INFORMS Annual Meeting Nashville November 13, 2016

Transcription

1 Carsharing Fleet Location Design with Mixed Vehicle Types for CO2 Emission Reduction Joy Chang Joint work with Siqian Shen (U of Michigan IOE) and Ming Xu (U of Michigan SNRE) INFORMS Annual Meeting Nashville November 13,

2 Outline Introduction Mathematical Models Computational Results Conclusions 2

3 What is carsharing? Short-term car rentals One-way or round-trip 3

4 Industry growth Worldwide membership tripled over 4 years Worldwide fleet sizes tripled over 4 years ,251, , , , , , South America Australia Asia Europe North America Worldwide South America Australia Asia Europe North America Worldwide Adapted from Carsharing and personal vehicle services: worldwide market developments and emerging trends, S.A. Saheen. 4

5 Carsharing providers Private companies Nonprofit Government Entity Zipcar City CarShare Seattle Vehicles removed (foregone buying or sold) Reduced vehicle miles 15 privately owned vehicles for every Zipcar 90% of members drive 5,500 less miles 17,000 1,200 1, million miles N/A 5

6 Carshare design and optimization Consider strategic decisions Car types to purchase to appeal to larger customer base? Carbon emissions limit? Evaluate the impact Case study (Zipcar Boston) Mathematical modeling Optimize profitability and quality of service via models that Incorporate round-trip and one-way demands Incorporate carbon emissions constraint Make strategic decisions about diverse portfolio of vehicle types 6

7 Outline Introduction Mathematical Models Computational Results Conclusions 7

8 Framing the problem Carsharing companies need a diverse vehicle portfolio How does demand for different vehicle types affect: Profitability Quality of service One-way and round-trip Denied trip Trip fulfillment Purchasing decisions Carbon emissions 8

9 Building the spatial-temporal network Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t 9

10 Round-trip arcs Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t Type Volume Origin Destination Start End One-way Round-trip

11 One-way arcs Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t Type Volume Origin Destination Start End One-way Round-trip

12 Idle arcs Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t Type Volume Origin Destination Start End One-way Round-trip

13 Relocation arcs Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t Type Volume Origin Destination Start End One-way Round-trip

14 Final spatial-temporal network Example: Zones 1, 2 Time periods 0, 1, 2, 3 n it : Zone i at time t Type Volume Origin Destination Start End One-way Round-trip

15 Defining Model 1 Inputs Car purchase cost and emissions generated Car rental price Arc capacity (demand) Objective Maximize total revenue of operating cars over set time 15

16 Defining Model 1 Decision variables Number and type of cars purchased at each zone Number of cars to route along each arc Constraints Number of cars entering each node equals number of cars leaving Carbon emission produced does not exceed limit Car purchase cost does not exceed limit 16

17 Assumptions A set of service zones and a finite number of service periods Serve one-way and round-trip rentals Cars can be relocated, to balance vehicle distributions Unsatisfied demand is immediately lost 17

18 Network arc parameters 18

19 Network arc parameters 19

20 Network arc parameters 20

21 Network arc parameters 21

22 Model 1 Max σ aεa σ jεj k aj y aj Maximize total revenue s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F y aj u aj a ε A, j ε J x ij ε Z +, y aj ε Z + a ε A, j ε J 22

23 Model 1 Max σ aεa σ jεj k aj y aj Flow balance constraint s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F y aj u aj a ε A, j ε J x ij ε Z +, y aj ε Z + a ε A, j ε J 23

24 Model 1 Max σ aεa σ jεj k aj y aj s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F Budget limit y aj u aj a ε A, j ε J x ij ε Z +, y aj ε Z + a ε A, j ε J 24

25 Model 1 Max σ aεa σ jεj k aj y aj s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F Carbon emissions limit y aj u aj a ε A, j ε J x ij ε Z +, y aj ε Z + a ε A, j ε J 25

26 Model 1 Max σ aεa σ jεj k aj y aj s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F y aj u aj a ε A, j ε J Capacity constraint x ij ε Z +, y aj ε Z + a ε A, j ε J 26

27 Model 1 Max σ aεa σ jεj k aj y aj s.t. σ aεδ + (n it ) y aj σ aεδ (n it ) y aj = ቊ x ij if t = 0 0 if t ε {1,, T 1} n it ε N, j ε J σ aεa σ jεj e aj y aj H σ iεi σ jεj m j x ij F y aj u aj a ε A, j ε J x ij ε Z +, y aj ε Z + a ε A, j ε J Integer restriction 27

28 Extension to Model 1 (Model 2) First-come first-serve (FCFS) principle: If there is a car available (idle) at that node when a customer comes in, you must serve the customer Model 2 (M2) enforces FCFS Denied trip percentage serves as metric New binary variable introduced at each node 28

29 Extension to Model 1 (Model 2) Add the following constraints to M1: y (nit,n i,t+1 ),j v j max z it j i ε I, t = 0, 1,, T 1, j ε J σ aεδ + (n it ) (A O A U ) (u aj y aj ) v j max (1 z it j ) i ε I, t = 0, 1,, T 1, j ε J z it j ε {0, 1} i ε I, t = 0, 1,, T 1, j ε J 29

30 Extension to Model 1 (Model 2) Add the following constraints to M1: y (nit,n i,t+1 ),j v j max z it j i ε I, t = 0, 1,, T 1, j ε J σ aεδ + (n it ) (A O A U ) (u aj y aj ) v j max (1 z it j ) i ε I, t = 0, 1,, T 1, j ε J z it j ε {0, 1} i ε I, t = 0, 1,, T 1, j ε J If z it j is 1, then idle cars can flow from that node. Else, no idle cars can flow from that node. 30

31 Extension to Model 1 (Model 2) Add the following constraints to M1: y (nit,n i,t+1 ),j v j max z it j i ε I, t = 0, 1,, T 1, j ε J σ aεδ + (n it ) (A O A U ) (u aj y aj ) v j max (1 z it j ) i ε I, t = 0, 1,, T 1, j ε J z it j ε {0, 1} i ε I, t = 0, 1,, T 1, j ε J If z it j is 1 (idle cars can flow from that node), then all capacity must be fulfilled. 31

32 Extension to Model 1 (Model 2) Add the following constraints to M1: y (nit,n i,t+1 ),j v j max z it j i ε I, t = 0, 1,, T 1, j ε J σ aεδ + (n it ) (A O A U ) (u aj y aj ) v j max (1 z it j ) i ε I, t = 0, 1,, T 1, j ε J z it j ε {0, 1} i ε I, t = 0, 1,, T 1, j ε J All capacity must be fulfilled to have idle cars flow from the node. 32

33 Outline Introduction Mathematical Models Computational Results Conclusions 33

34 Data description Zipcar operations for Greater Boston Timeframe from Oct. 1 to Nov. 30, 2014 # of reservations made each hour for 60 zip codes 34

35 Car type description 4 sedan types Gasoline powered, electric, hybrid, plug-in hybrid electric 35

36 Computational efficiency Tests run for M1 and M2 Vary one-way demand M1 significantly faster than M2 *Use Python + Gurobi 6.0.3, Intel(R) Core(TM) i5-4200u CPU with 6GM RAM 36

37 Carbon emissions constraint Vary carbon emission constraint between 3 x 10 6 and 6 x 10 6 grams Demand: 40% LX, 20% Hybrid, 20% PHEV, 20% EV Gasolinepowered 37

38 Carbon emissions constraint Vary carbon emission constraint between 3 x 10 6 and 6 x 10 6 grams Demand: 40% LX, 20% Hybrid, 20% PHEV, 20% EV Nongasoline powered 38

39 Quality of Service (QoS) Vary one-way proportion between 0%, 40%, 80%, 100% M1 enforces high QoS and FCFS principle Deny trip percentage between 0.1% and 1% 39

40 Quality of Service (QoS) Vary one-way proportion between 0%, 40%, 80%, 100% M1 enforces high QoS and FCFS principle Deny trip percentage between 0.1% and 1% 40

41 Quality of Service (QoS) Vary one-way proportion between 0%, 40%, 80%, 100% M1 enforces high QoS and FCFS principle Deny trip percentage between 0.1% and 1% 41

42 Trip fulfillment for 40% one-way setting Capacity 42

43 Trip fulfillment for 40% one-way setting Capacity Trips taken 43

44 Outline Introduction Mathematical Models Computational Results Conclusions 44

45 Conclusions Carsharing companies want to Expand market demographic Provide reliable service Benefit environment by lowering carbon emissions Our model Determines diverse vehicle portfolio Enforces high QoS and first-come first-serve principle Enforces carbon emissions constraints while still maximizing profit 45

46 The future: service-based transportation Ford s expanded business plan is to be both an auto and a mobility company General Motors invested $500 million in Lyft, a ridesharing service Future work: Developing more strategies to expand ridesharing services Integrating shared autonomous vehicles into daily life 46

47 Questions? 47