A Novel Dynamic Pricing Model for the Telecommunications Industry

Transcription

1 A Novel Dynamic Pricing Model for the Telecommunications Industry Kholoud Dorgham 1, Mohamed Saleh 1, Amir F.Atiya 2 1 Department of Operations Research, Cairo University, Cairo, Egypt {k.dorgham, m.saleh }@fci-cu.edu.eg 2 Department of Computer Engineering, Cairo University, Cairo, Egypt aatiya1@gmail.com Abstract Telecommunications industry is a highly competitive one where operators strategies usually rely on significantly reducing minute rate in order to acquire more subscribers and thus have higher market share. However, in the last few years, the numbers of customers are noticeably increasing leading to more stress on the network, and higher congestion rate, i.e. worse quality of service (QoS). Because of this, pricing has emerged as a useful tool for simultaneously limiting congestion, and increasing revenue. In this paper a dynamic pricing model is proposed for the mobile calls based on a Monte-Carlo simulation that emulates the processes of calls arrivals, calls durations and the effect of price on both. This model is then integrated with a meta-heuristic evolutionary based optimization algorithm to determine the optimal dynamic pricing schemes according to the call parameters. This integrated framework is a novel approach to dynamic pricing that aims at maximizing revenue and enhancing the QoS. Keywords: Telecommunications, Revenue Management, Dynamic Pricing, Optimization, Monte-Carlo Simulation 1 Introduction In developing countries, the telecommunications market is highly competitive. All operators use price as their main competitive edge to gain market share. They rely on reducing minute rate in order to acquire more subscribers, often without regard to using scientific approaches for optimizing prices. However, pricing calls too cheaply can cause losing higher revenue from price-insensitive users, i.e. lost opportunity, while setting too high of a price could noticeably reduce demand. This calls for the application of a revenue management approach, for optimally determining this tradeoff pricing. Revenue management is the science of managing the amount of supply to maximize revenue by dynamically controlling the price (or quantity) offered. It has had a long history of research and application in several industries, for example airline companies, hotels, and retail chains, where advanced revenue optimization policies are becoming key drivers of the companies performance. The primary aim of revenue management is based on the motto: selling the right product to the right customer at the right time for the right price.

2 There have been two general approaches for revenue optimization. The first one is performed by customer segmentation. Different prices are set for the different customer segments, and what is being controlled (for the purpose of optimizing revenue) is the amount of merchandise allocated to each segment. This approach is more prevalent in the airline industry. The other approach of revenue management is the so-called dynamic pricing approach, in which the price is continually adjusted to take advantage of demand variation. This approach is particularly prevalent in some online hotel reservations, and some online retail product sales. The online nature makes it easily possible to update the price periodically. The trend has been moving more towards applying the dynamic pricing approach or a combination between the two approaches. There has been some previous work on price optimization in the telecommunications domain, specifically in mobile services. However, dynamic pricing is still a nascent but promising research topic in that domain, and much research is still needed to explore its benefits and prospects. Dynamic pricing implies having variable pricing of minutes that is based on traffic, network capacity, time of the day and customer segment (value based). It can be a tool for improving revenues as well as controlling congestion for better customer experience. Current trends include nighttime-weekend discounts, bundle-based pricing, promo-based pricing, usage-based pricing or flat pricing. However, true dynamic pricing is adopted in very few countries, most notably in India and in some African countries. In the last few years, due to the aggressive competition, the numbers of customers in telecommunications industry increased noticeably, leading to more traffic on different network cells -- specifically in highly populated regions. The uneven distribution of traffic, and the congestion on some network cells can lead to an increased number of blocked calls; i.e. worse quality of service (QoS). This eventually reduces revenues as shown in figure 1. Fig. 1. Problem definition diagram The purpose of this work is to develop a new dynamic pricing model for mobile calls that maximizes revenue and enhances QoS. This can be achieved by encouraging customers via price incentives to use network cells in their "off peak" hours.

3 A more uniform distribution of traffic would decrease the number of blocked calls, enhance customer experience and increase revenue. The main idea is that the pricing scheme is updated periodically, and is procedurally performed by having a fixed reference rate and a variable discount that varies within a certain pre-specified range. An improved pricing system -- even by trivial amounts per call -- can lead to huge increases in profits due to the large amount of calls at stake. In the proposed approach we assume that the pricing is based on a reference price that is set by the telecom operator multiplied by some multipliers that vary around one and produce discounts or premiums over the reference price. The multipliers are the control parameters that are optimized in order to maximize revenue, subject to a bound on the blocking rate. To obtain their effect on the revenue, a Monte Carlo simulation is developed that emulates all call processes, such as arrivals and durations, as faithfully as possible. In Appendix I, the related work is discussed (due to paper size limitation). In summary, dynamic pricing and revenue optimization have potential prospects in the telecommunications industry, where its application by telecom operators is still in its infancy. As such, further studies and development of this topic will certainly advance its application and benefit the telecom market. 2 Proposed System 2.1 Overview The proposed framework is based on an optimization model that sets the price of every incoming call in a dynamic setting. The idea is to maximize the revenue, and enhance the QoS i.e. reduce the number of blocked calls taking into account current demand, the demand-price sensitivity of the caller s segment (e.g. pre-paid, post-paid or enterprise), the timing slot and the overall load level. Embedded in the optimization model is a Monte Carlo simulation that simulates the incoming calls and their durations as faithfully as possible. This simulation yields an estimate of the revenue and the load for the next few time slots, and its output will therefore directly influence the pricing parameters and its function. The detailed idea will be illustrated below. 2.2 Framework and Methodology The proposed formulation assumes that an incoming call s price is set be a reference price multiplied by two different multipliers to obtain the final price (Bayoumi et al., 2012). The reference price is the baseline or benchmark price set by the telecom operator. It could possibly vary according to the caller s segment such as pre-paid, post-paid or enterprise. In addition, the two multipliers represent the control variables that vary around the value of 1. This means that a value lower than one corresponds to a discount with respect to the reference price (such as 0.9 means the price is lower by 10 percent). On the other hand, a value that is higher than one represents a premium price regarding the reference price as well. However, the final price is strictly kept in some predefined range (within a minimum and a maximum price). The reason for price adjustments using a reference price and multipliers that

4 vary around one is that it is sensible to have the price based on the existing price. This will keep the proposed price in check, and will make the system more readily accepted by telecom operators that probably use their long business experience in setting their prices. Each of the two multipliers corresponds to a variable that is having an influencing effect on price calculation. According to industry experts in Egypt, the most two significant variables are: 1. The remaining capacity of the incoming call cell node (cell load capacity) 2. Timing slot of the incoming call (time of the day) This model works on any generic cell, so it could be applied within cities or villages. Therefore, in general, the relation between cell capacity and time of the day can vary. In this paper, we treat them as separate variables; nevertheless in future work, we will investigate the dependency between them. There exists a multiplier for each of the above influencing variables. For simplicity, these multipliers are considered to be as linear or piecewise linear function, whose level and slope are determined by the optimization algorithm. The piecewise linear functions are selected based on logically expected relations identified by telecom experts. For example, if the remaining cell node capacity is high (off-peak hours), then the multiplier should be low in order to attract more calls in the network. On the other side, if the remaining capacity is low (peak hours), the call price should be higher than the norm in order to reduce the load off the network and decrease the number of blocked calls. Therefore, a linear function is used that is monotonically decreasing with the remaining cell capacity. Similar idea applies for the other multiplier, and this will be explained further. The final price of the incoming call is given by the product of the reference price and the multipliers, as follows: Price = Reference Price Day Time multiplier Cell Capacity multiplier (1) The resulting price will correspond to the combined effect of the discounts and premiums of the control variables. This reflects the aggregate need for either boosting or attenuating traffic. Figure 2 shows the overall proposed dynamic pricing framework. The components of the block diagram will be explained in detail next. Initially, the customers are segmented into three different segments according to the Telecom operators definitions for the type of the subscriber acting as pre-paid, post-paid and enterprise. Essentially, a so-called Monte Carlo simulator is designed where its function is to emulate the calls processes such as the arrivals, and call duration as faithfully as possible. This simulation is based on a probabilistic or stochastic modelling of each of the processes. This simulator will provide a forecast of future arrivals and durations. Based on the simulator s forecast, the expected total future revenue in addition to the total number of blocked calls is estimated. These are passed forward to the optimization module that seeks to maximize this total revenue. The parameters of the price multipliers e.g. the line slopes and levels are the decision variables of the

5 optimizer. Once they are obtained, they successively will determine the suggested price through the price multiplier formula (1). A price elasticity function is estimated using a linear function in order to determine how much the new suggested price will influence the demand, e.g. the arrivals rate. From this relation, a new demand factor will be obtained for the price which is suggested by the optimization algorithm. The new demand will therefore be amplified or reduced according to this demand factor. Subsequently, the new demand represented in a proportionally higher or lower arrival rate, due to respectively lower or higher pricing, will be taken into account in a new run of the Monte Carlo simulator producing a new forecast of the expected total revenue as well as the total number of blocked calls. The optimization algorithm will work on another set of price parameters, and continue in a new iteration of the whole loop as shown in figure 2. The optimizer/simulator framework keeps looping around for several iterations, until reaching the best parameter selections that lead to maximum total revenue. Once the optimal parameters are obtained, the final output is the price of every incoming call. 2.3 Price Multipliers Fig. 2. Proposed framework block diagram The following is an illustration of the idea of the reference price along with the two multipliers that determine the final suggested price. Reference Price According to the nature of the telecommunications market, the reference price should vary along with the subscriber type (e.g. segment) as well as the tariff model for each type as illustrated in table 1 for the telecommunications market in Egypt. Thus, for each incoming call, a mapping between the subscriber type and tariff model with its call reference price will take place.

6 Time of the Day Multiplier The time of the day of an incoming call can be an essential controlling variable for the call s price. For example some hours coincide with peak demand, and therefore higher pricing would at the same time lead to reducing demand, and increasing revenue. Conversely, most of the cell nodes are underutilized in their off-peak hours due to the minimal flow of the call arrivals, and a boost in call volume could increase revenue. Accordingly, Figure 3 shows the proposed price multiplier (y-axis) against the time slots (x-axis). For simplicity these multipliers are considered to be a piecewise linear function. The day is divided into four time intervals whereas the peak hours are starting from 6:00 pm to 12:00 am followed by the next peak interval from 6:00 am to 12:00 pm. At the beginning of the day, the price should be low in order to encourage the customers to utilize the network on its off-peak hours e.g. from 12:00 am to 6:00 am, and thus, the time multiplier will start from a low level y 1 T. Thereafter from the second slot, the multiplier s value increases as the network congestion could get serious (corresponding to the multiplier s value y 3 T ). The highest price should be assigned to the peak interval with multiplier level y 4 T to discourage the incoming calls and offload the network, in an attempt to limit the number of blocked calls. The final interval which lies between the two peak slots e.g. from 12:00 pm to 6:00 pm will have an intermediate multiplier level y 2 T.Briefly, the idea is to evenly distribute the traffic across all the day through either a negative (premium) or a positive (discount) incentive. Fig. 3. Time of the day multiplier curve Cell-load Capacity Multiplier For the cell load capacity multiplier, a highly utilized cell with traffic close to its full capacity should have a higher pricing to discourage further calls. Conversely, for lightly loaded cells, pricing should be discounted. Therefore an upward sloping linear function should exist for the price, as shown in figure 4. The x-axis represents the cell capacity in percentage or so-called server utilization, and the y-axis represents the value of the multiplier. If the network cell is under 75% from its capacity, then one has to offer some incentives, and therefore the capacity multiplier is at its lowest value y 1 C. The multiplier s value then increases sharply as the remaining capacity of the network cell node is decreased beyond 75%, until it

7 reached the maximum value y 2 C, at which point there is no remaining capacity, and calls start to be blocked. Fig. 4. Cell load capacity multiplier curve 2.4 Optimization Variables and Constraints The average value of each multiplier function is assumed to be equals one. The reason is that these multipliers are considered correcting factors that will be multiplied by the reference price. Thus, they should vary around one, with a roughly equal average amount of discount pricing and premium pricing. The optimization variables are as follows: Time of the Day Multiplier: y 1 T, y 2 T & y 3 T ; and Cell Load Capacity Multiplier: y 1 C. These are the variables that the optimization algorithm will determine such that the revenue is maximized. The other multiplier parameters are dependent, as they will be set such that the average value of each multiplier function equals one. The second expression of equation 2 is computed by assuming that the area under the curve is unity (as in this case, the maximum value of the x-axis is also unity) y 4 T = 4 (y 1 T + y 2 T + y 3 T ) y 2 C = 8 7 y 1 C (2) There are also inequality constraints that will guarantee that the multiplier functions are well behaved and produce logically accepted relation: Time of the Day Multiplier: Cell Load Capacity Multiplier: 0 y T 1 y T 2 y T T 3 y 4 T 1 y 4 T 0 C C 0 y 1 y 2 C 1 y 2 C 0 The first and third constraints are meant to preserve the intended shape of the multiplier function. The second and the fourth constraints are bounds on the parameters that should be determined with the help of a telecom business expert. The expert should determine the maximum deviation from the reference price that is

8 acceptable by the company from a business point of view. For the system implemented, T 0 and C 0 are set to be 1.3. In addition to these multiplier-specific constraints, there is a global constraint for the overall price correction e.g. the product of all multipliers. Again, the maximum deviation from a reference price should not exceed a certain percentage that is determined based on business considerations. The rationale is that it is detrimental to the good will of the customer, if the price is increased too much. In our system this percentage is set to be 30 percent, which means that the final price has to be within plus or minus 30 percent of the reference price. 2.5 Proposed Model Simulator In order to compute the future revenue that is going to be optimized, the future incoming calls as well as the calls durations need to be forecasted. For this reason, a call simulator has been developed using Matlab s SimEvent. SimEvent is a tool that provides a discrete-event simulation engine and component library for Simulink. To the best of our knowledge, it is the first time that SimEvent is used for this purpose. This Monte Carlo simulator takes the call s price parameters from the optimization algorithm and applies the simulation. The simulator is designed so that it emulates processes of call arrivals, calls durations and the effect of price on both as shown in figure 5 below: Fig. 5. Proposed System Structure As demonstrated in the previous figure, calls are divided into three segments based on the customer type such as pre-paid, post-paid or enterprise. Besides, there are number of components in this system, as follows: Calls Inter-arrival generation: The proposed method is based on assuming that arrival rates of incoming calls follow an inhomogeneous Poisson process (IHPP)

9 (see Nawar et al 2014). Subsequently, a Bayesian approach is applied that gives the probability density of the forecasted arrival rates. The IHPP process is defined as a Poisson process with an arrival rate (t) that is a function of time. Thus, certain periods of the day have high arrival rate (t) i.e. peak hours, and therefore one observes many calls initiated in this period. Conversely, some periods, such as early morning i.e. off-peak hours, have low arrival rates, and therefore a small number of calls fall in them. In this Bayesian approach a Gaussian prior is assumed for the arrival rates of the different time slots that implicitly take into account seasonal relations. Subsequently, the posterior distribution is derived, and this distribution is used to generate future arrival rate values, and then actual call arrivals (for details see Nawar et al 2014). Calls Durations: Calls durations are assumed to be distributed as exponential. Telecom data is used to estimate the mean of the distribution. Subsequently, this distribution is used to generate calls durations. Blocking Calls: If the number of calls inside the network cell node reached the maximum cell node capacity i.e. 100 percent utility, then further calls will be precluded from entering the cell node and will be counted as blocked call. Conversely, if there is a remaining capacity in the cell node, then the call will be served. The simulator computes the number of blocked calls in a standalone block. In Appendix II, we explain the price elasticity formulation (due to paper size limitation). Revenue Calculation: Total revenue is then calculated after all the simulation processes. As follows: Total Rev = n i=1 Duration i Price i (5) where n = total number of calls In order to have statistically accurate estimates, several Monte Carlo runs are generated, and the average total revenue is computed. Then it is passed to the optimization algorithm. The optimizer will keep exploring other sets of price parameters until it reaches the maximum revenue producing parameters. In Appendix III, we explain the optimization solver used (due to paper size limitation). 3 Model Evaluation In order to test the effectiveness of the proposed methodology, it is compared with the static model that is applied in a real market (in the Egyptian market). By static model we mean a model with fixed prices. We used in the benchmark the exact same price packages used in the Egyptian telecom market (see Table 1). The goal is to test whether this approach leads to an improvement in the revenue over the baseline. Hence, the test case is divided into two phases: 1- Run the overall proposed dynamic pricing model 2- Test the outcome of the dynamic model versus the static one across several days.

10 The final set of multipliers coming from phase one after applying thousand runs is as follows: 0.8, 0.9, 1.1, 1.2, 0.97 and 1.21 for y 1 T, y 2 T, y 3 T, y 4 T, y 1 C and y 2 C respectively. Afterwards, the dynamic price-based approach is tested in comparison with the static pricing across ten days. As seen from table 2 and figure 8, one can observe that the proposed approach succeeds in improving the revenue by about 10 percent over the static model. Moreover, the improvement in revenue is consistent across all days. These results confirm the fact that dynamic pricing, if optimized well, should lead to better revenues. We note that in our case the optimization is performed only once, and once the multipliers are available, the pricing is obtained in a simple and straightforward way by applying the price multiplier functions. Table 1: Revenue improvement over the baseline tested across ten days Days Total Revenue (EGP Pounds) Improvement Dynamic Price Static Price Percentage Day 1 36,400 33, % Day 2 38,304 32, % Day 3 38,298 32, % Day 4 36,573 34, % Day 5 36,153 33, % Day 6 37,741 35, % Day 7 39,423 34, % Day 8 41,446 34, % Day 9 36,709 34, % Day 10 39,573 36, % Average 38,062 34, % Fig. 6. Total Revenue performance in day 10

11 4 Conclusion and Future Work A novel system for dynamic pricing mobile calls is developed in this study. The idea is to create a realistic model of the processes of mobile calls, and based on that determine the effect of price on demand, and hence on revenue. A pricing function is proposed, given in terms of price multipliers that frame the price as discounts or premiums over a given reference price. The proposed system gives a versatile and realistic way to assess pricing strategies, and it can also help in scenario analysis for any suggested strategy. In future work, we will investigate the relationships between various inputs; as there might be dependency between them. Moreover, the model will be tested using real data from telecom operators, and will be benchmarked with the current implemented static module. Appendices I, II and III Pdf file in References H. Abdel Aziz, M. Saleh, N. El Gayar, H. El-Shishiny: A randomized model for group reservations in a hotel s revenue management system. In: Proceedings of INFOS 08 (2008) H. Abdel Aziz, M. Saleh, H. El-Shishiny, and H. Rasmy: Dynamic pricing model for hotel revenue management systems. In: Egyptian Informatics Journal (2011) B. Al-Manthari, N. Nasser, N. A. Ali, and H. Hassanein: Efficient bandwidth management in Broadband Wireless Access Systems using CAC-based dynamic pricing. In: Proceedings, 33rd IEEE Conference on Local Computer Networks, LCN R. Andrawis, A. F. Atiya, and H. El-Shishiny: Forecast combination model using computational intelligence/linear models for the NN5 time series forecasting competition. In: International Journal of Forecasting, Vol. 27, No. 3, pp (2011) R. Andrawis, A. F. Atiya, and H. El-Shishiny: Combination of long Term and short term forecasts, with application to tourism demand forecasting. In: International Journal of Forecasting, Vol. 27, No. 3, pp (2011) Bayoumi, A. E. M., Saleh, M., Atiya, A. F., & Aziz, H. A.: Dynamic pricing for hotel revenue management using price multipliers. In: Journal of Revenue & Pricing Management, 12(3), (2011)

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