Optimisation and cross-validation of an e-hailing hybrid pricing algorithm using a supervised learning classification and regression tree model: a heuristic approach

2.1 The supervised learning

The supervised learning (SL) relies on supervision and is used to train machines using a labelled dataset, while the algorithm predicts the outcome based on the training. Thus, the machine is first trained with input and output before the outcomes are determined with the training datasets. The two types of SL are classification and regression. Classification is performed on patterns in the sample data, followed by constant calculations to predict the result. Classification aids price forecasting, such as in stock trading. Inversely, regression identifies, understands, and groups objects into pre-set classes. Spam or non-spam e-mail filtering is the ideal example. Despite the variety of SL, the three most frequently used supervised algorithms are the decision tree (DT, classification, and regression tree [CART]), naïve Bayes, and support vector machine (SVM). Specifically, DT SL is used in associated issue or problem classification and regression and is also a classification-related resolution technique. The DT is also known as a predictive model that involves decision and leaf nodes. The decision node addresses various sub-branches while the leaf node is a decision output (Johnson, 2022). The predictive method is fast or accurate and easy to build to yield better results. Thus, the method can be used to create well-defined conditions to build pricing strategies and other critical solutions.

2.2 The unsupervised learning

In unsupervised (USL), a computer is provided with an unlabelled dataset and predicts results without supervision (human intervention) (Hastie et al., 2009). The USL aims to categorise or group unsorted data according to similarities, patterns, and differences.

2.3 The reinforcement learning

The RL depends on interactions with the environment to achieve a specific objective. The RL-based agent learns from its circumstances in an iterative procedure (Horie et al., 2019). The agent obtains data from its environment until all probabilities have been examined and the agent has reached the goal state. An agent learns its behaviour via a reinforcement signal, which is a simple form of incentive feedback. Table 1 summarises the different ML models, their definitions, key information, and common usage (Ahmed et al., 2010).

2.4 Current price algorithm issues

According to Branda et al. (2020), the transportation, aviation, tourism, and e-commerce industries widely use DP policies. The pricing model (algorithm) facilitates revenue folding by allowing the same product or service to be sold at a higher price when the demand increases (Aubrey, 2022). Companies adopted DP to gain profits, such as by increasing hand sanitiser prices by 100 % to 200 % during the pandemic due to high demand.

Fig. 1 depicts surge pricing during peak hours when the booking rate is higher. The figure illustrates the method through which the DP model applies to Malaysian e-hailing products and creates unfair or discriminatory pricing, which eventually affects riders and drivers. The chronological perception of the world by the RL programme results in it not considering surrounding factors, which leads to less accurate results. For example, when demand is lower at night, drivers who provide services during these odd hours are not remunerated fairly by the algorithm. Nevertheless, this case does not apply to the traditional taxi system, where drivers gain additional night allowances in accordance with local transportation rules (SPAD, 2017). Similarly, the RL algorithm does not address other factors, such as traffic and trip duration during peak hours. Surge pricing occurs regardless of whether trip duration is standard or long. The pricing model also fails to adjust pricing based on business performance, which does not benefit any party. For example, drivers do not secure jobs, service providers do not gain commissions, and riders searching for alternate transportation options are dissatisfied (Santos et al., 2020).

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Fig. 1

Current e-hailing model using RL.

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2.5 Limitations

E-hailing incorporates a mutual agreement between users and service providers for travel bookings with a digital application. E-hailing considered the smoothest and easiest transportation option for users due to the associated benefits and comfort regarding vehicle booking (Jais & Marzuki, 2020). Nonetheless, pricing is the most crucial factor for all businesses, which users consider before using any service. The current e-hailing providers use RL to build DP strategies to charge their consumers (riders and drivers). Nevertheless, limitations on the current pricing model have led to customers feeling that the offered pricing is biased and manipulated. In Malaysia, the Minister of Transport Management referred to the current pricing strategy as a tactic to gain more profit (Palansamy, 2019). This statement was followed by the instruction to the top management of e-hailing service providers to clarify the factors for the unreasonable price hikes (Malaymail, 2022).

Currently, e-hailing service quality is compared to that of taxi services (which predate e-hailing), where the price is excessively high and unjustified, specifically during peak hours (Pan et al., 2020). The Common Taxi Across Malaysia (GTSM) President stated that e-hailing providers increased trip prices in Kuala Lumpur by over 40 % during peak hours. Both e-hailing riders and drivers reported issues that could further deter the transportation industry (e-hailing) growth.

The e-hailing DP strategy uses RL. The RL perceives the world as chronological, while previous data support allows the BOT to greatly increase trip prices (‘price surge’) based on a high number of requests without considering other vital factors, such as traffic conditions, trip duration, and the time of day (Vanoutrive & Zijlstra, 2018). This condition leads to unfair pricing for both drivers and riders. For example, the Malaysian land public transport agency (APAD, which was previously known as SPAD) defined a 30 %-night surge as fair pay for drivers who work at night and odd hours. Nonetheless, the RL pricing model increases the price only when demand is higher, yet demand is lower at night (SPAD, 2017). Similarly, the term ‘peak hours’ refers to when the reinforcement pricing model (algorithm) surge price creates an unfair situation for riders. Specifically, the system records a high number of demands although it does not ensure whether the trip duration remains the same due to traffic or other climatic conditions. This situation affects both riders and drivers, as riders do not make bookings when the trip price is high and drivers do not conduct business during price surges. Simultaneously, the e-hailing company also loses minimum business. Overall, RL limitations contribute to these issues as it does not consider the surrounding factors.

2.6 Statistical analysis

To build a hybrid pricing algorithm for e-hailing using the ML CART model. The researcher first performed detailed survey to which more than 500 responses received. The survey result shows 55 % Malaysians prefer e-hailing over public and private transport and most used e-hailing riders across Malaysia. Around 57 % reported unhappiness over price offerings. In next step the historical dataset of e-hailing ride was collected for three hundred trips. The collected data set which contains information rides such as popular destinations, time of the day, average trip fares (Ringgitplus., 2023). Post collection of the dataset the research involves following steps to build a hybrid pricing algorithm (Tzenios, N. 2023).

1. Collect a dataset of historical e-hailing rides.

2. Prepare the data for training.

3. Split the data into training and test sets.

4. Train the CART model.

5. Evaluate the performance of the model on the test set.

6. Deploy the model into prototype and conclude.

5.1 Scenario 1: Time-based price surge

In Scenario 1, all requests were tested between 00:00 midnight and 6:59 a.m. The night charges were included in the algorithm to test the time-based price surge condition. Fig. 4 depicts the time-based price adjustment. In Scenario 1, a total of 12 requests were made for four origins and destinations (see Table 2). In all the requests, the price offered by the pricing algorithm was higher by 30 %, which was defined in the decision to address unfair wages to drivers who work during odd hours.

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Fig. 4

The DT for night surge in Scenario 1.

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In Scenario 1, the test results indicated that RL failed to offer fair pricing to drivers when demand was low. This situation could further jeopardise driver availability and quality services following the current low remuneration offered to Malaysian e-hailing providers who work at night.

5.2 Scenario 2: Surge based on traffic conditions

In Scenario 2, testing was performed from 07:00 a.m. to 11:59p.m. to test the proposed algorithm during peak hours, where Malaysian e-hailing providers currently surge ride prices using RL DP. In this scenario, origins and destinations were selected randomly but included popular and frequently visited locations where the Malaysian urban population resided. The pricing was tested in real-time with a total of 10 origins and destinations and 30 trips from two different providers, which included the proposed prototype algorithm. Fig. 5 depicts the occurrence of the smart price surge based on traffic conditions.

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Fig. 5

The DT for high and low demand surges.

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Table 3 demonstrates that both providers A and B surged trip prices by 25 % to 50 % during peak hours. Contrastingly, the prices offered by the POC remained significantly lower compared to those of providers A and B. The POC trip price only increased during high-traffic conditions as compared to high-demand conditions.

In Scenario 2, RL based algorithms failed to offer fair pricing to riders by selling similar services at a higher price upon increased demand. This classic example represents the traditional taxi system issues when drivers and riders negotiate trip prices. E-hailing services emerged promising to address security, pricing, and flexible payments (Grab, 2022).

5.3 Scenario 3: Price optimisation based on real-time customer behaviour

In Scenario 3, a unique condition was included in the hybrid pricing algorithm logic to optimise the trip price (see Fig. 6). For example, a demand higher than the RL model during Christmas or New Year would lead to surge pricing based on the number of requests. Nonetheless, the RL system does not consider whether users were making actual bookings or merely screening the trip price. Similar to Scenario 2, the algorithm progressed towards surge price in this condition without considering the fact that users reviewed trip prices frequently for a lower price before agreeing to accept the price to start their ride.

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Fig. 6

Situation-based trip price optimisation.

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In Scenario 3 (see Table 4), testing was performed by making bookings to four origins and destinations. Analysis of the test cases determined that the proposed algorithm reduced trip prices when customers were screening prices instead of making actual bookings. Nevertheless, provider A and B prices remained unchanged during peak or high-demand hours. This condition indicated that providers did not have a mechanism to identify whether the customer was making bookings or merely screening trip prices.

Service providers A and B could not offer lower rates; instead, the system considered that demand was high based on users’ price screening, where users frequently reviewed origins and destinations. This condition increased the trip price, which is one of the main drawbacks of RL due to its perception of the world as sequential. Thus, the trend would remain due to the inability to offer optimised pricing.