Pricing Algorithm Research Articles

Reimbursement of combined antihypertensive medicenes in Ukraine: aspects of inclusion and external reference pricing

Cardiovascular diseases (CVD), in particular arterial hypertension (AH), are the main causes of morbidity and mortality, Ukraine is on the 1st place in Europe for mortality from these diseases. Modern clinical guidelines emphasize the use of combined antihypertensive drugs, and improving the accessibility of these medicines for Ukrainian patients with hypertension is relevant. In Ukraine, at the end of 2022, there were no combined antihypertensive drugs in the List of reimbursed drugs. Therefore, there is a need to develop scientific and practical approaches to improve the «Affordable Medicines» reimbursement program in accordance with modern trends in the treatment of hypertension.
 The aim of the study is to formulate scientific and practical proposals for the inclusion of combined antihypertensive drugs in the state reimbursement program «Affordable Medicines» and to improve external reference pricing.
 Оbjects of the study were Orders of the Ministry of Health of Ukraine, national and international clinical guidelines, WHO ATC/DDD methodology guidelines. The study used content analysis, methods of comparative and logical analysis.
 At the 1st stage of the study, it was found that the current legislation of Ukraine does not prohibit the inclusion of combined antihypertensive drugs in the National List of Essential Medicines, and it is not limited solely to WHO recommendations. In the second stage of the study, it is proposed to use the data of pharmacoepidemiological studies and data of studies of actual consumption of combinated antihypertensive drugs in Ukraine, for further state HTA assessment and inclusion in the National List of Essential Medicines and «Affordable Medicines» program. The third and fourth stages of the study showed that the mechanism of external reference pricing needs to be improved and an algorithm for conducting external reference pricing for combined antihypertensive drugs, consisting of five consecutive stages, was developed and proposed.
 The current regulatory framework of Ukraine provides the possibility of including combined antihypertensive drugs in the state program «Affordable Medicines», and the initiation of the inclusion of medicines is within the competence of the Ministry of Health and the NHSU. A scientific and practical approach to the use of pharmaco-epidemiological research data to identify the most used doses of combined antihypertensive drugs as potential candidates for inclusion in the «Affordable Medicines» program is proposed. A scientific and practical algorithm for external reference pricing for combinated antihypertensive drugs was developed, considering current regulatory and methodological aspects.

A novel modified tunicate swarm algorithm for optimal charge scheduling and pricing of electric vehicles with user priority‐based charging station selection

SummaryIn recent days, electric vehicles (EVs) are seen as a viable transportation alternative by industry people to minimize the greenhouse gas emissions problems of regular fuel vehicles. While EVs' performance is limited due to their restricted battery power, charging wait for service, and high resource costs, they are still a viable option. To enhance the EV's performance, this work introduced an optimized priority‐based charge scheduling with dynamic pricing model. For this, a novel modified tunicate swarm algorithm method, which is the enhanced form of the standard tunicate swarm algorithm, is proposed. When an EV arrives at the charging station, the EV user is permitted to choose the type of charging based on his/her requirements. In general, when charging EVs in public stations or during peak hours, customers must be patient and wait for significant periods of time. The introduced model ignores this negative effect. EV users have also mentioned the issue of controlled charging rates as a key barrier. This is a difficult task, but it is accomplished in this study, which optimizes total charge costs. Finally, the results acquired are discussed under overall cost and energy consumption.

Facility location and pricing problem: Discretized mill price and exact algorithms

The joint optimization of facility location and service charge arises in many industrial and business contexts. This paper investigates a facility location and mill pricing problem (FLMPr), where a company aims to maximize its profit by locating service facilities and setting appropriate service charges to customers. For each facility, the number of pricing levels are finite, and the company will select exactly one level for each facility if it is open. We visualize the problem from a fully decentralized perspective, i.e., each customer acts as an independent decision-maker. Under mill pricing, customers visiting the same facility encounter the same service charge. The problem is formulated as a bilevel program, in which the company makes location and pricing decisions at the upper level, and customers decide whether to seek the service from a facility at the lower level. To solve FLMPr, we leverage three types of closest assignment constraints to reformulate the problem as mixed-integer linear programs (MILPs), which can be directly solved by modern solvers. However, this approach suffers from a time-consuming solver compiling process and cannot handle large-scale instances effectively. This observation motivates us to design a branch-and-cut algorithm by exploring the bilevel structure and deriving a feasibility cut to efficiently eliminate bilevel infeasible solutions. Our extensive experiments reveal that the proposed algorithm can solve large-scale FLMPr satisfactorily and outperforms the MILP approach by a large margin. Finally, we conduct sensitivity analysis and draw interesting observations.

Proximal policy optimization algorithm for dynamic pricing with online reviews

This study investigates whether the presence of both quality- and value-based online reviews help firms make decisions. To adapt to a complex real-world environment, we construct two simulated environments with high and low initial consumer-perceived quality and employ a Proximal Policy Optimization algorithm (PPO) to derive optimal pricing strategies. The simulation results show that retailers can gain higher revenue by considering quality-based reviews only when the consumers' initial perceived quality is low. In addition, retailers must choose an appropriate promotion method based on the social learning speed of the consumer group. When the social learning speed is slow, retailers should invest more in promotion costs to improve the initial perceived quality of consumers and thus increase revenue. Compared to the Advantage Actor-Critic algorithm, the PPO algorithm exhibits better performance, provides a new approach for complex and continuous revenue management problems, and can be applied to a wider range of areas.

Branch and Price Algorithm for Multi-Trip Vehicle Routing with a Variable Number of Wagons and Time Windows

Motivated by the transportation needs of modern-day retailers, we consider a variant of the vehicle routing problem with time windows in which each truck has a variable capacity. In our model, each vehicle can bring one or more wagons. The clients are visited within specified time windows, and the vehicles can also make multiple trips. We give a mathematical programming formulation for the problem, and a branch and price algorithm is developed to solve the model. In each iteration of branch and price, column generation is used. Different subproblems are created based on the different capacities to find the best column. We use CPLEX to solve the problem computationally and extend Solomon’s instances to evaluate our approach. To our knowledge, ours is the first such study in this field.

A Multilateral Transactive Energy Framework of Hybrid Charging Stations for Low-Carbon Energy-Transport Nexus

This article proposes a multilateral multienergy trading framework for synergetic hydrogen (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) and electricity transactions among renewable-dominated hybrid charging stations (HCSs). In this framework, each autonomous HCS with various renewable energy resource (RES) endowment can harvest local renewables for internal green H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and electricity generation to simultaneously meet demands of electric vehicles (EVs) and hydrogen-powered vehicles (HVs) from the transportation network. The surplus electricity/H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> production of the HCS is accommodated by external multilateral transactions to increase the additional profit. Besides, each HCS is modeled as a sustainable energy hub, and multiple hubs with multienergy transactions contribute toward a low-carbon energy-transport nexus. A partial differential equation model based on fluid dynamic theory is formed to capture the temporal and spatial dynamics of traffic flows for estimating the EV/HV loads at HCSs. Furthermore, a distributed multilateral pricing algorithm is developed to iteratively derive the optimal prices and quantities for transactive electricity and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . Comparative studies corroborate the superiority of the proposed methodology on economic merits and RES accommodation.

Antitrust, Pricing Algorithms and the Liable Humans Behind Them

Antitrust, Pricing Algorithms and the Liable Humans Behind Them

Interval scheduling with economies of scale

Motivated by applications in cloud computing, we study interval scheduling problems exhibiting economies of scale. An instance is given by a set of jobs, each with start time, end time, and a function representing the cost of scheduling a subset of jobs on the same machine. Specifically, we focus on the max-weight function and non-negative, non-decreasing concave functions of total schedule weight. The goal is a partition of the jobs that minimizes the total schedule cost, where overlapping jobs cannot be processed on the same machine. We propose a set cover formulation and a column generation algorithm to solve its linear relaxation. For the max-weight function, which is already NP-hard, we give a polynomial-time pricing algorithm; for the more general case of a function of the total weight, we have a pseudo-polynomial algorithm. To obtain integer solutions, we extend the column generation approach using branch-and-price. We computationally evaluate our methods on two different functions, using both random instances and instances derived from cloud computing data; our algorithm significantly outperforms known integer programming formulations (when these are available) and is able to provably optimize instances with hundreds of jobs.

A fast exact pricing algorithm for the railway crew scheduling problem

The railway crew scheduling problem consists of selecting a least cost set of duties that cover all tasks. Large-scale crew scheduling problems are typically solved with column generation, where in each iteration a pricing problem needs to be solved. When the duty constraints consist in a maximum duty length, a meal break constraint, and the requirement to start and end at the same crew depot, the fastest known exact pricing algorithm has O(|N|3) complexity, |N| being the number of tasks. In this work we propose an O(|N|2) exact pricing algorithm. We compare the two algorithms on randomly generated instances and show that a reduction in computation time of 95% is attained on instances of size |N|=1,250.

Machine-Learning–Based Arc Selection for Constrained Shortest Path Problems in Column Generation

Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem and one or more pricing problems (PP). The total computing time taken by the method is divided between these two parts. In routing or scheduling applications, the problems are mostly defined on a network, and the PP is usually an NP-hard shortest path problem with resource constraints. In this work, we propose a new heuristic pricing algorithm based on machine learning. By taking advantage of the data collected during previous executions, the objective is to reduce the size of the network and accelerate the PP, keeping only the arcs that have a high chance to be part of the linear relaxation solution. The method has been applied to two specific problems: the vehicle and crew scheduling problem in public transit and the vehicle routing problem with time windows. Reductions in computational time of up to 40% can be obtained. Funding: The authors thank Giro, Inc., and the Natural Sciences and Engineering Research Council of Canada for financial support [Grant CRDPJ 520349-17].

Batching and scheduling in a continuous-discrete hybrid flowshop: Lagrangian relaxation-based heuristic algorithms

ABSTRACT We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently.

Context‐based dynamic pricing with online clustering

We consider a context‐based dynamic pricing problem of online products, which have low sales. Sales data from Alibaba, a major global online retailer, illustrate the prevalence of low‐sale products. For these products, existing single‐product dynamic pricing algorithms do not work well due to insufficient data samples. To address this challenge, we propose pricing policies that concurrently perform clustering over product demand and set individual pricing decisions on the fly. By clustering data and identifying products that have similar demand patterns, we utilize sales data from products within the same cluster to improve demand estimation for better pricing decisions. We evaluate the algorithms using regret, and the result shows that when product demand functions come from multiple clusters, our algorithms significantly outperform traditional single‐product pricing policies. Numerical experiments using a real data set from Alibaba demonstrate that the proposed policies, compared with several benchmark policies, increase the revenue. The results show that online clustering is an effective approach to tackling dynamic pricing problems associated with low‐sale products.

The resource constrained clustered shortest path tree problem: Mathematical formulation and Branch&amp;Price solution algorithm

AbstractIn this article, the Resource Constrained Clustered Shortest Path Tree Problem is defined. It generalizes the classic Resource Constrained Shortest Path Tree Problem since it is defined on an undirected, complete and weighted graph whose set of nodes is partitioned into clusters. The aim is then to find a shortest path tree respecting some resource consumption constraints and inducing a connected subgraph within each cluster. The main support and motivation for studying this problem are related, among the others, to the design of telecommunication networks, and to Disaster Operations Management. In this work, we present a path‐based formulation for the problem, addressing the case of local resource constraints, that is, resource constraints on single paths. For its resolution, a Branch&amp;Price algorithm featuring a Column Generation approach with Multiple Pricing Scheme is devised. A comprehensive computational study is conducted, comparing the proposed method with the results achieved by the CPLEX solver, adopted to solve the mathematical model. The numerical results underline that the Branch&amp;Price algorithm outperforms CPLEX, both in terms of solution cost and time.

The emerging threat of artificial intelligence on competition in liberalized electricity markets: A deep Q-network approach

According to Sustainable Development Goals (SDGs), societies should have access to affordable, reliable, and sustainable energy. Liberalized electricity markets have been established to provide affordable electricity for end-users through advertising competition. Although these new markets are designed to serve competition, there are recorded incidents where participants abused their market power and disrupted the competition through collusion. Unfortunately, modern autonomous pricing algorithms may further assist myopic players to discover collusive strategies with a minimum amount of sensitive information. Therefore, in this study, we investigate the impact of emerging learning algorithms on the bidding strategies of Power Generating Companies (GenCos) and compare their performance against game-theoretic expectations. A novel deep Q-network (DQN) model is developed, by which GenCos determine the bidding strategies to maximize average long-term payoffs in a day-ahead market. The presented DQN model assumes that GenCos have no information regarding the rivals’ true generation costs and profits. To the best of the authors’ knowledge, this is the first study that thoroughly investigates players’ behavior utilizing a modern DQN model and compares its results with equilibria of the non-cooperative single-stage and infinitely-repeated games in the context of electricity markets. The outcomes articulate that GenCos equipped with advanced learning models may be able to collude unintentionally while trying to ameliorate long-term profits. Moreover, GenCos that employ the presented DQN model could discover and sustain more profitable (e.g., collusive) strategies vis-à-vis a conventional Q-learning method. Collusive strategies can lead to exorbitant electric bills for end-users, which is one of the influential factors in energy poverty. Thus, policymakers and market designers should be vigilant regarding the combined effect of information disclosure and autonomous pricing, as new models exploit information more effectively.

Option pricing with the control variate technique beyond Monte Carlo simulation

Although mostly used alongside Monte Carlo simulation, the control-variate (CV) technique can be applied to other numerical algorithms in option pricing. This paper studies the conditions under which a numerical method (simulation-based or not) can benefit from the CV technique and what approximators can serve as CVs. We demonstrate the ideas with Carr and Madan’s Fourier transform-based algorithm, convolution-based pricing algorithms, and classic binomial trees. Numerical results are provided to show that the CV-enhanced versions are more efficient than the original algorithms.

Wirkung der Energiesteuersenkung auf Kraftstoff preise

AbstractThe German federal government intended to alleviate the burden of increasing fuel prices by introducing a temporary reduction of energy taxes on gasoline and diesel. In order to evaluate the impact of this measure on consumer prices at the filling stations the development of procurement costs for crude oil as well as the downstream development of refinery and distribution margins have to be taken into account. It turns out that about 80 % of the tax reduction has been passed on to end consumers on and around the effective date of the tax relief. However, within the first month the impact of the tax reduction has been wiped out for diesel completely as the gross margin of the mineral oil groups have substantially improved since then. On the other hand, for gasoline (E10) at least part of the impact can still be observed as the initial margin improvement has come down in the meantime. For a detailed analysis the German antitrust authority should look into the pricing algorithms of all 14,000 filling stations in Germany.

Dynamic air ticket pricing using reinforcement learning method

This paper studies a dynamic air ticket pricing problem in a strategic and myopic passengers co-existence market. The strategic or myopic passengers can be further divided into high-valuation and low-valuation groups according to how they evaluate their purchases. The strategic passengers have different strategic levels. When the airline sets a ticket price, every passenger makes his or her purchase decision according to his or her type and the strategic level, or might select “wait” or “leave (the market)”. The paper firstly proposes a dynamic pricing algorithm in which the utilities of both the airline and passengers are considered. The reinforcement learning (RL) is employed to deal with the progressive or dynamic decision-making framework, in which the dynamic pricing problem is formulated as a discrete finite Markov decision process (MDP) and the Q-learning is adopted to solve the problem. By using this method, the airline can adaptively decide the ticket price based on passengers strategic behaviors and the time-varying demand. The effects of the passenger type proportion and strategic level are analyzed. The computational results show the higher proportion of strategic passengers is, the smaller price increase the airline can adopt, and the higher proportion of high-valuation strategic passengers is, the larger price increase the airline can put to use under the same strategic level. If the proportion of low-valuation strategic passengers is higher, the price increase should be gentle and step by step when the price increase strategy is adopted. If the airline uses price-cut policy, the adjustment should be small. In addition, the high-valuation passenger mainly affects high-price periods and the low-valuation passenger mainly affects low-price periods. When the proportion of strategic passengers is fixed, the lower the passenger strategic level is, the larger the price slope is. These findings can provide some references for the airline to make more precise and flexible pricing decisions.

Mergers, Acquisitions and Merger Control in an Algorithmic Pricing World

Abstract This paper considers whether pricing algorithms present novel issues that existing merger control frameworks and practices are inadequate to address, particularly in relation to pre-merger disclosure of pricing algorithms and the suitability of current tests and remedies for addressing coordinated effects. Through a comparative and critical analysis of the merger control regimes and practices of the European Union, United Kingdom, and Australia, this paper finds that whilst such regimes and practices are broadly adequate for dealing with algorithmic transactions, there are nonetheless potential areas for improvement. Disclosure of a pricing algorithm may contravene prohibitions on the sharing of competitively sensitive information. As such, merger parties may need to rethink aspects of their usual due diligence procedures. Pricing algorithms may also increase the potential for coordinated effects to arise in some markets that would ordinarily have been considered too complex, asymmetric, opaque, or insufficiently concentrated for tacit coordination to occur, or be used to retaliate more effectively against deviations from a coordinated equilibrium, or to raise the height of barriers to entry. Competition authorities may therefore need to amend their standard approach to investigating and assessing coordinated effects, as well as their traditional approach to remedies.

Distributed asynchronous column generation

We propose a revision of the classical column generation algorithm for solving Dantzig–Wolfe decompositions of mixed integer programs. It is meant to fully exploit the availability of distributed computing resources, making optimization algorithms in general purpose solvers to scale better.The main idea is to trigger massive parallelism by fully decoupling the computing flow of each component, including the resolution of the master problem, thus allowing different pricing algorithms to concurrently work on different sets of dual variables, and the master algorithm to asynchronously update dual information as soon as new columns are available.Our algorithms ensure the same optimality convergency properties of the classical method. Experiments on mixed integer programs for three benchmark problems from the combinatorial optimization literature prove our approach to be one order of magnitude faster than state-of-the-art general purpose solvers in computing high quality root node dual bounds. Even if devised to exploit clusters of machines which do not share memory space, our algorithms show to be faster than earlier attempts from the literature also when run on virtual machines hosted on a single physical one, proving this improvement to derive from our algorithmic methodology rather than technological factors.

Optimal deployment of virtual network functions for securing telecommunication networks against distributed denial of service attacks: A robust optimization approach

Distributed Denial of Service (DDoS) cyberattacks represent a major security risk for network operators and internet service providers. They thus need to invest in security solutions to protect their network against DDoS attacks. The present work focuses on deploying a network function virtualization based architecture to secure a network against an on-going DDoS attack. We assume that the target, sources and volume of the attack have been identified. However, due to 5G network slicing, the exact routing of the illegitimate flow in the network is not known by the internet service provider. We seek to determine the optimal number and locations of virtual network functions in order to remove all the illegitimate traffic while minimizing the total cost of the activated virtual network functions. We propose a robust optimization framework to solve this problem. The uncertain input parameters correspond to the amount of illegitimate flow on each path connecting an attack source to the target and can take values within a predefined uncertainty set. In order to solve this robust optimization problem, we develop an adversarial approach in which the adversarial sub-problem is solved by a Branch & Price algorithm. The results of our computational experiments, carried out on medium-size randomly generated instances, show that the proposed solution approach is able to provide optimal solutions within short computation times.