How does Uber’s surge price vary at different times?

## **Short Answer**

Uber is a firm that provides a ride sharing platform that matches willing drivers with customers looking for rides. Founded in 2009, it is an emerging leader in the ride sharing economy. It is now available in over 200 cities in 57 countries with 160,000 drivers in the United States alone.

An application for mobiles which is responsible for a two sided market is provided by this technology firm. To determine the availability of rides and to get estimated prices, the clients use a client app whereas the drivers use a partner app to indicate the willingness to accept fares. The passenger requests are routed to the nearest driver and the passenger’s credit card is automatically charged at the end of the trip. Riders using this service are charged based on the time taken to complete their trip and also the distance covered during the trip. When the demand is high, it introduces a ‘surge multiplier’ to increase the prices. There are two main reasons for introducing surge pricing:

1.  Reducing demand by cutting some customers out of the market which in turn reduces the wait time for the other customers.

2. Increasing profit for drivers which encourages more people to come out and drive when the demand increases.

A service fee of 20% for uber is deducted from this fare payed by the riders and the rest of the fare is the income earned by the drivers. Uber divides all the cities into ‘surge areas’ and calculates the surge multiplier independently for each area. The surge price gets updated every five minutes and this price is highly correlated with supply and demand. Surge price is set algorithmically and not manually.

There are different types of uber based on the type
of service provided and the type of vehicle. UberX and uberXL are the basic sedan and SUV, UberBlack and SUV are luxury vehicles, UberFamily is a car equipped with car seats, UberWAV is a wheelchair accessible vehicle and UberPool allows carpooling.

UberX is a peer to peer service provided by uber. Uber X partners have the flexibility to decide when they can work. Once qualified to drive on the UberX platform, these driver partners have the freedom to choose on what days and for how many hours they want to work on this platform. Uber is not responsible for the decisions of the drivers as it neither employs drivers nor owns cars. All the driver partners are self employed and are independent agents

### 1.**Connection between Uber users and drivers**

Users use an uber client app to connect users with the drivers. A pingClient message is sent by the app to uber’s server every 5 seconds after the user opens the
app and authenticates with uber. Every pingClient message consists of the user’s current geolocation. Once the server receives a pingClient message, it will respond back with a list of information about all the types of cars available at the user’s location. For every car type, the nearest eight cars along with the estimated wait time and the surge multiplier are given. Every car has its own Unique ID, location and a path vector which traces the car’s movements.

#### **2. The surge pricing algorithm:** On the Uber platform, fares for rides are determined by a dynamic pricing algorithm known as surge pricing.

##### **2.1.Origin of uber’s dynamic pricing (Surge Pricing):**

In 2012, a problem was noticed in Boston by Uber. The number of requests that went unfulfilled increased significantly during the weekends, i.e. on Friday and Saturday nights past 1 AM. This was because uber drivers would become inactive and get back home during this time as they are independent agents and did not have any fixed working hours which gave them the flexibility to choose when they wanted to work. This was the exact time at which party goers would want to get back home. This caused an imbalance in supply and demand and left many customers dissatisfied.

Uber’s team came up with a solution to this problem and decided to offer higher prices to drivers if they stayed active on the system for much longer times during the peak hours till about 3 AM. This encouraged drivers and the supply increased by 70-80%.

This problem led Uber to come up with the dynamic pricing model or the surge pricing which could come into effect only when the demand is higher compared to the supply. Surge pricing varies from area to area depending on the demand and also the wait times for the customers.

## **Long Answer**

In an area, whenever the rider requests are much higher than the available drivers then the price for each trip is automatically increased by an algorithm which determines the surge pricing.

### **3. Dynamic pricing algorithm:**

In the dynamic pricing strategy, the prices for products or services are not fixed and are flexibly set by the businesses depending on the demands of the current market. Different algorithms for dynamic pricing give any business the feasibility to change prices. These algorithms take into account several factors like supply and demand, competitor pricing, and other external factors.

A dynamic pricing model establishes the relationship between demand and the changes in prices. In this model, the initial inventory is given by *S*0. Demands appear at times 1, 2,L,*T* . The
demand at time *t* is represented by *xt.*

The price at time *t* is denoted by *pt,* and is a function of the demand and the time *pt* = *p* ( *xt* , *t* ) .

We assume that there exists a one-to-one relationship between demand and price at any time *t* ∈{1,2,L*T* }. Thus when the price is fixed the demand is provided by the relation *xt = x* ( *pt* , *t* ).

The problem can be expressed as:

Maximize

Subject to

Here ptmin is the minimum value of pt.

The objective is to maximize the total revenue. The first constraint is introduced to guarantee that the total demand doesn’t exceed the initial inventory. The second constraint sees to it that the demand is never less than zero.

Solution:

This problem can be solved by using the Lagrange multipliers.

As *pt* is a function of *xt* , therefore *pt xt* is also a function of *xt* . Considering the constraints of the problem, the Lagrangian is given as

The goal is to solve the T equations

Along with the 2T+1 equations

µt.xt = 0  for *t* ∈{1, 2,...,*T*}

Hence the 3T+1 unknowns can be calculated from 3T+1 equations as

A solution to these sets of equations can be computed by considering 𝜆 ≥ 0, µt ≥ 0, lt ≥ 0

Hence we can obtain the results as

    Example of this algorithm: Consider a given price function

Consider the case:

Where A, B and D are positive constants.

Maximize

Subject to

xt is either equal to 0 or ,

Then µt = lt = 0  and the equation becomes

Let xt = A/B ,  then µt = 0 and the equation becomes

Now let xt = 0 and lt = 0, the equation then becomes

Therefore, according to

Finally, let xt ε (0,A/B) In this case, µt = lt = 0 and

As a result, xt ε (0,A/2/B]  and

**Example:**

If we give values to A, B and D

Let A= 200, B= 10, and D= 10, then

Initial inventory level: 150

Demands: 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Prices (per item): 90.91, 83.33, 76.92, 71.43, 66.67, 62.5,
58.82, 55.56, 52.63, 50

Total demand: 100

Revenue: 6687.71

### **4. Surge Multiplier:**

The fare calculation in uber depends on the local
transportation laws. It consists of a minimum base fare, cost per mile, cost per minute, fees, tolls and taxes. For every different type of vehicle, the base fare and distance per time vary. A surge multiplier was introduced in 2012 and whenever the surge pricing is effective, this price is multiplied by the output of the surge algorithm which is known as the surge multiplier. This surge multiplier is visible to both the rider and the driver and only after riders confirm this multiplier on the mobile app, a ride request can be made. The surge multiplier is typically 1 but increases when the demand increases. It varies from place to place and is updated every 3-5 minutes. The surge multiplier will be shown to the users only when they make an attempt to request an uber and also only when the multiplier is greater than 1.

These surge multipliers are not fixed as they are
determined by the time of the day and the demand. They vary from a minimum of 1.2 to a maximum increment that has been set by a particular city.

The surge multiplier is derived from the generator surge multiplier (GSM). At a point in time, Uber makes an estimate of the actual price for the rides in a market. This is given by the generator surge multiplier (GSM). Surge multiplier on the other hand is the price that has been implemented by uber. The maximum step size which determines the extent to which surge multiplier increments or decrements from its previous value and the cap size which determines the maximum surge multiplier for a particular city have an impact on the generation of surge multiplier from the generator surge multiplier. In general, SM and GSM are the same unless there are special conditions applied.

#### **4.1. Surge Pricing:**

**a)  Cost of surges:**

How often does surge pricing occur in uber?

The cost of surges varies from place to place. A study was conducted in San Francisco and Manhattan in which both the cities showed drastically different characteristics. In Manhattan, 86% of the time there was no surge and also the maximum surge multiplier was only 2.8 whereas in San Francisco, only 43% of the time there was no surge and the maximum surge multiplier was 4.1. However, the surge multiplier was <= 1.5 during most of the time in both the cities. This is shown in figure 1. Introducing a surge multiplier makes uber 25-50% more expensive but it can sometimes even be doubled, tripled or quadrupled.

**b) Surge duration and updates:**

How long does surge last?

Surge duration is the continuous length of time for which the surge multiplier is greater than 1. The data collected in February 2015 from a study in San Francisco and Manhattan showed that 90% of surges had duration that were multiples of five minutes. The data collected in April showed the same five minute pattern. In these two cases, 40% surges lasted five minutes whereas 20% surges lasted ten minutes. Data was again collected at the end of April and there was a complete change in the behavior of the surge price algorithm. 40% of the surges lasted less than a minute whereas the remaining 60% still followed the five minute pattern. This proves that uber updates surges every five minutes. Figure 3.a shows the datastream from API where surge

changes every five minutes. Figure 3.b shows that the client app surge multipliers are updated every five minutes with short periods of jitter. This short period of jitter breaks up a five minute interval into smaller intervals. This is the main reason why most of the surges do not last for more than a minute.

    **c) Surge areas:**

How do surge prices vary by location?

Surge prices must vary from place to place as a rural area is different from a city. To find out how surge prices vary by location, a study was conducted in San Francisco and Manhattan and surge prices were observed throughout these cities. All the adjacent surge areas with equal surge multipliers were observed. These regions are showed in figure 4 and 5. The results show the granularity in uber’s surge price algorithm in which surge multipliers are individually calculated for each surge area.

### **5. Categorization of sessions:**

First approach is to study the decision of the drivers as to how many hours in a day they wish to work. The time of the trip activity along with the application activity that happens without a break of more than 4 hours is defined as a session. The activity of a driver after being inactive for four hours is considered a new session. The time for which the driver is active on the app is defined as the length of a session and during this length the driver could be either serving a ride or maybe available to accept a ride request.

Uber drivers usually tend to drive multiple short sessions which range between 2-5 hours rather than fewer long sessions.

The surge pricing is affected by the length of a session of each driver and also when a driver decides to end a session.

#### **5.1. Length of a session: (OLS/2SLS)**

Longer sessions occur when drivers decide to drive during the time at which earnings are high, i.e during the period when surge multiplier is in effect.

The length of sessions driven by an uber driver is given by the equation:

Log(HoursOnShift) is the dependent variable. The ratio of sum of all the fares earned during a session to the number of hours on a shift gives the Log(HourlyFares).

Where, ‘F’ is the fares earned during the session and ‘h’ is the number of hours on the session.

is the measure of the driver’s supply elasticity. The set of effects due to the driver partner are given by Di and the set of effects due to time are given by Tt. Several other weather controls and temperature effects are also included.

As Log(HourlyFares) is the ratio, there arises the problem of division bias where any miscalculation of hours on shift will effect. To address this, a two stage model has been designed where a driver partner’s hourly fare is taken as the average hourly fares of all the driver partners in that same city. In the first stage equation, hourly fares is calculated first as

Then from this calculation we calculate the hours on shift

The 2SLS estimates are substantially higher when compared to the estimates of the OLS model. The concern that the OLS estimate will be downward biased due to an error in the measurement of hourly fares can be neglected by using the 2SLS estimation.

#### **5.2. Ending a session - Modeling the decision to stop:**

The earnings of a driver when surge pricing is in effect are determined by the driver’s decision as to when they want to stop driving and end their session. This is driven by the surge multiplier. This decision In turn causes variations in the surge multiplier as an increment or decrement in the supply may cause an increment or decrement in the surge multiplier.

The decision of a driver as to when they want to end a session depends on the measure of the session which includes the fare, distance travelled and the number of trips during that session and also the present weather conditions.

Where,

Ctrips– The cumulative trips during a session.

Cfares– The cumulative fares earned during a session.

Chours– The cumulative hours in a session.

Cdist– The cumulative distance travelled during a session.

Gi– Effects due to the geofence or the area in which the surge multiplier is in effect.

Probability of ending a session is the dependent variable. Surge multiplier is an independent variable which gives the surge multiplier that is in effect in the geofence or the region in which the trip ends. This is the surge price that would apply to the next trip of the driver after completing their last trip. -----is the driver’s supply elasticity.

Overall, this dynamic pricing model encourages a short time supply growth on the uber platform as it encourages driver partners to be active for more time than they usually would have been.

#### **6. Algorithm features and forecasting:**

What are the features used by uber to calculate surge pricing?

Uber uses the cross correlation between supply, demand and the estimated wait time (EWT) versus the surge pricing to calculate the surge price. The cross correlation coefficient is calculated at a time shift ‘dt’ using the surge price at time ‘t’. These values lie in the interval

[t + dt - 5, t + dt]

Figure 6 shows the cross correlation between
supply/demand and the surge price. From this graph it can be observed that a strong negative correlation is observed when dt = 0. This implies that when the supply/demand difference shrinks, the surge multiplier increases.

Figure 7 shows the cross correlation between EWT and the surge price. From this graph it can be
observed that a strong positive correlation is observed when dt = 0. This implies that EWT and the surge price increase at the same time. It is extremely difficult to forecast the future surge multipliers.

### **7. Impact of surge on supply and demand:**

Surge pricing is most common during the peak times of weekends and during certain holidays. The goals of surge pricing are to increase supply and to intentionally reduce demand.

From the Boston experiment it was observed that the number of drivers increased by 70-80% after introducing surge.

From the graph (Fig 8) it can be observed that increase in prices increases the supply and on the demand side, it can be observed that when there is a surge in the prices the number of requests which is the demand decreases.

### **8.**  **Conclusion:**

Uber is a ride sharing platform that introduces a surge multiplier to increase supply when the demand is high and this multiplier is not the same always and varies based on the dynamic pricing algorithm. Surge pricing is effected by the driver's decision regarding their session schedules as to what the length of their session is and when they want to end their session. This surge price can be avoided as well.

#### Avoiding surge pricing:

Even with a large amount of data available from uber, it is not possible to forecast
short term surge pricing. This is a disadvantage as predicting changes in the surge price could be useful for the driver as well as the passenger. However, there could be an alternative to obtain a lower price from uber by locating a lowest price car in a particular location. Suppose a surge multiplier at the current location of a user is and  is the set of adjacent surge areas then we can find the surge multiplier ma, the estimated wait time ea and the walking time wa to each area using the uber API.

If  ma < m, and

wa ≤ ea

Then the user can immediately book an uber for a low price and walk to the pickup point in the adjacent area before the car arrives.

## References:

1. Chen, L., Mislove, A., & Wilson, C. (2015). Peeking Beneath the Hood of Uber. *Proceedings of the 2015 ACM Conference on Internet Measurement Conference - IMC '15*.
2. Lee, M. K., Kusbit, D., Metsky, E., & Dabbish, L. (2015). Working with Machines. *Proceedings of the 33rd Annual ACM Conference on Human Factors in Computing Systems - CHI '15*.
3. Chen, M. K., & Sheldon, M. (2015). Dynamic Pricing in a Labor Market: Surge Pricing and Flexible Work on the Uber Platform. Retrieved December 11, 2015.
4. Gallego G, Van Ryzin G (1994) Optimal dynamic pricing of inventories with stochastic demand over finite horizons. *Manag. Sci.* 40:999–1020.

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