Revenue Maximization Problem Research Articles

Piecewise SOS-convex moment optimization and applications via exact semi-definite programs

This paper presents exact Semi-Definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the optimal value and an optimal probability measure of the original moment problem. This is done by establishing an SOS representation for the non-negativity of a piecewise SOS-convex function over a projected spectrahedron. Finally, as an application and a proof-of-concept illustration, the paper presents numerical results for the Newsvendor and revenue maximization problems with higher-order moments by solving their equivalent SDP reformulations. These reformulations promise a flexible and efficient approach to solving these models. The main novelty of the present work in relation to the recent research lies in finding the solution to moment problems, for the first time, with piecewise SOS-convex functions from their numerically tractable exact SDP reformulations.

Scheduling Slice Requests in 5G Networks

Network slicing is a 5G paradigm that enables the creation of on-demand logical networks over shared physical infrastructure. In this paper, we present a framework that allows users to make advance slice reservations with the End-to-End Orchestrator (EEO). Our reservation mechanism enables the EEO to make admission decisions instantly upon request arrival, providing guarantees as to when the request can be enabled. We then proceed to address a relevant revenue maximization problem through an optimal solution, which has factorial time complexity. We also propose a low-complexity algorithm that can efficiently allocate resources for the online version of the problem. We conduct evaluations that demonstrate how the reservation mechanism can potentially improve EEO’s revenue. Additionally, we conduct a study on scenarios where the arrival rates of slice requests exhibit a positive correlation with reservation discounts provided by EEO.

Hotel overbooking based on no-show probability forecasts

In this paper, a novel data-driven overbooking model is developed. Unlike traditional models in this area, our new model first applies some machine learning techniques to classify the customers for predicting the “no-show” probability of each customer, then utilizes this personal information to determine the best overbooking limits. In this way, without any prior assumption, a better overbooking system is built to obtain the accurate “no-show” probability forecast of each customer, which can lead to higher profits. Besides, an over-sampling procedure is introduced to handle the general imbalanced data in the hotel booking. The proposed model is formulated as an expected revenue maximization problem, where the approximate optimal overbooking solution can be numerically obtained with high efficiency. Finally, a real-life panel-style registration data set is applied to demonstrate the advantages of our proposed model in the numerical experiment.

Data-Driven Transportation Network Company Vehicle Scheduling With Users’ Location Differential Privacy Preservation

With the popularity of mobile devices with global positioning system (GPS), transportation network company (TNC) service has become an indispensable option of people's daily commute. However, it also provides opportunities for malicious parties to compromise TNC users’ location privacy. There are great challenges to preserve TNC users’ location privacy while improving the revenue of TNC and its quality of service (QoS). To address this issue, we propose a novel scheme to schedule the TNC vehicles while preserving the TNC users’ location differential privacy. Briefly, we add high dimensional Laplace noises to guarantee the TNC users’ geo-indistinguishability. Due to the differential private obfuscation, the demand for TNC vehicles in an area becomes uncertain. Thus, we employ the data-driven approach to characterize users’ demand uncertainty, formulate the TNC's revenue maximization problem into risk-averse stochastic programming, and provide corresponding feasible solutions. Using the released public data of Didi Chuxing, we conduct extensive simulations to evaluate the performance of the proposed scheduling scheme and compare the results under different <inline-formula><tex-math notation="LaTeX">$\zeta$</tex-math></inline-formula> -structure metrics. The results show that the proposed scheme can efficiently schedule the TNC vehicles, maximize the TNC's revenue and provide a better service for TNC users while protecting the TNC users’ location privacy.

Maximizing Revenue With Adaptive Modulation and Multiple FECs in Flexible Optical Networks

Flexible optical networks (FONs) are being adopted to accommodate the increasingly heterogeneous traffic in today’s Internet. However, in presence of high traffic load, not all offered traffic can be satisfied at all time. As carried traffic load brings revenues to operators, traffic blocking due to limited spectrum resource leads to revenue losses. In this study, given a set of traffic requests to be provisioned, we consider the problem of maximizing operator’s revenue, subject to limited spectrum resource and physical layer impairments (PLIs), namely amplified spontaneous emission noise (ASE), self-channel interference (SCI), cross-channel interference (XCI), and node crosstalk. In FONs, adaptive modulation, multiple FEC, and the tuning of power spectrum density (PSD) can be effectively employed to mitigate the impact of PLIs. Hence, in our study, we propose a universal bandwidth-related impairment evaluation model based on channel bandwidth, which allows a performance analysis for different PSD, FEC and modulations. Leveraging this PLI model and a piecewise linear fitting function, we succeed to formulate the revenue maximization problem as a mixed integer linear program. Then, to solve the problem on larger network instances, a fast two-phase heuristic algorithm is also proposed, which is shown to be near-optimal for revenue maximization. Through simulations, we demonstrate that using adaptive modulation enables to significantly increase revenues in the scenario of high signal-to-noise ratio (SNR), where the revenue can even be doubled for high traffic load, while using multiple FECs is more profitable for scenarios with low SNR.

Networked Energy Cooperation in Dual Powered Green Cellular Networks

Designing solar-enabled and power grid connected, ‘dual-powered’, cellular networks is challenging due to the double stochasticity arising from energy harvest and user traffic, resulting in spatio-temporally varying traffic-energy imbalances. Improper strategy to optimize the power grid connectivity results in generation of significant carbon footprint. In this paper, we present an analytical framework to mathematically capture the traffic-energy imbalances in such a dual-powered network and propose to improve the temporal network energy utilization by exploiting these imbalances through a cooperative energy sharing mechanism among the base stations (BSs), via the grid infrastructure itself. The cooperative communication system is designed and optimized independently from two perspectives, namely, grid energy procurement and carbon emission minimization (in carbon free ‘energy producer’ mode) and operator revenue maximization (in ‘energy prosumer’ mode). The energy producer mode involves the BSs, without the flexibility to procure energy and acting as distributed energy source to the power grid. The energy prosumer mode provides additional flexibility of grid energy procurement to the BSs in addition to energy sharing and selling. For a given capital expenditure (CAPEX), both the optimization problems are reformulated into convex quadratic problems and closed form expressions for the optimal quanta of energies to be shared/procured through/from the grid are obtained. The optimal CAPEX for the proposed modes of network operation are obtained via linear revenue maximization problem formulation. The results demonstrate that the proposed cooperative energy framework significantly improves the temporal network energy utilization, thereby reducing the grid energy procurement and providing significant revenue gains compared to the state-of-art.

Robust Revenue Maximization Under Minimal Statistical Information

We study the problem of multi-dimensional revenue maximization when selling m items to a buyer that has additive valuations for them, drawn from a (possibly correlated) prior distribution. Unlike traditional Bayesian auction design, we assume that the seller has a very restricted knowledge of this prior: they only know the mean μ j and an upper bound σ j on the standard deviation of each item’s marginal distribution. Our goal is to design mechanisms that achieve good revenue against an ideal optimal auction that has full knowledge of the distribution in advance. Informally, our main contribution is a tight quantification of the interplay between the dispersity of the priors and the aforementioned robust approximation ratio. Furthermore, this can be achieved by very simple selling mechanisms. More precisely, we show that selling the items via separate price lotteries achieves an O (log r ) approximation ratio where r = max j (σ j /μ j ) is the maximum coefficient of variation across the items. To prove the result, we leverage a price lottery for the single-item case. If forced to restrict ourselves to deterministic mechanisms, this guarantee degrades to O ( r 2 ). Assuming independence of the item valuations, these ratios can be further improved by pricing the full bundle. For the case of identical means and variances, in particular, we get a guarantee of O (log ( r/m )) that converges to optimality as the number of items grows large. We demonstrate the optimality of the preceding mechanisms by providing matching lower bounds. Our tight analysis for the single-item deterministic case resolves an open gap from the work of Azar and Micali (ITCS’13). As a by-product, we also show how one can directly use our upper bounds to improve and extend previous results related to the parametric auctions of Azar et al. (SODA’13).

A Computation Offloading Game for Jointly Managing Local Pre-Processing Time-Length and Priority Selection in Edge Computing

Edge computing has been regarded as an enabling technology for supporting future smart applications, such as industrial Internet of Things. In this paper, a novel computation offloading framework for edge computing is proposed. Unlike existing studies, this work considers that end users can intentionally reserve some time for local pre-processing before requesting the computation offloading service (instead of always declaring their offloading requests immediately when heavy-duty tasks are generated). By doing so, each task’s offloading cost may decrease because of less edge resource demand, while the delay cost may increase due to the later report of its offloading request. Furthermore, end users can select their preferred priority levels in the offloading scheduling by paying premium service charges. To maximize the individual utility, each end user may strategically and jointly determine its local pre-processing time-length and priority selection in computation offloading. For characterizing strategic interactions among end users and the quality-of-service (QoS) of the scheduling system with congested nature, a computation offloading game built upon a queueing model is formulated. On top of this, a revenue maximization problem for the interest of edge operator is also investigated. Simulations evaluate the performance of the proposed solution, and shows its superiority over counterparts.

Can AI Abuse Personal Information in an EV Fast-Charging Market?

In order to alleviate the range anxiety of electric vehicle users (EVUs), several researches focus on facilitating the efficiency of fast-electric vehicle charging stations (fast-EVCSs) using artificial intelligence (AI). This paper first proposes a fast-EVCS revenue maximization pricing policy using an AI approach, and we argue that the AI algorithm can learn to abuse EVUs information for maximizing its revenue. In order to investigate the hypothesis, firstly, a simulation environment is developed using vehicle performance models and an EVU’s charging station selection game. Then, we formulate the charging station revenue maximization problem as a Markov decision process (MDP) and propose a personalized dynamic pricing policy using a model-free reinforcement learning (RL) algorithm. From numerical simulation results, it is found that if the RL approach focuses solely on increasing revenue of the fast-EVCSs, it can learn to misuse personal information without any human intervention. To prevent such abuse, we suggest intuitive guidelines for policymakers and urban planners via numerical experiments.

Dynamic Pricing with Online Reviews

This paper investigates how the pricing policy of a revenue-maximizing monopolist is influenced by the social learning dynamics of customers who use online reviews to estimate the quality of the product. A salient feature of our problem is that the customers’ willingness to pay, and hence the demand function, evolves over time in conjunction with the online reviews. The monopolist strives to maximize its total expected revenue over a finite horizon by adjusting prices in response to these dynamics. The revenue maximization problem is studied using two different review models: a quality-based review model, where customers report their experienced quality, and a value-based review model, where reviews internalize experienced quality as well as the purchase price. To formulate the problem in tractable form, we derive a fluid model that provides a good approximation of the system dynamics when the volume of sales is large. This formulation lends itself to key structural insights into the interactions between optimal pricing policies and review dynamics. In particular, we identify critical time scales and social learning regimes that sharply separate the efficacy of dynamic pricing vis-à-vis fixed-price strategies. Furthermore, we demonstrate the impact of the quality-based and value-based review models on key structural properties of the optimal pricing policies. These structural insights are also elucidated in an illustrative simulation study based on data from an online marketplace. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Supplemental Material: Data and the e-companion are available at https://doi.org/10.1287/mnsc.2022.4387 .

Revenue targeting for a prosumer with storage under gross and net energy metering policies

This paper deals with the revenue targeting for a prosumer with solar photovoltaic generation and storage. We consider inelestic prosumer load demand under time-varying prices for two types of billing policy, namely Net Energy Metering (NEM) and Gross Energy Metering (GEM). The storage enables to exploit the price fluctuations by shifting consumption to off-peak price and generation to peak price instants to get maximum revenue. We propose computationally efficient Dynamic Programming (DP) and Linear Programming (LP) methods to solve the revenue maximization problem. The complexity of both methods is compared with the Mixed Integer Linear Programming (MILP) method. The DP method has better performance under uncertainties and has the potential for processor-based implementation. A Model Predictive Control (MPC) scheme is used for real-time implementation with a rolling horizon. The load, generation, and prices are predicted using seasonal Auto Regressive Moving Average (ARMA) models.The results show that the value of storage exhibits a minimum at a certain selling to buying price ratio under NEM policy. Moreover, the fast charging batteries earn higher revenue than the slower ones. However, fast-charging batteries are also more vulnerable to uncertainties. Therefore, we advocate the appropriate derating of the battery power capacity to hedge against uncertainties. The techno-economic analysis reveals that the battery will become an attractive option for lower ratios of selling to buying price in near future.

Quality-speed trade-offs in customer-intensive services with boundedly rational customers and retrials

We consider a system in which one server provides customer-intensive services and the service reward increases in the length of service time. However, longer service times also lead to longer waits for customers and more congestion for the system. Considering the trade-off between the service speed and service quality, in this paper, we investigate the optimal service speed and service fee from the perspectives of revenue maximization and social welfare maximization. The customers are boundedly rational and decide whether to join the system or not according to a logit model. We find that under the revenue maximization, a decrease in the degree of rationality can alleviate congestion, but harms the social welfare. If the social planner determines the service speed and price directly, we show that bounded rationality is detrimental to service managers but beneficial to customers, while social welfare remains constant. Defining the ratio between the social welfare under the revenue-optimal strategy and socially optimal strategy as the price of anarchy (PoA), which quantifies the inefficiency of the strategy of the service provider, we obtain its upper bound and lower bound and demonstrate that the PoA is decreasing when customers become more boundedly rational and the sign of customer’s actual utility is determined by both the level of customer rationality and retrial rate. Moreover, when customers are heterogeneous in terms of perceiving service, we classify customers into two classes and the revenue maximization problem is investigated through the Particle Swarm Optimization algorithm.

Deep Learning Based Auction-Driven Beamforming for Wireless Information and Power Transfer

In this paper, we design a deep learning based resource allocation framework, in the form of an auction, for simultaneous information and power transfer from a hybrid access point (AP) to information devices and energy harvesting devices, respectively. Using Myerson’s lemma and the concept of virtual welfare maximization, we develop an optimal dominant-strategy incentive-compatible mechanism for the AP to maximize its expected revenue, based on the devices’ bid profiles, valuation distributions, demand profiles, and channel state information. In so doing, we formulate the revenue maximization problem, which is a mixed-integer non-linear program, and propose an efficient Branch-and-Bound (BnB) algorithm to solve the problem using semidefinite relaxation technique in each branch. Since the problem has exponential time complexity, using BnB algorithms can be impractical for real-time applications. To circumvent this, a deep neural network (DNN) is proposed, and trained to predict the optimal mechanism for beamforming the data and the energy towards the information and energy devices, respectively. We use the BnB algorithm to solve the problem offline and populate the training dataset. The proposed DNN architecture is indeed a multi-layer perceptron, which is trained well to map the heterogeneous input to the desired output with high accuracy. Furthermore, we propose a heuristic iterative solution whose accuracy performance is comparable to that of the DNN-based solution. The heuristic solution has polynomial time complexity whereas the DNN-based solution has linear time complexity.

Data Boundary and Data Pricing Based on the Shapley Value

Data pricing is to price data as asset to promote the healthy development of data share, exchange, and reuse. However, the uncertain value index and neglection of interactivity lead to information asymmetry in the transaction process. A perfect data pricing system and a well-designed data market can widely promote data transactions. We take a three-agent data market in this paper, the data owner who provides the data record, the model buyer who is interested in buying machine learning (ML) model instances, and the broker who interacts between the data owner and the model buyer. Two interaction scenarios are defined. In scenario 1, we introduce the Shapley value (SV) to measure values of data records fairly and construct a revenue optimization problem based on the sum of the SV for data boundary. The optimal solution is obtained by calculating their derivatives. In scenario 2, we utilize market research and construct a revenue maximization (RM) problem to price the ML models. Further, An Integer Linear Programming for the RM problem (RM-ILP) process is proposed to transform the RM problem into an equivalent integer linear programming (ILP) problem and solve it with the Gurobi solver. Finally, we conduct extensive experiments, which validate that the RM-ILP process can provide high revenue to the broker and high affordability to the model buyers compared to the benchmarks.

Revenue Maximization Through Cell Switching and Spectrum Leasing in 5G HetNets

Even though dynamic cell switching is a prominent approach for energy optimization in heterogeneous wireless communication networks, it results in spectrum under-utilization as the spectrum originally occupied by the base stations that are turned off remain dormant. In order to make the businesses of primary network (PN) operators, who hold the spectrum license, more profitable and sustainable as well as to avoid spectrum under-utilization, this dormant spectrum can be leased to the secondary network (SN) operators who cannot afford to purchase the spectrum license. In this study, first, the cell switching problem, which solely focuses on the amount of energy saved, is translated to a problem of revenue maximization by including the spectrum leasing concept and converting the energy saving to monetary saving from reduced electricity bills. In this regard, two spectrum demand scenarios are considered for the SN operator: delay tolerant (DT), for non-real time applications, and non-delay tolerant (NDT), for real time applications. Then, a cell switching and spectrum leasing framework based on simulated annealing algorithm is developed to maximize the revenue of the PN while respecting the quality-of-service constraints. The simulation results reveal that the DT spectrum demand is more beneficial to both PN and SN operators as it results in greater revenue for the former while the latter is able to access more spectrum to meet higher service demands. This finding suggests that if the application can tolerate delays, then it makes more sense for both PN and SN to adopt the DT scenario. In addition, it is observed that the performance of the proposed framework is very close to that of the optimal solution with a significant reduction in the computation complexity.

Optimal pricing and seat allocation schemes in passenger railway systems

This paper examines optimal pricing and seat allocation schemes in passenger railway systems, where ticket pricing and seat allocation (or capacity allocation) are both Origin-Destination specific. We consider that the demand is sensitive to the ticket price, and a non-concave and non-linear mixed integer optimization model is then formulated for the ticket pricing and seat allocation problem to maximize the railway ticket revenue. To find the optimal solution of the ticket revenue maximization problem effectively, the proposed non-concave and non-linear model is reformulated such that the objective function and constraints are linear with respect to the decision variables or the logarithms of the decision variables. The linearized model is then further relaxed as a mixed-integer programing problem (MILP). Based on the above linearization and relaxation techniques, a globally optimal solution can be obtained by iteratively solving the relaxed MILP and adopting the range reduction scheme. Two numerical examples are presented for illustration.

A stochastic model for the optimal allocation of hydropower flexibility in renewable energy markets

This paper considers the revenue maximization problem for a hydropower company. The company can generate excess electricity by releasing water from a reservoir and then sell it to the energy market. On the other hand, the company has an obligation to keep the reservoir level above a pre-determined level, which may require the company to purchase electricity in order to fulfill the customers’ power demand. The electricity price and reservoir level are both represented by diffusion processes. We refer to a one-factor diffusion model for electricity price, which is known to fit the data well. After applying Bellman dynamic programming principle, we derive the associated state-constrained Hamilton-Jacobi-Bellman (HJB) equation to characterize the value function. Then we prove that the value function is the viscosity solution of the state-constrained HJB equation and it is unique in this constrained optimization problem.

Network Operator Revenue Maximization in Dual Powered Green Cellular Networks

Traffic-energy imbalance poses a major challenge on enabling of green-communication through dual-powered green networks, which are becoming increasingly attractive due to their cost efficiency and low carbon footprint. Dual-powered networks are prone to traffic-energy imbalance mainly due to spatio-temporal traffic variation and random solar energy harvest. Thus, it becomes imperative to study the effects of this traffic-energy imbalance in green networks and to formulate network operation strategies. We present an analytical framework for computing the operator’s revenue while fulfilling the users’ service guarantee. The revenue maximization problem is solved algorithmically through proposed network operation and green energy allocation strategies. The network is subjected to heterogeneous skewed traffic of varying degrees and operated using two distinct strategies, the conventional without coverage adjustment (WCA) and the proposed cooperative coverage adjustment (CCA) model. In the conventional WCA model the cells do not dynamically adjust their coverage areas, whereas the proposed CCA model involves the radio network controller (RNC) for adjusting the cell coverage areas based on traffic load and energy availability. Our analysis and simulation results demonstrate that the proposed CCA model is highly effective in addressing traffic-energy imbalance at the cellular level and significantly improves the revenue as compared to the conventional WCA model. Our results demonstrate that with the proposed CCA model, the revenue gain increases with an increase in traffic skewness. For example, it provides a gain up to 61% under high (80%) traffic skewness while serving about 25% of more users.

Towards Revenue Maximization with Popular and Profitable Products

Economic-wise, a common goal for companies conducting marketing is to maximize the return revenue/profit by utilizing the various effective marketing strategies. Consumer behavior is crucially important in economy and targeted marketing, in which behavioral economics can provide valuable insights to identify the biases and profit from customers. Finding credible and reliable information on products’ profitability is, however, quite difficult since most products tend to peak at certain times w.r.t. seasonal sales cycles in a year. On-Shelf Availability (OSA) plays a key factor for performance evaluation. Besides, staying ahead of hot product trends means we can increase marketing efforts without selling out the inventory. To fulfill this gap, in this paper, we first propose a general profit-oriented framework to address the problem of revenue maximization based on economic behavior, and compute the O n-shelf P opular and most P rofitable P roducts (OPPPs) for the targeted marketing. To tackle the revenue maximization problem, we model the k-satisfiable product concept and propose an algorithmic framework for searching OPPP and its variants. Extensive experiments are conducted on several real-world datasets to evaluate the effectiveness and efficiency of the proposed algorithm.

Resource Pricing and Demand Allocation for Revenue Maximization in IaaS Clouds: A Market-Oriented Approach

With more users outsourcing their applications to the cloud, resource pricing becomes an important issue for IaaS cloud management. Jointly considering her own bidding budget and the price of cloud resources, each user is self-motivated to purchase cloud resources according to her resource demand which maximizes her own utility. Meanwhile, the cloud service provider (CSP) regulates the price of cloud resources with a certain profitability objective achieved. With an elaborate resource pricing strategy, the goals from users and the CSP are balanced and respectively satisfied to some extent. This article provides an insight into the market-oriented cloud pricing strategy. In specific, we propose an auction market in the IaaS cloud, where multiple users with heterogeneous bidding budgets and QoS requirements subscribe cloud resources according to their resource demands. The resource pricing and demand allocation scheme targeting revenue maximization also satisfies essential properties including budget feasibility, incentive compatibility and envy-freeness. To attack the NP-hardness and non-convexity of revenue maximization problem, we design a price-incentive resource auction mechanism namely RARM, which preserves an ( 1+α) approximation ratio on revenue maximization. Finally, we evaluate our RARM mechanism based on the real-world dataset to certify the efficacy of our proposed approach.