Pricing Algorithm Research Articles

The multi-trip container drayage problem with synchronization for efficient empty containers re-usage

We study a typical daily drayage problem concerning the last-mile logistics at seaports for inland container supply chains. A set of trucks available at an inland container terminal must fulfil shippers’ requests of transporting containers within time windows and, to do so, can perform multiple daily trips. A request may entail picking up or delivering containers either at the shippers’ premises, the inland terminal or the seaport. Demand for empty containers can be satisfied by either using the available limited stock at the inland terminal, by street-turning or, ultimately, by retrieving them at a local depot for empties resulting in extra mileage. Hence, the minimization of routing costs also entails synchronizing trucks’ trips that retrieve and add empty containers to the inland terminal stock to avoid unnecessary visits to the empty depot. After modelling the problem mathematically, we develop an exact column-and-row generation approach embedded in a branch-and-price framework. To accelerate the solving process of the pricing problem, we propose effective strategies by combining a set of tailored pricing algorithms. These strategies perform well on a set of adapted Solomon’s instances up to 100 nodes and against a standard branch-and-cut solver. Finally, experiments on real-world instances, inspired by a case study of an inland terminal at the Port of Rotterdam region, provide insights into current planning practices.

P2P Multigrade Energy Trading for Heterogeneous Distributed Energy Resources and Flexible Demand

This paper proposes a novel peer-to-peer (P2P) multi-grade energy trading design to encourage demand side flexibility to locally absorb the uncertainty of renewable distributed energy resources (DERs) in distribution networks. In particular, a reliability credit (RC) assignment method is developed for customers to differentiate the energy grades considering the heterogeneity in energy supplying reliability of DERs and the consumption preferences of customers. Later, an innovative P2P multi-grade energy trading model is introduced where different types of demand are matched up with the corresponding grades of energy. The market clearing is modeled as a social welfare maximization problem considering the net utilities of customers and the profits of DER producers. Furthermore, a fast decentralized pricing algorithm is developed that achieves the maximum of social welfare and also preserves the privacy of individual participants. To substantially improve the computational efficiency, a fast solution method is devised for customers to solve the optimal energy procurement combination problem, and closed-form solutions are derived for DER producers to allocate energy optimally. Numerical tests on a 69-node distribution feeder validate the superiority of the proposed P2P multi-grade energy trading scheme compared to the benchmark scheme. The high efficiency and scalability of the proposed fast pricing algorithm are corroborated by the simulation on the IEEE 8500-node distribution system.

Blockchain-Based Resource Trading in Multi-UAV-Assisted Industrial IoT Networks: A Multi-Agent DRL Approach

With the Industrial Internet of Things (IIoT), mobile devices (MDs) and their demands for low-latency data communication are increasing. Due to the limited resources of MDs, such as energy, computation, storage, and bandwidth, IIoT systems cannot meet MDs’ quality of service (QoS) and security requirements. Recently, UAVs have been deployed as aerial base stations in the IIoT network to provide connectivity and share resources with MDs. We consider a resource trading environment where multiple resource providers compete to sell their resources to MDs and maximize their profit by continually adjusting their pricing strategies. Multiple MDs, on the other hand, interact with the environment to make purchasing decisions based on the prices set by resource providers to reduce costs and improve QoS. We propose a novel intelligent resource trading framework that integrates multi-agent deep reinforcement Learning (MADRL), blockchain, and game theory to manage dynamic resource trading environments. A consortium blockchain with a smart contract is deployed to ensure the security and privacy of the resource transactions. We formulated the optimization problem using a Stackelberg game. However, the formulated optimization problem in the multi-agent IIoT environment is complex and dynamic, making it difficult to solve directly. Thus, we transform it into a stochastic game to solve the dynamics of the optimization problem. We propose a dynamic pricing algorithm that combines the Stackelberg game with the MADRL algorithm to solve the formulated stochastic game. The simulation results show that our proposed scheme outperforms others to improve resource trading in UAV-assisted IIoT networks.

Stackelberg game-based dynamic resource trading for network slicing in 5G networks

Network slicing (NS) has been envisioned as the main technology in 5G to accommodate different virtualized operators with versatile service requirements, on a common substrate infrastructure. NS has come to radically reform the interaction among different entities in the resource sharing market, where resource is exchanged for monetary gains as a way of ensuring efficient resource utilization. However, resource exchange is only attractive to entities if they are able to achieve their respective benefits in a win–win situation. In this paper, we design an economic model that analyzes the pricing and purchasing interaction between multiple mobile virtual network operators (MVNOs) and their respective users for resource trading in NS. We formulate the pricing and purchasing problem as a two-stage multi-leader multi-follower (MLMF) Stackelberg game where the MVNOs as leaders set their unit price first, and then users as followers respond by determining their purchasing volume. Then, we theoretically prove the existence and uniqueness of a Nash equilibrium (NE). To obtain an optimal dynamic pricing solution for the MVNOs, we transform the game-based optimization problem into a stochastic Markov decision process (MDP) problem and propose a method based on multi-agent dueling deep Q-Network (DQN) algorithm. Simulation results show that the proposed algorithm achieves convergence under competitive pricing scheme (CPS) and independent pricing scheme (IPS), while ensuring high MVNOs’ profit and users’ utility at acceptable levels. In terms of cumulative profits, the proposed dueling DQN-based pricing algorithm achieves percentage gains of 15.3%, 30.4%, and 71.4% against Q-learning-based pricing, premium pricing, and undercut pricing algorithms as benchmarks.

Stackelberg game-based task offloading and pricing with computing capacity constraint in mobile edge computing

The task offloading technology in mobile edge computing can improve the benefits of each device. Moreover, designing reasonable prices for computing resources is critical to balancing the interests of end servers and devices. However, unbalanced information availability complicates this issue. To address this problem, the Stackelberg game is introduced to describe the relationship between the MEC server and end users (EUs). Then, the task offloading decision problem of EUs is simplified and proved by derivation. Last, uniform pricing and differentiated pricing algorithms are proposed. The differentiated pricing strategy is proposed by the PSO-based pricing optimization algorithm (DPOA), which can precisely constrain the offloading of each EU. Simulation results show the DPOA effectively improve profit of the server, and reduce latency of EUs.

A Review of Common Techniques for Visual Simultaneous Localization and Mapping

Mobile robots are widely used in medicine, agriculture, home furnishing, and industry. Simultaneous localization and mapping (SLAM) is the working basis of mobile robots, so it is extremely necessary and meaningful for making researches on SLAM technology. SLAM technology involves robot mechanism kinematics, logic, mathematics, perceptual detection, and other fields. However, it faces the problem of classifying the technical content, which leads to diverse technical frameworks of SLAM. Among all sorts of SLAM, visual SLAM (V-SLAM) has become the key academic research due to its advantages of low price, easy installation, and simple algorithm model. Firstly, we illustrate the superiority of V-SLAM by comparing it with other localization techniques. Secondly, we sort out some open-source V-SLAM algorithms and compare their real-time performance, robustness, and innovation. Then, we analyze the frameworks, mathematical models, and related basic theoretical knowledge of V-SLAM. Meanwhile, we review the related works from four aspects: visual odometry, back-end optimization, loop closure detection, and mapping. Finally, we prospect the future development trend and make a foundation for researchers to expand works in the future. All in all, this paper classifies each module of V-SLAM in detail and provides better readability to readers. This is undoubtedly the most comprehensive review of V-SLAM recently.

A column generation-based heuristic for brachytherapy patient scheduling with multiple treatment sessions considering radioactive source decay and time constraints

Imbalanced and inefficient schedules of brachytherapy treatment result in long waiting times and a large number of waiting patients, which may raise many subsequent problems. In this paper, we solve the brachytherapy patient scheduling problem with multiple treatment sessions, simultaneously considering the half-life decaying effect of radioactive sources, as well as the strict time constraints on the time interval between any two consecutive treatment sessions and the unavailable time of treatment. Patients on the waiting list are given different weights (priorities) according to the severity of their illness and waiting time. The studied problem aims to efficiently schedule patients in a rolling way to maximize the sum of the weights of the chosen patients from the current waiting list on the premise that the already arranged patients can complete their multiple treatment sessions in the future under strict time constraints. We formulate the problem as an integer programming model and develop a column generation-based heuristic approach on a set partitioning. We propose a pricing algorithm that can add many good patient plans at one iteration and a speed-up strategy to improve the performance of column generation. Computational studies are conducted on abundant test instances generated based on real-world data to demonstrate the efficiency and the high-quality solutions of the proposed approach by comparing with the integer programming model, the set partitioning model, the globally optimal solution, and the “Sessions on the Same Day Every Week” (SSEW) rule currently used in most real-world hospitals. Furthermore, we validate that the proposed approach can reduce the number of waiting patients compared with the SSEW rule. Sensitivity analysis is carried out on critical parameters, and further managerial insights are derived.

Dual Pricing Optimization for Live Video Streaming in Mobile Edge Computing With Joint User Association and Resource Management

Mobile live video streaming is expected to become mainstream in the fifth generation (5G) mobile networks. To boost the Quality of Experience (QoE) of streaming services, the integration of Scalable Video Coding (SVC) with Mobile Edge Computing (MEC) becomes a natural candidate due to its scalability and the reliable transmission supports for real-time interactions. However, it still takes efforts to integrate MEC into video streaming services to exploit its full potentials. We find that the efficiency of the MEC-enabled cellular system can be significantly improved when the requests of users can be redirected to proper MEC servers through optimal user associations. In light of this observation, we jointly address the caching placement, video quality decision, and user association problem in the live video streaming service. Since the proposed nonlinear integer optimization problem is NP-hard, we first develop a two-step approach from a Lagrangian optimization under the dual pricing specification. Further, to have a computation-efficient solution and less performance loss, we provide a one-step Lagrangian dual pricing algorithm by the convex transformation of non-convex constraints. The simulations show that the service quality of live video streaming can be remarkably enhanced by the proposed algorithms in the MEC-enabled cellular system.

Patient appointment scheduling at hemodialysis centers: An exact branch and price approach

Scheduling patient appointments at a hemodialysis center presents a unique setting. Unlike other appointment scheduling problems in healthcare systems, patients are scheduled for a series of dialysis treatment appointments instead of a single appointment. In this study, we formulate this multiple-appointment system as a set-partitioning problem that allows partial schedules to be feasible. We employ a Branch and Price (BP) algorithm to solve the problem, however, the pricing sub-problem proves to be exceedingly challenging for state-of-the-art dynamic programming algorithms. Therefore, we propose a novel decomposition of the sub-problem and design an efficient embedded Column Generation (CG) algorithm to find the optimal solution. We further design a greedy heuristic that enhances the computational efficiency of the BP algorithm. Our proposed BP algorithms efficiently solve challenging instances that are simulated based on the data from a collaborating hemodialysis center. Specifically, the Enhanced CG-embedded BP algorithm accelerates the CPU time on average by 78% compared to the Base BP algorithm (32% and 59% compared to the Enhanced and the CG-embedded BP algorithms, respectively). We also compare the optimal results with the current scheduling policy at the center. Our proposed Enhanced CG-embedded BP algorithm improves the percentage of leftover appointments by 98% on average and the hours of deviations per patient by 46% on average, compared to the current policy.

When does it pay to invest in pricing algorithms?

AbstractNowadays, firms frequently use big data and pricing algorithms to offer consumers personalized prices according to their willingness to pay. Advances in information technologies have further facilitated the use of customized pricing, which we consider an important facet of transformative marketing. At the outset, personalized pricing may appear to reduce the asymmetry of information between the firm and consumers, and benefits the firm but hurts consumers. To investigate this view, we consider a novel setting in which consumers must incur search costs to make an informed purchase from the firm. Contrary to conventional wisdom, we find that personalized pricing can sometimes make both the firm and consumers better off, thus leading to a win–win situation. We also show that an imperfect pricing algorithm can outperform a perfect one, thereby explaining why certain retailers like Amazon are adopting imperfect pricing algorithms. On the one hand, a moderately reliable pricing algorithm gives high‐preference consumers a chance to be misclassified as low‐preference consumers and obtain a low price, thereby encouraging consumer search. On the other hand, a highly reliable pricing algorithm significantly reduces consumers' surplus, which stifles consumer search. As a result, both firm profit and consumer surplus can be nonmonotone in the reliability of the algorithm. To the best of our knowledge, this is the first paper that documents the effect of personalized pricing under consumer search.

Minimizing online retailers’ revenue loss under a time-varying willingness-to-pay distribution

We study revenue management for an online retailer that offers a single product to customers with a time-varying willingness-to-pay (WTP) distribution. When the WTP distribution changes at an unknown time point (i.e., the change point), the original price quoted to customers may not be optimal. The retailer’s objective is to minimize his revenue loss by determining when to quote a new price to incoming customers and what the new price is. We formulate the problem as an optimization model, which is challenging to solve due to the presence of the unknown change point. To overcome this challenge, we first characterize the probability distribution of the estimated change point using maximum likelihood estimation. We then develop two pricing algorithms to solve the model by leveraging the characterized distribution. Lastly, through numerical studies, we illustrate the effectiveness of the proposed algorithms in identifying change points and recommending optimal post-change selling prices. The numerical results suggest that the proposed pricing algorithms significantly reduce the frequency of false change detection in the early stages of a selling season. The proposed pricing algorithms also outperform the benchmark pricing algorithm in reducing the retailer’s revenue loss.

Hub-and-Spoke Conspiracies: Can Big Data and Pricing Algorithms Form the Rim?

A hub-and-spoke conspiracy is a metaphor used to describe an antitrust cartel that includes a firm at one level of a supply chain—such as a buyer or supplier—who acts like the “hub” of a wheel. Vertical agreements up or down the supply chain act as the “spokes,” and a horizontal agreement among the spokes acts as the “rim” of the wheel. Courts have considered hub-and-spoke conspiracies for more than eighty years, and there is large body of case law that pertains to the evidence that is necessary for proving this type of antitrust conspiracy. With the rise of modern digital technologies, firms have increased their reliance on “big data” and data-driven pricing algorithms to determine the prices for their products and services. Using big data, current pricing algorithms can quickly monitor market conditions, including the behavior of rival competitors, and adjust prices in near real-time. Analytical pricing tools that adjust prices based on supply-and-demand conditions and/or costs can create procompetitive benefits because they have the potential to increase efficiency. Anticompetitive effects can occur, however, when multiple competitors use the same pricing algorithm and data set supplied by a common service provider who acts as a hub. This article will explain the history, structure, and characteristics of hub-and-spoke conspiracies. It also will discuss agreements among competitors to exchange confidential price information, which itself can result in antitrust violations under certain circumstances. Finally, the article will summarize and comment on a new wave of antitrust lawsuits that allege hub-and-spoke conspiracies based on competitors’ mutual use of big data and algorithms to set prices.

Explainable AI and Pricing Algorithms: A Case For Accountability in Pricing

Explainable AI and Pricing Algorithms: A Case For Accountability in Pricing

An Economic Test for an Unlawful Agreement to Adopt a Third-Party's Pricing Algorithm

An Economic Test for an Unlawful Agreement to Adopt a Third-Party's Pricing Algorithm

PRINCIPRO: Data-Driven Algorithms for Joint Pricing and Inventory Control under Price Protection

PRINCIPRO: Data-Driven Algorithms for Joint Pricing and Inventory Control under Price Protection

Pricing and inventory Decision Optimization under subscription mode in Supply chain management

This paper investigates the current situation of subscription mode, applies it to the joint management of pricing and inventory in supply chain management, builds the product pricing and inventory model under subscription mode, and verifies the model derivation and results based on the joint decision model of pricing and inventory, and simulates the decision-making process of the model by computer programming. By comparing the difference between the theoretical model of joint decision of pricing and inventory under uncertain supply and demand conditions and the model of joint decision of pricing and inventory under subscription mode, analyzing the influencing factors and exploring the optimization method of product pricing and inventory model algorithm under subscription mode. The results show that: (1) in supply chain management, it is necessary to solve the problem of supply and demand balance through effective joint decision of pricing and inventory, and effectively improve the competitiveness of logistics enterprises.(2) The introduction of subscription mode in the joint management of pricing and inventory can reduce the uncertainty of both sides, so as to better solve the problem of inventory replenishment strategy and pricing decision under the condition of supply and demand uncertainty than the traditional decision-making model, so as to achieve the coordination of supply chain under the uncertain environment.

Platform Design When Sellers Use Pricing Algorithms

We investigate the ability of a platform to design its marketplace to promote competition, improve consumer surplus, and increase its own payoff. We consider demand‐steering rules that reward firms that cut prices with additional exposure to consumers. We examine the impact of these rules both in theory and by using simulations with artificial intelligence pricing algorithms (specifically Q‐learning algorithms, which are commonly used in computer science). Our theoretical results indicate that these policies (which require little information to implement) can have strongly beneficial effects, even when sellers are infinitely patient and seek to collude. Similarly, our simulations suggest that platform design can benefit consumers and the platform, but that achieving these gains may require policies that condition on past behavior and treat sellers in a nonneutral fashion. These more sophisticated policies disrupt the ability of algorithms to rotate demand and split industry profits, leading to low prices.

Algorithm for accounting for the cost of International freight transportation: influencing factors and information support

The article describes the peculiarities of accounting for the cost of international freight transportation. The purpose of the article is to generalize the cost accounting experience and develop proposals for improving the pricing algorithm under different conditions. The results of the study are based on questionnaire data of 20 enterprises and entrepreneurs-carriers of the Volyn region, whose main type of service is international transportation. Most of them (18 out of 20 enterprises) belong to the general classification of micro- and small enterprises, which characterizes this business as small, 2 enterprises belong to the average in terms of the number of employees and the currency of the balance sheet. For the purpose of research, they were divided into 3 groups: small (0–10 employees), medium (11–20 employees), large (21–30 employees). In order to study the peculiarities of cost formation, their distribution was carried out by the number of cars, as this affects the number of transportations. The main principles of formation and calculation of the cost of freight transportation, types of cost of freight transportation, composition of cost items that form the cost of transportation are considered. The main influencing factors that led to changes in the cost of road transportation are characterized: the influence of military actions, the influence of the size of the enterprise, the influence of the volume of work performed by a unit of motor vehicles. According to the results of the assessment of the factors affecting the cost of road transportation, it was established that the share of production costs decreases with the increase in the size of the enterprise, while the share of general production and other costs increases, that is, micro-enterprises are more flexible.

算法个性化定价的法律规制

算法个性化定价的法律规制

Branch and price for submodular bin packing

The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems under various conditions. SMBP is a hard binary nonlinear programming optimization problem. In this paper, we propose a branch-and-price algorithm to solve this problem. The resulting price subproblems are submodular knapsack problems, and we propose a tailored exact branch-and-cut algorithm based on a piece-wise linear relaxation to solve them. To speed up column generation, we develop a hybrid pricing strategy to replace the exact pricing algorithm with a fast pricing heuristic. We test our algorithms on instances generated as suggested in the literature. The computational results show the efficiency of our branch-and-price algorithm and the proposed pricing techniques.