Profit Maximization Problem Research Articles

A Reinforcement Learning Approach to Optimize Discount and Reputation Tradeoffs in E-commerce Systems

Feedback-based reputation systems are widely deployed in E-commerce systems. Evidence shows that earning a reputable label (for sellers of such systems) may take a substantial amount of time, and this implies a reduction of profit. We propose to enhance sellers’ reputation via price discounts. However, the challenges are as follows: (1) The demands from buyers depend on both the discount and reputation, and (2) the demands are unknown to the seller. To address these challenges, we first formulate a profit maximization problem via a semi-Markov decision process to explore the optimal tradeoffs in selecting price discounts. We prove the monotonicity of the optimal profit and optimal discount. Based on the monotonicity, we design a Q-learning with forward projection (QLFP) algorithm, which infers the optimal discount from historical transaction data. We prove that the QLFP algorithm convergences to the optimal policy. We conduct trace-driven simulations using a dataset from eBay to evaluate the QLFP algorithm. Evaluation results show that QLFP improves the profit by as high as 50% over both Q-learning and Speedy Q-learning. The QLFP algorithm also improves both the reputation and profit by as high as two times over the scheme of not providing any price discount.

Transmission Network Investment Using Incentive Regulation: A Disjunctive Programming Approach

A well-planned electric transmission infrastructure is the foundation of a reliable and efficient power system, especially in the presence of large scale renewable generation. However, the current electricity market designs lack incentive mechanisms which can guarantee optimal transmission investments and ensure reliable integration of renewable generation such as wind. This paper first proposes a stochastic bilevel disjunctive program for optimal transmission investment based on the newly proposed theoretical H-R-G-V incentive mechanism. The upper level is a profit-maximization problem of an independent transmission company (Transco), while the lower level is a welfare maximization problem. The revenue of the Transco is bounded by a regulatory constraint set by the regulator in order to induce socially optimal investments. The application of the H-R-G-V mechanism allows the regulator to ensure social maximum transmission investments and helps to reduce transmission congestion and wind power spillage. The transmission investment under the H-R-G-V mechanism is modeled as a stochastic bilevel disjunctive program. To solve the developed mathematical model we first propose a series of linearization and reformulation techniques to recast the original model as a stochastic mixed integer linear problem (MILP). We exploit the disjunctive nature of the reformulated stochastic MILP model and further propose a Bean decomposition algorithm to efficiently solve the stochastic MILP model. The proposed decomposition algorithm is also modified and accelerated to improve the computational performance. The computational performance of our MILP modeling approach and modified and accelerated Bean decomposition algorithm is studied through several examples in detail. The simulation results confirm a promising performance of both the modeling approach and its solution algorithm.

An Efficient Algorithm for Dynamic Pricing Using a Graphical Representation

We study a multi‐period, multi‐item dynamic pricing problem faced by a retailer. The objective is to maximize the total profit by choosing prices, while satisfying several business rules. The strength of our work lies in our graphical model reformulation, which allows us to use ideas from combinatorial optimization. We do not make any assumptions on the structure of the demand function. The complexity of our method depends linearly on the number of time periods but is exponential in the memory of the model (number of past prices that affect current demand) and in the number of items. We prove that the profit maximization problem is NP‐hard by showing an approximation preserving reduction from the weighted Max‐3‐SAT problem. We next introduce the discrete reference price model which is a discretized version of the reference price model, accounting for an exponentially smoothed contribution of all past prices. We show that our problem can be solved efficiently under this model. We then approximate common demand functions using the discrete reference price model. To handle cross‐item effects among multiple items, we propose to use a virtual reference price that assigns a reference price for each category of items (as opposed to a reference price for each item). To enhance the tractability of our approach, we cluster items into blocks and show how to adapt our method to include business constraints across blocks. Finally, we apply our solution approach using demand models calibrated with supermarket data and validate its practical performance.

Less is More: Service Profit Maximization in Geo-Distributed Clouds

Nowadays cloud providers purchase a good deal of bandwidth from Internet service providers to satisfy the growing requests from corporate customers for the exclusive use of inter-datacenter bandwidth. For exclusive bandwidth services, neither maximizing the revenue nor minimizing the cost can bring the maximal profit to cloud providers. The diversity of bandwidth prices and the random arrival time of user requests further increase the difficulty in economically scheduling the services to meet user requests from cloud providers. In this article, we propose to help cloud providers maximize their service profits by properly selecting user requests to serve rather than satisfying them all. We formulate the problem of service profit maximization and prove its NP-hardness. To handle offline request submission, we propose a solution that maximizes the service profit by alternately maximizing the service revenue and minimizing the service cost. To maximize service profit under online request submission, we propose an online scheduling algorithm that carefully handles the risk of not being able to pay off the incremental service cost and makes scheduling decisions in real time. Our extensive evaluations demonstrate that our solutions can achieve more than 1.6x the service profits of existing solutions.

Constraint aware profit maximization scheduling of tasks in heterogeneous datacenters

The extensive use of cloud services in different domains triggers the efficient use of cloud resources to achieve maximum profit. The heterogeneous nature of data centers and the heterogeneous resource requirement of user applications create a scope of improvement in task scheduling. The resource requirements in terms of task constraints must be fulfilled for the tasks to be admitted to the system. Once a task admitted to the system, it may violate service level agreement and incurs penalty due to the disproportionate resource allocation at run time. The latency-sensitive and short-lived workloads need effective scheduling to gain more profit. In this work, we propose Heuristic of Ordering and Mapping for Constraint Aware Profit Maximization (HOM-CAPM) problem for efficient scheduling of tasks with constraints and deadlines to gain maximum profit. The HOM-CAPM approach considers estimation of task execution time in a heterogeneous environment, efficient task ordering, and profit-based task allocation to maximize the overall profit of the cloud system. To gain maximum profit the proposed heuristic considers two cases, (a) not allowing the tasks for execution if it expected to miss its deadline and (b) allowing the task which earns substantial profit even though it is expected to miss its deadline. The results of the extensive simulation using Google trace data as input show that our proposed HOM-CAPM approach generates more profit than other state-of-the-art approaches.

Reducing Product Expiration by Aligning Salesforce Incentives: A Data‐driven Approach

Product expirations at retail stores erode profits and burden the environment. We investigate whether manufacturers can leverage salesforce compensation design as a waste‐reduction tool. We propose a data‐driven framework that uses structural econometric modeling and agency theory. Our analysis starts with a game theoretic model in which a salesperson interacts with a manufacturer that reimburses retailers and penalizes its own salesforce for expired products. We then use our model’s equilibrium outcome to estimate factors that determine the effort exerted by the sales representatives of a consumer‐packaged‐goods manufacturer. We first show theoretically that a manufacturer can simultaneously increase profits and reduce waste by increasing its sales representatives’ penalty for product expiration that occurs at the retailer. Based on this, we formulate a manufacturer’s profit maximization problem to compute optimum expiration penalties. Solving this problem for the manufacturer, we find the potential to simultaneously reduce waste and improve profits for 14% of the product–market combinations in our dataset. For these cases, we find that charging the salesperson 2.1 times the commission (on average) for each expired unit can increase the manufacturer’s profits by 0.58% and reduce waste by 23.3%. This study determines that a profit‐seeking manufacturer can reduce waste at retailers by optimizing its salesforce incentive structure. Our work bridges the salesforce compensation and sustainable operations literatures. Furthermore, our framework allows consumer‐packaged‐goods manufacturers to identify win‐win opportunities for the environment and their bottom line.

Discount advertisement in social platform: algorithm and robust analysis

As a marketing strategy, discount promotion is adopted by plenty of companies, which can be regarded as a variant of the previous Profit Maximization (PM) problem. Based on a discount-based marketing scenario, we propose a Profit Maximization with Discount Advertisement (PMDA) problem. Then, we show that the objective function of PMDA is submodular but not monotone, which can be categorized as an instance of Unconstrained Submodular Maximization problem. Even that similar problem has been studied before, the approximation performance is not satisfactory. Learned from the latest results, we combine the idea of greedy algorithm and randomized double greedy algorithm to solve our problem, which overcomes the shortcomings of both and obtains a more acceptable approximation ratio. It can be used as a general algorithmic framework. Moreover, the existing researches about PM only considered to maximize total profit based on certain diffusion probabilities. Because of the uncertainty of diffusion probabilities, we study the robustness of PMDA and propose Robust-PMDA problem further. It aims to acquire the maximum worst ratio between the profit of selected seed set and the optimal seed set. To solve the Robust-PMDA, we design LU-PMDASolver algorithm first, and then, we propose P-UniSampling algorithm to improve the robustness by reducing the uncertainly of diffusion probabilities, which is implemented by the technique of uniform sampling. Finally, the correctness and performance of our proposed algorithms are verified by conducting experiments on real-world social networks.

Budgeted Coupon Advertisement Problem: Algorithm and Robust Analysis

Coupon advertisement is everywhere in people's daily lives, and it is a common marketing strategy adopted by merchants. A problem, Budget Profit Maximization with Coupon Advertisement, is formulated in this article, which is a branch of classical profit maximization problem in social networks. Profit maximization has been researched intensively before, but its theoretical bound is not satisfactory usually because of NP-hardness, budget constraint and non-monotonicity. Learned from the lastest results, we proposed the B-Framework, which combines the ideas of Random Greedy and Continuous Double Greedy to obtain a more acceptable approximation ratio for this problem. For Continuous Double Greedy, it can be implemented by multilinear extension and discretized techniques. In addition, most of existing researches consider only maximizing total profit, however, in real scenarios, the diffusion probability is hard to determine due to the uncertainty. Then, we study the robustness for budgeted profit maximization, which can be used as a general strategy to analyze the robustness of non-monotone submodular function. It aims to obtain the best solution maximizing the ratio between the profit of any feasible seed set and the optimal seed set. We design LU-B-Framework first, and then we apply the method of uniform sampling to improve the robustness by reducing the uncertainty. The effectiveness and correctness of our algorithms are evaluated by heavy simulation on real-world social networks eventually.

A Stackelberg Game Pricing Through Balancing Trilateral Profits in Big Data Market

With the popularity of the Internet of Things (IoT) and large-scale deployment of sensors, data have exploded. Big data is utilized to extract useful knowledge and information and served as data services to consumers. While most of the current researches in the field of big data services focus on developing and improving algorithms for data mining and information extraction, and rarely studies “big data” from an economic perspective. This article thus studies the pricing and profit maximization problems in big data markets from an economic perspective. First, a method of quantifying the value of data is proposed to study the utility of raw data. Then, we build an economic model of the data market, which consists of three parties: 1) data vendor; 2) service provider; and 3) service users. The data vendor gathers various raw data and sells them to the service provider. The raw data are further processed into data services by a service provider, who provides service subscriptions to users to obtain profits. The interactions among them are formulated as a Stackelberg game to maximize the profits of all participators. The existence and uniqueness of equilibria pricing strategies are proved. Finally, numerical results show that the participators of the data market can achieve the maximum profit through the proposed pricing mechanism and economic model.

Geography-Aware Task Scheduling for Profit Maximization in Distributed Green Data Centers

Infrastructure in Distributed Green Data Centers (DGDCs) is concurrently shared by multiple different applications to flexibly provide a growing number of services to global users in a cost-effective way. A highly challenging problem is how to maximize the total profit of the DGDC provider in a market where Internet Service Provider (ISP) bandwidth price, availability of green energy, price of power grid, and revenue brought by the execution of tasks all vary with geographical locations. Unlike existing studies, this article proposes a Geography-Aware Task Scheduling (GATS) approach by considering spatial variations in DGDCs to maximize the total profit of the DGDC provider by intelligently scheduling tasks of all applications. In each time slot, the formulated profit maximization problem is solved as a convex optimization one via the interior point method. Trace-driven simulations show that GATS achieves larger total profit and higher throughput than two typical task scheduling approaches.

Robust Online Composition, Routing and NF Placement for NFV-Enabled Services

Network function virtualization (NFV) fosters innovation in the networking field and reduces the complexity involved in managing modern-day conventional networks. Via NFV, the provisioning of a network service becomes more agile, whereby virtual network functions can be instantiated on commodity servers and data centers on demand. Network functions can be either mandatory or best-effort. The former type is strictly necessary for the correctness of a network service, whereas the latter is preferrable yet not necessary. In this paper, we study the online provisioning of NFV-enabled network services. We consider both unicast and multicast NFV-enabled services with multiple mandatory and best-effort NF instances. We propose a primal-dual based online approximation algorithm that allocates both processing and transmission resources to maximize a profit function, subject to resource constraints on physical links and NFV nodes. The online algorithm resembles a joint admission mechanism and an online composition, routing and NF placement framework. The online algorithm is derived from an offline formulation through a primal-dual based analysis. Such analysis offers direct insights and a fundamental understanding on the nature of the profit-maximization problem for NFV-enabled services with multiple resource types.

Markets for Goods with Externalities

I consider the welfare and profit maximization problems in markets with externalities. I show that when externalities depend generally on allocation, a Pigouvian tax is often suboptimal. Instead, the optimal mechanism has a simple form: a finite menu of rationing options with corresponding prices. I derive sufficient conditions for a single price to be optimal. I show that a monopolist may ration less relative to a social planner when externalities are present, in contrast to the standard intuition that non-competitive pricing is indicative of market power. My characterization of optimal mechanisms uses a new methodological tool—the constrained maximum principle—which leverages the combined mathematical theorems of Bauer (1958) and Szapiel (1975). This tool generalizes the concavification technique of Aumann and Maschler (1995) and Kamenica and Gentzkow (2011), and has broad applications in economics.

Maximization of Unit Present Profit in Inventory Management Systems

We consider a profit maximization model for a trading company taking into account the intensity of the sale of goods and the costs of purchase, delivery, storage and sale, as well as the possibility of alternative placement of free capital. We show that the profit function, depending on the period of delivery of the goods, has a single maximum point. We construct a model and develop algorithms for solving the profit maximization problem in multinomenclature systems with bounded floating capital.

Multi-Item Auction Based Mechanism for Mobile Data Offloading: A Robust Optimization Approach

The opportunistic utilization of access devices to offload mobile data from cellular network has been considered as a promising approach to cope with the explosive growth of cellular traffic. To foster this opportunistic utilization, we consider a mobile data offloading market where mobile network operator (MNO) can sell bandwidth made available by the access points (APs) to increase MNO's profit. We formulate the offloading problem as a multi-item auction and study MNO's profit maximization problem. We discuss the conditions to (i) offload the maximum amount of data traffic, (ii) foster the participation of mobile subscribers (MSs) (individual rationality), (iii) prevent market manipulation (incentive compatibility) and (iv) preserve budget feasibility of MSs. Then, we propose a robust optimization based method to implement multi-item auction mechanism. We further propose two iterative algorithms that efficiently solve the offloading problem. The simulation results show the efficiency and robustness of our proposed methods for cellular data offloading.

Optimal pricing strategy of power‐retailing companies considering demand response in block bidding markets

Block bidding market (BBM) is a new electricity market mode in the day-ahead market, which is in the stage of development and promotion in China. It is based on the idea that energy should have the same price according to the continuous duration of load. In this study, the authors propose an optimisation model of pricing and purchasing strategy for power-retailing companies in BBMs, based on bilateral contracts with customers and portfolio management of demand response resources. The model consists of an expected profit maximisation problem of supplying energy to end-customers, and a total cost minimisation problem concerning the dispatching of fixed loads and shiftable loads. The proposed model is formulated as a bi-level mixed-integer non-linear program. A load division method is proposed to get better division result by eliminating duration restrictions on divided blocks. The proposed approximate solving algorithm overcomes the diculties in linearisation and gets rid of the inuence of initial value. The strategy is applied to an actual case and is simulated based on real data. Simulation results show that the proposed model has great peak-shaving effects, and can effectively bring more profit to the power-retailing companies while reducing electricity bills of customers.

Efficient solving of strategic bidding issues under no Karush–Kuhn–Tucker optimality constraints

A typical bidding procedure is to maximize the profit of the strategic producers, in a manner that the offer curve yields solutions to the ISO marketing clearing problem. The literature portrays the procedure in the form of a searching problem with dual levels, wherein the minimization of the market clearing function along with profit maximization is yielded using the offer curve. But, the elevated levels of complexity in computing and solving the bi-level searching problem have forced the researchers to transform it as a one-level maximization problem through employing Karush–Kuhn–Tucker (KKT) optimality conditions. Yet, serious problems emerge with the profit maximization algorithms incorporating KKT optimality conditions (for instance, the classical optimization algorithms). The complexity grows in size, if the transmission constraints get vital in the deregulated environment. Our research contribution devises the profit maximization problem to be a minimization function, lacking consideration on KKT optimality conditions for the ISO market clearing functions, the operating limits and the transmission constraints. A modified form of group search optimizer (GSO), one of the currently popular optimization algorithms, provides solutions to the developed model. The conventional GSO, an optimization algorithm that operates using population, has its motivation from the animals’ searching activities. The modified GSO changes the maximum pursuit angle of the animal searching activity relative to the number of iterations. The testing of the proposed method employs both the IEEE 30 bus system as well as the IEEE 14 bus system. Performance comparison among the proposed method, the strategic bidding approaches that rely on the particle swarm optimization, the genetic algorithm and the GSO reveal excessive profit maximization and superiority for the proposed method.

Day-ahead profit-based reconfigurable microgrid scheduling considering uncertain renewable generation and load demand in the presence of energy storage

Due to the penetration of renewable energy sources (RESs) with probabilistic natures into microgrids (MGs), optimal scheduling and reconfiguration (RG) processes are associated with uncertainty. This paper presents the stochastic profit-based optimal day-ahead scheduling of a reconfigurable microgrid (RMG) as a new generation of the conventional microgrid. The proposed algorithm finds the optimal RMG's topology from the profit maximization point of view, the optimal hourly MG's unit set-points like micro-turbines (MTs) and energy storage, and power exchange with the main grid, simultaneously. The generated power of wind turbine (WT) and PV panel, as well as load demand are considered as uncertain parameters. To solve the profit maximization problem of RMG, time-varying acceleration coefficients particle swarm optimization (TVAC-PSO) algorithm is employed. Also, to ensure simulation accuracy in the presence of high-level uncertainties, the autocorrelation model is used based on actual data for the uncertainty of renewable power output. The feasibility and applicability of the proposed framework are demonstrated on a 69-bus radial RMG with various distributed generators in different cases. The results show the effectiveness of the proposed model.

Strategic offering of a flexible producer in day-ahead and intraday power markets

The increase in intraday electricity market volumes due to intermittent renewable generation may give a strategic producer an opportunity to exert market power. We study offering strategies of a flexible producer in day-ahead and intraday markets using a bi-level model in which the upper level represents the profit-maximization problem of the producer and the lower-level problems clear the day-ahead and intraday markets sequentially. Using a three-node network, we first demonstrate that a flexible producer with perfect forecasts can increase its profit in both markets by coordinating its offer so as to cause transmission grid congestion or lack of competitive generation capacity. Moreover, we show that strategic behavior is possible even when the day-ahead and intraday markets are cleared simultaneously to lower balancing costs. We next assess these market designs in a Nordic test network and offer an explanation for high Nordic intraday prices. Finally, via an annual simulation using the Nordic market data, we verify that strategic offering in day-ahead and intraday markets under imperfect forecasts leads to increased profits vis-à-vis perfect competition but are mitigated through simultaneous market clearing.

Optimal production allocation of load-following nuclear units in an electricity market in the early stages of competition

Electricity systems are quitting monopoly for an operation framed by competitive markets. It therefore questions how the operation of nuclear plants capable of load-following is expected to change at the transition stage in a challenging economic environment for nuclear producers given the high penetration of renewables and the increase of nuclear production costs for renovation and safety reasons. To answer this question, we are focusing on a month-by-month management horizon of the nuclear fuel given the technico-economical features of the operation of flexible nuclear plants. The resolution of the month-by-month profit maximization problem contributes to identify potential difficulties and limits of production optimization and provides us with an equilibrium which proves the existence of an optimal production path. This benchmark could serve as a reference providing valuable insight on the resolution of more complex optimisation problems.

Analysis of Profit Maximization Problem in Multiperiod Energy Markets with Uncertain Photovoltaics Power

We formulate and analyze a profit maximization problem for one participant (aggregator) in a multiperiod electricity market with the consideration of profit fluctuations caused by uncertain photovo...