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, 2016 1
Outline • Introduction • Mathematical Models • Computational Results • Conclusions 2
What is carsharing? • Short-term car rentals • One-way or round-trip 3
Industry growth Worldwide membership tripled Worldwide fleet sizes tripled over 4 over 4 years years 32,665 1400000 35000 1,251,504 1200000 30000 1000000 25000 19,403 800000 20000 670,762 600000 15000 11,501 346,610 400000 10000 200000 5000 0 0 2006 2008 2010 2006 2008 2010 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
Carsharing providers Private companies Nonprofit Government Entity Zipcar City CarShare Seattle Vehicles removed 15 privately owned 17,000 1,200 – 1,600 (foregone buying vehicles for every or sold) Zipcar Reduced vehicle 90% of members 140 million miles N/A miles drive 5,500 less miles 5
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
Outline • Introduction • Mathematical Models • Computational Results • Conclusions 7
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
Building the spatial-temporal network • Example: • Zones 1, 2 • Time periods 0, 1, 2, 3 • n it : Zone i at time t 9
Round-trip arcs • Example: Type Volume Origin Destination Start End • Zones 1, 2 • Time periods 0, 1, 2, 3 One-way 3 2 1 0 3 • n it : Zone i at time t Round-trip 2 2 2 3 10
One-way arcs • Example: Type Volume Origin Destination Start End • Zones 1, 2 • Time periods 0, 1, 2, 3 One-way 3 2 1 0 3 • n it : Zone i at time t Round-trip 2 2 2 3 11
Idle arcs • Example: Type Volume Origin Destination Start End • Zones 1, 2 • Time periods 0, 1, 2, 3 One-way 3 2 1 0 3 • n it : Zone i at time t Round-trip 2 2 2 3 12
Relocation arcs • Example: Type Volume Origin Destination Start End • Zones 1, 2 • Time periods 0, 1, 2, 3 One-way 3 2 1 0 3 • n it : Zone i at time t Round-trip 2 2 2 3 13
Final spatial-temporal network • Example: Type Volume Origin Destination Start End • Zones 1, 2 • Time periods 0, 1, 2, 3 One-way 3 2 1 0 3 • n it : Zone i at time t Round-trip 2 2 2 3 14
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
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
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
Network arc parameters 18
Network arc parameters 19
Network arc parameters 20
Network arc parameters 21
Model 1 Maximize total revenue Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 22
Model 1 Flow balance constraint Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 23
Model 1 Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ Budget limit σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 24
Model 1 Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ Carbon emissions limit σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 25
Model 1 Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ Capacity constraint 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 26
Model 1 Max σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑙 𝑏𝑘 𝑧 𝑏𝑘 𝑦 𝑗𝑘 if 𝑢 = 0 s.t. σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 − σ 𝑏𝜗𝜀 − (𝑜 𝑗𝑢 ) 𝑧 𝑏𝑘 = ቊ ∀ 𝑜 𝑗𝑢 𝜗 N, 𝑘 𝜗 𝐾 0 if 𝑢 𝜗 {1, … , 𝑈 − 1} σ 𝑏𝜗𝐵 σ 𝑘𝜗𝐾 𝑓 𝑏𝑘 𝑧 𝑏𝑘 ≤ ℋ σ 𝑗𝜗𝐽 σ 𝑘𝜗𝐾 𝑛 𝑘 𝑦 𝑗𝑘 ≤ ℱ 𝑧 𝑏𝑘 ≤ 𝑣 𝑏𝑘 ∀ a 𝜗 A, j 𝜗 J Integer restriction 𝑦 𝑗𝑘 𝜗 ℤ + , 𝑧 𝑏𝑘 𝜗 ℤ + ∀ a 𝜗 A, j 𝜗 J 27
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
Extension to Model 1 (Model 2) Add the following constraints to M1: 𝑘 𝑛𝑏𝑦 𝑨 𝑗𝑢 𝑧 (𝑜 𝑗𝑢 ,𝑜 𝑗,𝑢+1 ),𝑘 ≤ 𝑤 𝑘 ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 𝑘 ) 𝑛𝑏𝑦 (1 − 𝑨 𝑗𝑢 σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 )∪(𝐵 𝑃 ∩𝐵 𝑉 ) (𝑣 𝑏𝑘 − 𝑧 𝑏𝑘 ) ≤ 𝑤 𝑘 ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 𝑘 𝑨 𝑗𝑢 𝜗 { 0, 1 } ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 29
Extension to Model 1 (Model 2) Add the following constraints to M1: 𝑘 𝑛𝑏𝑦 𝑨 𝑗𝑢 𝑧 (𝑜 𝑗𝑢 ,𝑜 𝑗,𝑢+1 ),𝑘 ≤ 𝑤 𝑘 ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 𝑘 ) 𝑛𝑏𝑦 (1 − 𝑨 𝑗𝑢 σ 𝑏𝜗𝜀 + (𝑜 𝑗𝑢 )∪(𝐵 𝑃 ∩𝐵 𝑉 ) (𝑣 𝑏𝑘 − 𝑧 𝑏𝑘 ) ≤ 𝑤 𝑘 ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 𝑘 𝑨 𝑗𝑢 𝜗 { 0, 1 } ∀ i 𝜗 I, t = 0, 1, …, T – 1, j 𝜗 J 𝑘 is 1, then idle cars can flow from that node. If 𝑨 𝑗𝑢 Else, no idle cars can flow from that node. 30
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