time 6 Insights Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

33 Insights Insights 1 Profitability is key, and flexible routing is required to support profitability goal External fleet (heterogeneous fleet), contingengy planning, first mile customers 2 Routing has to be reliable and consistent, Quality routing solution must be obtained within minutes 3 Balance profitability and service quality / passengers comfort 4 The lateness index approach is very promising to handle the last mile problem under uncertain travelling time Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33

34 Insights Thank you very much! Nguyen Viet Anh () Routing and Planningfor the Last Mile Mobility System 30 October / 33