Pricing Algorithm Research Articles

Application of Linear Programming in Automatic Pricing and Replenishment Strategies for Vegetable Commodities

Vegetable commodities are indispensable parts of the current consumer market. Vegetables possess different characteristics such as seasonality, perishability and so on. Thus, it is critical to formulate reasonable automatic pricing and replenishment strategies for vegetable commodities. However, previous kinds of literature have either ignored some of the attributes of vegetables or restricted their application regions to some specific situations. This review compares the pros and cons of diverse linear programming methods and models in previous research, synthesizes the core method, and finally concludes with two relatively reasonable algorithms for pricing and replenishment strategies. It also gives an evaluation of these two algorithms and proposes suggestions for improvement. The purpose of this review is to provide guidelines for subsequent research to optimize existing methods and models to work out more objective and accurate optimal strategies. Ultimately, vegetable sales and supply can better meet the market demand, which can help rejuvenate economic vitality and bring in higher profits at the same time.

A branch-and-price approach for the nurse rostering problem with multiple units

In this paper, we study the nurse rostering problem that considers multiple units and many soft time-related constraints. An efficient branch and price solution approach that relies on a fast algorithm to solve the pricing subproblem of the column generation process is presented. For the nurse rostering problem, its pricing subproblem can be formulated as a shortest path problem with resource constraints, which has been the backbone of several solutions for several classical problems like vehicle routing problems. However, approaches that perform well on these problems cannot be used since most constraints in the nurse rostering problem are soft. Based on ideas borrowed from global constraints in constraint programming to model rostering problems, an efficient dynamic programming algorithm with novel label definitions and dominating rules specific to soft time-related constraints is proposed. In addition, several acceleration strategies are employed to improve the branch and price algorithm. Computational results on two sets of instances ranging from 2 to 4 units over a horizon of 2 or 4 weeks demonstrate the effectiveness of the proposed algorithms. The accelerated dynamic programming algorithm is able to solve pricing subproblems to optimality with the fewest extended labels. When contrasted with Cplex, the branch and price approach yields solutions that are either equivalent or superior across all instances.

Arc-flow formulation and branch-and-price-and-cut algorithm for the bin-packing problem with fragile objects

This study introduces an arc-flow formulation and the first branch-and-price-and-cut (BPC) algorithm designed to solve the bin-packing problem with fragile objects (BPPFO). This variant of the bin-packing problem originates in the field of telecommunications, particularly in the allocation of cellular calls to frequency channels. The arc-flow formulation is inspired by previous studies and modifies the graph construction method to accommodate fragility constraints. We proved the correctness of this formulation and demonstrated its superiority in instances with small maximum fragility through extensive experiments. The proposed BPC algorithm leverages advanced cutting and packing techniques and incorporates innovative elements such as problem reduction, additional cutting planes, and a label-setting-based exact pricing algorithm. The experimental results demonstrate that the proposed BPC algorithm is highly competitive with the state-of-the-art algorithm for solving the BPPFO and can successfully solve several previously unsolved instances.

An economic test for an unlawful agreement to adopt a third-party’s pricing algorithm

SUMMARY Artificial intelligence has helped fuel a growing market in the supply of pricing algorithms by software developers. While there is an efficiency rationale for outsourcing pricing, anticompetitive concerns have been expressed when competitors in a market adopt the same pricing algorithm. These concerns have resulted in private litigation claiming a third-party company (who developed the pricing algorithm) and firms (who adopted it) had an unlawful agreement. This study develops an empirical test for determining whether firms’ adoption decisions are coordinated. If adoption decisions are coordinated then adopters’ average price is increasing in the number of adopting firms, while if adoption decisions are independent then adopters’ average price does not depend on the number of adopting firms. This test could provide economic evidence to support a claim of an unlawful agreement between a third-party developer and adopting firms.

Algorithms in the marketplace: An empirical analysis of automated pricing in e-commerce

We analyze algorithmic pricing on the largest online marketplace in the Netherlands and Belgium. Based on two months of pricing data for around 2800 products, we find no significant correlation between the use of algorithms and an increase in prices of the Buy Box (the most prominently displayed offer for a product). We document that the presence of an algorithmic seller in monopoly markets goes hand-in-hand with lower prices. This effect is likely due to algorithms correcting excessively high human-set prices. We describe several characteristic algorithmic pricing patterns. While some of these pricing patterns are consistent with algorithmic collusion, such practice appears to be a fringe phenomenon. Overall, our findings call for careful policy with respect to pricing algorithms that remains alert to the possibility of algorithmic collusion but recognizes that pricing algorithms may benefit consumers.

A nonsmooth Levenberg–Marquardt method based on KKT conditions for real-time pricing in smart grid

The real-time pricing of smart grid, which is an important mean of demand side management, is an ideal method to adjust the power balance between the supply and demand in smart grid system. By transforming the social welfare maximization model into a nonsmooth system of equations based on KKT conditions and investigating the related nonsmooth-function’s generalized Jacobi, a nonsmooth Levenberg–Marquardt method with global convergence is proposed in this paper. Also, the local convergence rate is obtained under the local error bound, which is weaker than the nonsingular condition. Finally, numerical simulations show that the smaller the approximate parameter in smoothing Newton’s method, the closer the electricity price is to the value obtained by the proposed algorithm. And the price of the multi price based on the method is lower than that of the single price algorithm that does not consider user types. Meanwhile, compared with the distributed algorithm with different scales, it is found that the price is lower and the social welfare is higher, which shows that the algorithm is robust and effective.

Price Monitoring, or Where Surveillance Studies Meets the Sociology of Price Formation

This essay stages an encounter between surveillance studies and the sociology of price and price formation. I argue that surveillance is integral to the calculative operations of retail price strategies, especially during periods of high inflation, and that these calculative operations hinge on the human infrastructure of a precarious data-collecting workforce. I present my argument through a case study of competitor price monitoring, a corporate surveillance practice in which commercial actors record, process, and transmit information on competitors’ pricing, inventory, and display strategies. While pricing intelligence services like web-scraping and dynamic pricing algorithms are typically applied in e-commerce settings, I focus here on a firm that specializes in the collection of brick-and-mortar retail price data, with special attention to the labor practices involved in the manual (in-person, device-aided) production of retail price information at the national-industrial scale. Building on auto-ethnographic observations as a price data collector as well as analysis of employee reviews of the firm on sites like Indeed and Glassdoor, I argue that surveillance studies can contribute in significant ways to our understanding of the material practices, and politics, of price and price formation.

An electricity price and energy-efficient workflow scheduling in geographically distributed cloud data centers

The cloud computing platform has become a favorable destination for running cloud workflow applications. However, they are primarily complicated and require intensive computing. Task scheduling in cloud environments, when formulated as an optimization problem, is proven to be NP-hard. Thus, efficient task scheduling plays a decisive role in minimizing energy costs. Electricity prices fluctuate depending on the vending company, time, and location. Therefore, optimizing energy costs has become a serious issue that one must consider when building workflow applications scheduling across geographically distributed cloud data centers (GD-CDCs). To tackle this issue, we have suggested a dual optimization approach called electricity price and energy-efficient (EPEE) workflow scheduling algorithm that simultaneously considers energy efficiency and fluctuating electricity prices across GD-CDCs, aims to reach the minimum electricity costs of workflow applications under the deadline constraints. This novel integration of dynamic voltage and frequency scaling (DVFS) with energy and electricity price optimization is unique compared to existing methods. Moreover, our EPEE approach, which includes task prioritization, deadline partitioning, data center selection based on energy efficiency and price diversity, and dynamic task scheduling, provides a comprehensive solution that significantly reduces electricity costs and enhances resource utilization. In addition, the inclusion of both generated and original data transmission times further differentiates our approach, offering a more realistic and practical solution for cloud service providers (CSPs). The experimental results reveal that the EPEE model produces better success rates to meet task deadlines, maximize resource utilization, cost and energy efficiencies in comparison to adapted state-of-the-art algorithms for similar problems.

Fixed Automated stations location and UAVs routing problems in urban road Networks: A tailored Branch-&-price algorithm

Unmanned aerial vehicles (UAVs) serve as vital tools for collecting real-time traffic data, enabling rapid responses to events, and optimizing traffic management based on their cost-effectiveness, high flexibility, and wide coverage range advantages. The urban UAV cruising problem primarily focuses on selecting the locations of fixed automated station (FAS) and optimizing UAVs’ cruising routes. This paper introduces a strategy where UAVs can take off and land on different FASs to enhance urban UAVs’ cruising efficiency. Firstly, the problem is formulated as an integrated linear integer model (FU-ILP) which simultaneously determines the locations of FASs and the routes of UAVs. The objective is to minimize redundant cruising distance and cruising cycle time. The FU-ILP model takes into account UAV‘s flight capabilities, FAS’s signal coverage range, power requirements, and battery charging. Moreover, we design a tailored branch-and-price (TB&P) algorithm to decompose the FU-ILP model, which can reduce the variable scale for solving larger-scale cases. Finally, we test the model and the algorithm on the Sioux Falls Test Network. The TB&P algorithm improves computational efficiency by nearly 80%. Moreover, our strategy yields superior results compared to the strategy where UAVs must return to their take-off FASs for recharging. We also demonstrate that increasing the number of UAVs does not reduce redundant cruising distance in the whole network, but it can shorten the cruising cycle. These policy conclusions also apply to the case of Xiongan. This provides a basis for managers to calculate the minimum UAV’s configuration based on the cities’ actual cruising frequency requirements.

The Dilemma and Relief of Anti-monopoly Regulation in Personalized Pricing Algorithms

In the era of big data, online platforms utilizing algorithms for personalized pricing pose monopoly risks that harm competition, and contradict the economic market concepts of consumer protection and encouraging innovation. China's anti-monopoly laws face difficulties in defining relevant markets, and law enforcement agencies are at a loss when identifying abuse of market dominance. The defense rights originally granted to platforms by the law have been abused. In view of this, this paper proposes to establish an evaluation system for competition damage based on consumer protection, specifying the considerations for justifying damage, and suggests using user engagement intensity and activity level as statistical indicators, incorporating the influence of algorithmic computing power, and employing a relative market share assessment method as a determinant factor for judging market dominance.

Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios

On the Difficulty of Pricing Routes for Stochastic Vehicle Routing Problems Many approaches exist for dealing with the uncertainty in the vehicle routing problem with stochastic demands (VRPSD), but the most popular approach models the VRPSD as a two-stage stochastic program where a recourse policy prescribes actions that handle when the realized demands exceed the vehicle capacity. Similarly to other VRP variants, some state-of-the-art algorithms for the VRPSD use set-partitioning formulations that generate variables (routes) via a pricing problem. All of these algorithms, however, have strong assumptions on the probability distribution of customer demands, a simplification that might not be realistic in some applications. In “Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios,” Ota and Fukasawa examine the challenges associated with solving the pricing problem of the VRPSD when the customer demands are given by scenarios. They demonstrate that the VRPSD pricing problem is strongly NP-hard for a wide variety of recourse policies and route relaxations. This highlights the difficulty of developing efficient pricing algorithms for the VRPSD with scenario-based demand models.

An exact algorithm for simultaneous pickup and delivery problem with split demand and time windows

This study introduces a new variant of the vehicle routing problem (VRP) called the simultaneous pickup and delivery problem with split demand and time windows (SPDP-SDTW). The motivation behind this study stems from real-life urban and rural delivery scenarios, encompassing features such as split demand, simultaneous pickup and delivery, many-to-many pickup and delivery, and time windows. The study thoroughly investigates the properties of the optimal solution for the SPDP-SDTW. Based on these properties, an arc flow model is developed for the SPDP-SDTW. Dantzig Wolfe (DW) decomposition techniques are employed to obtain the master problem and the pricing subproblem. In order to effectively address the SPDP-SDTW, an improved branch and price (I-BP) algorithm is proposed, incorporating a tailored column generation (CG) algorithm, branching strategies, and dual stabilization strategies. The proposed CG algorithm provides a framework that combines the improved adaptive degree heuristic (I-AGH) algorithm and the solver Gurobi. This integration substantially mitigates the computational burden involved in solving the subproblem. Extensive computational experiments conducted on datasets of varying sizes, including small, medium, and large instances, consistently demonstrate that the I-BP algorithm performs the best in both solution quality and computational efficiency when compared to existing exact and heuristic algorithms.

The Heston–Queue-Hawkes process: A new self-exciting jump–diffusion model for options pricing, and an extension of the COS method for discrete distributions

We propose a new self-exciting jump–diffusion process, the Heston–Queue-Hawkes (HQH) model, which integrates the well-known Heston model with the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Similar to the Heston–Hawkes process (HH), the HQH model effectively captures both the slow and continuous evolution of prices, and the sudden and impactful market movements due to self-excitation and contagion. But a significant advantage of the HQH model is that its characteristic function is available in closed form, allowing for the efficient application of Fourier-based fast pricing algorithms, such as the COS method (which we extend to deal with discrete distributions). We also demonstrate that, by leveraging partial integrals of the characteristic function, which are explicitly known for the HQH process, we can reduce the dimensionality of the COS method, thereby decreasing its numerical complexity. Our numerical results for pricing European and Bermudan options indicate that the HQH model provides a broader range of volatility smiles compared to the Bates model, while maintaining a substantially lower computational burden than the HH process.

A Branch-and-Cut-and-Price Algorithm for Cutting Stock and Related Problems

In this project, we introduce a branch-and-cut-and-price framework to solve the Cutting Stock Problems with strong relaxations using the Set Covering (Packing) Formulations, which are solved through column generation. We propose an extended Ryan-Foster branching scheme tailored to non-binary models, a pricing algorithm that produces convergence in a few iterations, and a variable selection technique based on branching history. These strategies are combined with subset-row cuts and custom primal heuristics to create a framework that overcomes the current state-of-the-art of Cutting Stock Problem, Skiving Stock Problem, and other related problems, being at least twice faster in the first problem and at least 60% faster in the second one.

Deep reinforcement learning algorithms for dynamic pricing and inventory management of perishable products

A perishable product has a limited shelf life, and inefficient management often leads to waste. This paper focuses on dynamic pricing and inventory management strategies for perishable products. By implementing effective inventory control and the right pricing policy, it is possible to maximize expected revenue. However, the exponential growth of the problem size due to the shelf life of the products makes it impractical to use methods that guarantee optimal solutions, such as Dynamic Programming (DP). Therefore, approximate solution algorithms become necessary. We use Deep Reinforcement Learning (DRL) algorithms to address the dynamic pricing and ordering problem for perishable products, considering price and age-dependent stochastic demand. We investigate Deep Q Learning (DQL) solutions for discrete action spaces and Soft Actor-Critic (SAC) solutions for continuous action spaces. To mitigate the negative impact of the stochastic environment inherent in the problem, we propose two different DQL approaches. Our results show that the proposed DQL and SAC algorithms effectively address inventory control and dynamic pricing for perishable products, even when products of different ages are offered simultaneously. Compared to dynamic programming, our proposed DQL approaches achieve an average approximation of 95.5 % and 96.6 %, and reduce solution times by 71.5 % and 79.9 %, respectively, for the largest problem. In addition, the SAC algorithm achieves on average 4.6 % and 1.7 % better results and completes the task 56.1 % and 48.2 % faster than the proposed DQL algorithms.

Development of Models for Ticketing in Public Transportation System in Nigeria

Transportation is a system that humans use to carrying out their day-to-day activities. In the bid to do activities, transportation by any means has to be used. In the public transportation system, they use the manual or traditional method to process ticketing. This causes many flaws such as long queues, communication gap, miscalculation of tickets, improper records of commuters’ information etc. For commuters to gain a convenient platform for bus reservations, real-time information updates, and a smoother experience; and for the companies to benefit from automated reservations, improved communication, and data-driven insights for better decision- making, there is need to develop a model for ticketing in public transportation system. The models for ticketing in urban transportation system have methods that involve pricing algorithm and route algorithm where scaling factors and user capacity planning models are calculated. With the introduction of the ticketing model in transportation system, existing challenges in urban mobility are revolutionized. The intersection of technology and transportation are positioned in such a way that the model seeks to enhance the overall commuter experience seamlessly by integrating reservation processes, real-time updates, amount payable, time and date of travels and communication between branches. The study envisions a shift towards a more accessible, efficient, and user-centred urban transportation system. It represents a transformative catalyst in transportation system especially by land/roads which are being used by automobiles (buses, cars, tricycle etc).

An overview of dynamic pricing toll roads in the United States: Pricing algorithms, operation strategies, equity concerns, and funding mechanism

Toll roads with fully dynamic pricing schemes could play a key role in addressing the economic and environmental tolls imposed by increasing congestion levels in major metropolitan areas. Transportation professionals usually argue that they could provide additional revenue streams to accelerate the delivery of much-needed highway projects and serve as a tool for travel demand management. However, the number of dynamic pricing toll roads only increased recently in the U.S., and their performance has not been empirically evaluated systematically. This study provides a comprehensive review of U.S. dynamic pricing toll roads. Pricing is reactive to demand, and additional travel demand management strategies such as incentives for high occupancy vehicles, clean vehicles, and transit are commonly included. Both conventional project delivery methods and private–public partnerships have been used for such projects. Financial statements from a few P3 dynamic toll road projects suggest they are taking full advantage of TIFIA loans and are performing well during their short history. Equity issues are commonly raised, and many projects address them specifically through subsidies to vulnerable groups or re-investment in the community. Further quantitative analyses are needed to test if dynamic toll roads are an efficient tool to address the financial, economic, and environmental challenges major metropolitan areas face.

The impact of digital platform pricing algorithms on market equilibrium

The impact of digital platform pricing algorithms on market equilibrium

NAVIGATING JUSTICE AND LEGAL EQUILIBRIUM IN AUTOMATIC PRICING ALGORITHMS: A CROSS BORDER LEGAL APPROACH

Automatic pricing algorithms with artificial intelligence (AI) technology in e-commerce have a significant impact on the running of the industry. This creates benefits as well as reaps polemics. Discrimination against consumers is one of them. For this reason, comprehensive treatment is needed to prevent negative impressions from occurring and can lead to the creation of justice and fairness. This research is normative qualitative research with the support of case and comparison approaches. The research results show that the algorithm uses AI to set prices based on market factors, production costs, and competition, providing price flexibility, price relevance, and increased business efficiency. Positive impacts include increased efficiency, price relevance, and consumer reach, while negative impacts involve the risk of discrimination and supervisory difficulties. Regulation and supervision are needed to maintain justice and legal balance. Unfair competitive practices, such as sudden price fluctuations, need to be monitored. Explicit regulations are needed to address the gap between AI developments and the existing legal framework. The implementation of automatic pricing algorithms must pay attention to aspects of justice and legal balance.

Commodity Dynamic Pricing and Replenishment Decision Model Based on Cosine Annealing

The purpose of this paper is to analyze the relationship between commodity sales volume, commodity types, sales time, etc., and propose a decision model to predict future sales data through historical sales data to determine a reasonable pricing strategy. First, the collected data is preprocessed. Through correlation analysis, the most important influencing factors of commodity sales are obtained. Through the construction of XGBoost model to model the influence factors obtained, the wholesale prices of chili products (yuan/kg) from July 1 to 7, 2023 are 3.63, 6.68, 6.90, 5.44, 6.62, 6.90, 5.44, respectively. In order to further develop a reasonable pricing strategy, this paper constructs a model based on cosine annealing algorithm combined with dynamic pricing algorithm. Through this model, it is calculated that from July 1 to 7, 2023, the restocking quantity (kg) of chili products is 234.20, 95.85, 110.04, 179.77, 176.60, 110.04, respectively. 179.77. Profit (Yuan) is 148.81, 298.96, 347.82, 370.75, 287.54, 356.33, 383.00. By comparing the model with the actual data, the error of the model is small and the robustness is high, which provides an effective decision-making model for supermarkets to formulate commodity sales strategy.