Supply-demand imbalance in shared mobility: cost and consequence

Aug 21, 2020 · 8 min read

by Evan Fields, head of data science at Zoba. Evan holds a PhD in Operations Research from MIT, believes aggressively in cities, bakes enthusiastically, and can be found on Twitter at @evanjfields.

by Joseph Brennan, cofounder of Zoba. Originally from a small town, Joseph has fallen in love with more than a few cities on two wheels — Bangkok on a motorbike, Beijing on an electric moped, and Boston on a Bluebike. Joseph is a graduate of Harvard College and Peking University.

Zoba provides demand forecasting and optimization tools to shared mobility companies, from micromobility to car shares and beyond.

Mobility systems that may look similar on the surface differ in their fundamental physics. Operators of two-sided marketplaces such as Uber and Doordash have levers for inducing supply changes: surge pricing, recommending driver pre-positioning, etc. Fixed asset systems — such as car shares and micromobility — are different.¹ In these systems, vehicles are placed onto the street for users to ride; in the short term, operators have little control over supply position and even less over total supply levels. Operators have a set number of vehicles to deploy regardless of prevailing demand and changes in supply distribution are driven primarily by users. Every time a user makes a choice about when and where to start or end a ride, the spatial distribution of available vehicles changes.

Importantly, in a well-functioning and profitable fixed asset system, the volume of ‘user deployments,’ or vehicle locations resulting from user preference, dwarfs direct operator interventions. For example, imagine a scooter share system with 1,000 vehicles that receive 3 rides per vehicle per day. If the operator deploys or rebalances 30% of the fleet daily, the users decide the vehicles’ positions 10 times more frequently than the operator (3,000 trip ends vs. 300 deployments). The disparity between trip ends and operator deployments is often even starker for swappable battery vehicles or vehicles that the users are responsible for fueling/charging. Such a vehicle might see dozens of rides between rebalances or trips to a warehouse for maintenance.

This is a feature — not a bug! An operator deployment is ideal exactly if the deployed vehicle quickly captures lots of rides as users move it from high-demand area to high-demand area. An operator should hope their system is so active — and vehicles so frequently left in subsequently high demand areas — that the spatial distribution of vehicles is overwhelmingly determined by users.

On the flip side, this means a fixed asset operator needs to actively account for the supply patterns users will induce. Supply inelasticity — no amount of willingness to pay from users could increase supply from operators — raises the importance of the limited supply being in the right place at, or just before, the right time. Staying ahead of these patterns is especially critical because interventions — such as rebalancing vehicles on the street — are fairly expensive. Interventions should only be taken when unavoidable operationally (e.g. after charging a vehicle or maintenance) or when they’ll generate a net-positive improvement on the performance of the fleet to justify the cost.² Operators need a data-driven framework to assess the necessity of, and upside generated by, operational interventions or user incentives.

The first step is to have a system in place for measuring how user-determined supply patterns will evolve with no operator intervention.

Trends in user vehicle movement

Demand distributions — where users want vehicles, and where users want to take those vehicles — vary according to day of week, time of day, weather, and other external factors. However, there are intuitive repeated patterns in how demand distributions change over time. For example, on weekday mornings, commuters ride scooters from train stations to job centers; on weekday evenings, the pattern flips.

As demand evolves, the supply network also morphs as users position vehicles. The maps below show weekday vehicle circulation patterns in Austin, Texas (data previously publicly available). Teal circles indicate areas of the city that net attract vehicles; red circles indicate areas that net lose vehicles. The area of the circles corresponds to the magnitude of the net inflow/outflow. The left map, which shows weekday mornings, shows how in the morning the net effect of rides is to move vehicles from outlying areas to downtown and the University of Texas at Austin. On weekday afternoons (right map), the trend flips: vehicles net flow out of downtown and the University towards more outlying areas.

However, notice that the weekday morning and afternoon maps are not perfect mirror images of each other. The morning and afternoon net flows don’t quite perfectly balance out, so over the course of the day there is some net vehicle movement. These imbalances can occur for all kinds of reasons. Mornings are cooler than afternoons, which affects demand for bike and scooter rides. Students might take a bike to get to class on time in the morning but save money by walking home in the afternoon. An office worker might commute downtown by scooter, take a free-floating car share with friends to a restaurant, and take a rideshare home after a few drinks.

The operator imperative

Day after day, slight asymmetries in user flows add up. When we examine rides over an entire week’s worth of morning-afternoon-evening and weekday-weekend cycles, we see that some locations net attract vehicles from the rest of the network, and some locations net provide vehicles to the rest of the network. If left unchecked, this phenomenon results in accumulation of vehicles in the “attractor” locations while the “provider” locations are consistently under-supplied. This under-supply is especially suboptimal from a revenue and fleet management perspective. The locations that net lose vehicles do so because users want to start rides there; if those locations are empty of vehicles, then the desired rides cannot occur. Similarly, the vehicles that accumulate in the attractor locations provide little value; these locations are already adequately supplied.

These patterns vary dramatically not just across cities, but within cities — travel patterns change with the weather, the seasons, and local events. Spring may have more regular commuters taking longer, but predictable trips; summer may see tourists taking shorter trips within a network of popular attractions. Additionally, the ongoing coronavirus pandemic has disrupted these patterns, nearly eliminating the most predictable trip cycles: weekday trips to and from the office.

Inevitably, small patterns in net user flow add up and cause a market as a whole to become imbalanced. In an ideal world, vehicles are always located where demand is, ready to serve that demand. But if users are left to determine the supply distribution without intervention from the operator, the fleet will be increasingly concentrated in attractor locations, rather than high demand locations. Imbalance is the extent to which the fleet is inadequately positioned to serve demand. Some degree of imbalance is unavoidable — every time a customer takes a ride, they shift the spatial distribution of supply, and typically not towards the spatial distribution of demand.

While imbalance can never be entirely eliminated, operators should endeavor to minimize it: severe fleet imbalance can have overwhelming negative effects on ridership and revenue. To illustrate the opportunity cost of fleet imbalance, we performed a simulation with data from three example markets. For each market, we simulate the fleet beginning August 1st under an optimized spatial distribution and then evolving for two weeks as users take rides and the operator does not engage in corrective rebalancing. We also estimate the daily rides that would occur in each market if the market’s fleet started each day optimally distributed. The difference between the simulated rides and optimal rides (measured as a fraction of the optimal rides) is the cost of imbalance. For example, a cost of imbalance of 0.2 means the poorly-distributed fleet captured 20% fewer rides than an optimally distributed fleet would have.

The plot below shows results from this experiment. Each market is represented by a curve, with the X-axis denoting calendar day and the Y-axis the cost of imbalance. Because the simulation starts each market with an optimal vehicle distribution on August 1st, the initial costs of imbalance are all 0. But the cost of imbalance quickly rises: after two days without operator interventions to keep the fleet well-distributed, daily rides are down 9–12% relative to an optimized distribution. After two weeks, the cost of imbalance is 18–29% — that is, a failure to maintain the fleet’s spatial distribution can cost an operator over a quarter of potential rides. Fixed asset shared mobility is a tight margin business and this degree of imbalance would almost certainly erase any positive contribution margin, making it impossible to achieve positive unit economics.

The differences between these example markets suggest another important point: imbalance is highly contextual and depends on weather, geography, demand patterns, etc. In some markets, users will naturally keep a mobility fleet well balanced so that supply is positioned near demand; a fortunate operator in such a market need only apply a light touch to corral stray vehicles. In other markets, variable weather patterns and highly asymmetric demand distributions may combine to constantly imbalance a fleet.

For an operator to keep their fleet healthy, they must fight the natural entropic tendency of fleets to become imbalanced. And at a high level, there are only two tools available to operators: either they can move vehicles themselves, or they can incentivize users to do it for them. The upcoming posts in this series cover these options. Our next post covers user incentives such as dynamic pricing, and how operators can encourage users to take rides which will keep the distribution of vehicles in sync with expected future demand. The third and final post in this series covers the tools of rebalancing and how operators can use them efficiently to maximize revenue while minimizing operational costs.

¹ Fixed asset systems are characterized by vehicles that are owned by the system operator, often (but not always) operated directly by users. This broad category includes kick scooter and moped sharing, docked and dockless bike shares, station based and free floating car shares, and future autonomous vehicle services.

² Rebalancing one vehicle typically costs as much or more than the average revenue generated by one trip. To justify the costs, an operator must be confident in the upside being generated.

Zoba is developing the next generation of spatial analytics in Boston. If you are interested in spatial data, urban tech, or mobility, reach out at

Zoba Blog

Zoba uses demand forecasting and optimization to improve the performance of shared mobility services. On this blog, Zoba operations leaders, data scientists, and engineers write about the problems we solve for shared mobility operators and tools we use to solve those problems.


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Zoba increases the profitability of mobility operators through decision automation.

Zoba Blog

Zoba uses demand forecasting and optimization to improve the performance of shared mobility services. On this blog, Zoba operations leaders, data scientists, and engineers write about the problems we solve for shared mobility operators and tools we use to solve those problems.