Combinatorial Auctions Research Articles

Optimal scheduling on unrelated parallel machines with combinatorial auction

Optimal scheduling on unrelated parallel machines with combinatorial auction

Research on Multi-round First-price Sealed Bidding Strategy Based on Bidders' Incomplete Information Game

Bidding mechanisms are essential for the market and policies because bidding patterns have an impact on economic rationality and are crucial for the functioning of the construction industry. Thus, this paper consolidates the findings from the multiple rounds of combinatorial auctions, the winners curse in incomplete information auctions, and game theory. There is no doubt that bidding mechanisms play an important role in markets and policies in economic activities. This paper's related topics of interest would be multi-round combinatorial auctions, winners curses in project bidding, and game theory in incompletely informed auctions. This paper reviews the literature and employs the models based on the Nash equilibrium. There are many types of bidding strategies such as first, second, and successive bid bidding strategies, cooperative bidding, non-cooperative bidding, and how information asymmetry plays a critical role in these strategies. As mentioned before, criterion-based adaptive bidding strategies are not sensitive to market conditions and can provide near-optimal solutions. In the same way, iterative learning also prevents the occurrence of the winners curse in the multi-stage bidding context. UK auctions are seen as more efficient relative to other locations because information costs are lower, while game-theory-based strategies improve mechanisms for obtaining tasks and cost optimization in mobile crowdsourcing tasks. The use of electronic auctions can help a market become more fully rational and efficient. The methodology of game theory helps explain the outcomes of auctioning and emphasizes innovations in automation as well as policies. Therefore, this paper's implications are significant to the current and ongoing literature on efficiency, strategic behaviour, and policy in bidding mechanisms across different markets.

A branch-and-cut algorithm for the time-dependent vehicle routing problem with time windows and combinatorial auctions

The urban logistics industry typically faces traffic congestion problems that result in variation of travel times across the day and impose a great challenge in routing design. While companies may either use a private fleet of delivery vehicles or outsource the tasks to the third-party logistics (3PL) providers to fulfill their logistics demand, some companies might employ a combination of both when their resource is unable to cope with demand or if demand fluctuates significantly over time. To tackle both challenges, we focus on a new variant of the vehicle routing problem known as the time-dependent vehicle routing problem with time windows and combinatorial auctions (TD-VRPTWCA), which considers time-dependent travel times in the routing design of the private fleet while selecting competitive bids from the 3PLs to serve a subset of the customers economically. The goal is to minimize the sum of the travel cost incurred by the private fleet and the outsourcing cost charged by the 3PLs for the chosen bids. To solve this problem, we present an arc-flow model with nine families of valid inequalities to strengthen the linear relaxation of the model. Based on this, a branch-and-cut approach is developed and evaluated on instances adapted from the well-known Solomon’s benchmark data. Extensive computational results demonstrate the effectiveness of the proposed method.

An Iterative Procurement Combinatorial Auction Mechanism for the Multi-Item, Multi-Sourcing Supplier-Selection and Order-Allocation Problem under a Flexible Bidding Language and Price-Sensitive Demand

This study addresses the multi-item, multi-sourcing supplier-selection and order-allocation problem. We propose an iterative procurement combinatorial auction mechanism that aims to reveal the suppliers’ minimum acceptable selling prices and assign orders optimally. Suppliers use a flexible bidding language to submit procurement bids. The buyer solves a Mixed Integer Non-linear Programming (MINLP) model to determine the winning bids for the current auction iteration. We introduce a buyer’s profit-improvement factor that constrains the suppliers to reduce their selling prices in subsequent bids. Moreover, this factor enables the buyer to strike a balance between computational effort and optimality gap. We develop a separate MINLP model for updating the suppliers’ bids while satisfying the buyer’s profit-improvement constraint. If none of the suppliers can find a feasible solution, the buyer reduces the profit-improvement factor until a pre-determined threshold is reached. A randomly generated numerical example is used to illustrate the proposed mechanism. In this example, the buyer’s profit improved by as much as 118% compared to a single-round auction. The experimental results show that the proposed mechanism is most effective in competitive environments with several suppliers and comparable costs. These results reinforce the importance of fostering competition and diversification in a supply chain.

A flexible combinatorial auction bidding language for supplier selection and order allocation in a supply chain with price sensitive demand

This study addresses the multi-item multi-sourcing supplier selection and order allocation problem in a Combinatorial Auction (CA) framework. First, we propose a new flexible procurement CA bidding language, then prove that it can convey the same information as existing bidding languages while allowing more efficient auction outcomes and reduced computational complexity. Suppliers submit combinatorial bids to a single manufacturer. Each bid carries information about the supplier’s cost structure and potential discounts. The manufacturer purchases the items and assembles one or more product types that experience price-sensitive demand rates by end consumers. We use the realistic logit function to represent the price-sensitive demand rates of finished products. A Mixed Integer Non-Linear Programming (MINLP) model is developed to help the manufacturer make optimal supplier selection, order allocation, and pricing decisions under the proposed bidding language. The MINLP model considers purchasing, transportation, ordering, administrative, holding, and manufacturing costs. These considerations make the results of this study realistic with the potential to be used in practical applications. Also, we derive a set of necessary conditions that must exist in at least one optimal solution to the problem. These conditions can be utilized to design efficient solution mechanisms for this difficult problem in the future. Finally, an extensive numerical analysis is performed to illustrate the bidding language and the key results.

Combinatorial Auctions in Practice

We survey the uses of combinatorial auctions that have been deployed in practice, giving emphasis to their key representational and economic aspects. In addition, we discuss behavioral economics considerations on both the bidder and auctioneer sides of the market, and the interrelated topics of simplicity and trust, highlighting key opportunities for future work. (JEL D44, D91)

An Effective Two-Stage Algorithm for the Bid Generation Problem in the Transportation Service Market

This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm’s efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions.

Machine Learning-Powered Combinatorial Clock Auction

We study the design of iterative combinatorial auctions (ICAs). The main challenge in this domain is that the bundle space grows exponentially in the number of items. To address this, several papers have recently proposed machine learning (ML)-based preference elicitation algorithms that aim to elicit only the most important information from bidders. However, from a practical point of view, the main shortcoming of this prior work is that those designs elicit bidders' preferences via value queries (i.e., “What is your value for the bundle {A, B}?''). In most real-world ICA domains, value queries are considered impractical, since they impose an unrealistically high cognitive burden on bidders, which is why they are not used in practice. In this paper, we address this shortcoming by designing an ML-powered combinatorial clock auction that elicits information from the bidders only via demand queries (i.e., “At prices p, what is your most preferred bundle of items?''). We make two key technical contributions: First, we present a novel method for training an ML model on demand queries. Second, based on those trained ML models, we introduce an efficient method for determining the demand query with the highest clearing potential, for which we also provide a theoretical foundation. We experimentally evaluate our ML-based demand query mechanism in several spectrum auction domains and compare it against the most established real-world ICA: the combinatorial clock auction (CCA). Our mechanism significantly outperforms the CCA in terms of efficiency in all domains, it achieves higher efficiency in a significantly reduced number of rounds, and, using linear prices, it exhibits vastly higher clearing potential. Thus, with this paper we bridge the gap between research and practice and propose the first practical ML-powered ICA.

The impact of core constraints on truthful bidding in combinatorial auctions

Combinatorial auctions (CAs) offer the flexibility for bidders to articulate complex preferences when competing for multiple assets. However, the behavior of bidders under different payment rules is often unclear. Our research explores the relationship between core constraints and several core-selecting payment rules. Specifically, we examine the natural and desirable property of payment rules of being non-decreasing, which ensures that bidding higher does not lead to lower payments. Earlier studies revealed that the VCG-nearest payment method – a commonly employed payment rule – fails to adhere to this principle even for single-minded CAs. We establish that when a single effective core constraint exists, the payment maintains the non-decreasing property in single-minded CAs. To identify auctions where such a constraint is present, we introduce a novel framework using conflict graphs to represent single-minded CAs and establish sufficient conditions for the existence of single effective core constraints. We proceed with an analysis of the implications on bidder behavior, demonstrating that there is no overbidding in any Nash equilibrium when considering non-decreasing core-selecting payment rules. Our study concludes by establishing the non-decreasing nature of two additional payment rules, namely the proxy and proportional payment rules, for single-minded CAs.

Networked Combinatorial Auction for Crowdsourcing and Crowdsensing

Networked Combinatorial Auction for Crowdsourcing and Crowdsensing

Mechanism Design for Semantic Communication in UAV-Assisted Metaverse: A Combinatorial Auction Approach

Mechanism Design for Semantic Communication in UAV-Assisted Metaverse: A Combinatorial Auction Approach

Aggregating Large-Scale Residential Users for Regulation Reserve Provision: Truthful Combinatorial Auction Based Approach

Aggregating Large-Scale Residential Users for Regulation Reserve Provision: Truthful Combinatorial Auction Based Approach

A multi-agent resource bidding algorithm for order acceptance and assembly job shop scheduling

This study uses an agent-based approach with a combinatorial auction mechanism to solve the joint order acceptance and assembly job shop scheduling problem. A set of jobs is offered. Each job has a revenue, ready time, due date, deadline, and consists of a set of operations with precedence relationships. Jobs that deviate from their due dates incur earliness/tardiness penalties. An operation may require several units of capacity per time unit and a resource could have multiple units of capacity. The manufacturer can reject any job to satisfy the capacity constraints and maximise the overall profit. We develop a mathematical model for the problem, then use an agent-based approach to solve it. First, the relaxed problem is decomposed into a set of job-level subproblems. Each job is optimised individually without considering the capacity constraints. Profitable jobs at the individual level submit their optimal schedules as combinatorial bids to an auctioneer to acquire combinations of resource capacity-time units. Then, the auctioneer records the profit upper bound, resolves capacity conflicts to reach a feasible solution, records the profit lower bound, and updates the dual variables. Experimental results show that the proposed methodology can solve large-sized problems in reasonable CPU times.

Preallocation-Based Combinatorial Auction for Efficient Fair Channel Assignments in Multi-Connectivity Networks

We consider a general multi-connectivity framework, intended for ultra-reliable low-latency communications (URLLC) services, and propose a novel, preallocation-based combinatorial auction approach for the efficient allocation of channels. We compare the performance of the proposed method with several other state-of-the-art and alternative channel-allocation algorithms. The two proposed performance metrics are the capacity-based and the utility-based context. In the first case, every unit of additional capacity is regarded as beneficial for any tenant, independent of the already allocated quantity, and the main measure is the total throughput of the system. In the second case, we assume a minimal and maximal required capacity value for each tenant, and consider the implied utility values accordingly. In addition to the total system performance, we also analyze fairness and computational requirements in both contexts. We conclude that at the cost of higher but still plausible computational time, the fairness-enhanced version of the proposed preallocation based combinatorial auction algorithm outperforms every other considered method when one considers total system performance and fairness simultaneously, and performs especially well in the utility context. Therefore, the proposed algorithm may be regarded as candidate scheme for URLLC channel allocation problems, where minimal and maximal capacity requirements have to be considered.

Design of online combinatorial auction mechanism for urban land transfer.

With the wide application of the "Tender, Auction, and Listing" system for land in China, it is of paramount importance to establish a sound land auction mechanism so as to avoid unreasonable land allocation. However, existing studies only focus on developers who are merely concerned about land combinations and offline auctions with low efficiency and high land unsold rate. To further improve land auction mechanism, we modeled the problem of land allocation as an online combinatorial auction. On this basis, we defined a land correction coefficient and designed an optimal online combinatorial auction mechanism that enabled developers to submit multiple combinations of land. Our designed mechanism proved to satisfy both incentive compatibility (IC) and individual rationality (IR), which can prevent developers from lying in the auction while winning higher revenue, reducing land unsold rate, increasing developer turnover rate and promoting the stability of land resource allocation rate. Therefore, online combinatorial auction mechanism, both applicable and efficient, is a practical solution for improving land auctions in China.

Request acceptance with overbooking in dynamic and collaborative vehicle routing

We consider the problem setting of a less-than-truckload carrier serving stochastic customer requests. Each request must be answered dynamically by accepting or rejecting it immediately. On the next day, accepted requests are served in routes using a set of vehicles with limited load capacity and route duration. After the request acceptance phase and before the fulfillment, multiple carriers participate in a combinatorial auction to exchange requests. An auctioneer allocates the bundles of requests to carriers according to their bids in a cost-minimizing way and distributes the auction profits. This type of horizontal collaboration provides cost savings and contributes to reducing negative impacts of transportation. We describe the carrier’s optimization problem of maximizing profit as a Markov decision process that comprises the sequential decisions in all phases, i.e., request acceptance, request selection for the auction, bidding, and routing. For solving a version of the vehicle routing problem with pickups and deliveries, heuristic approaches are proposed that achieve efficient and balanced routes. We design overbooking policies for strategically accepting more requests bearing in mind the options provided by the auction. Computational results show that – by trading requests in an auction – carriers can accept more requests than they could serve on their own. The carriers’ request acceptance decisions impact their individual profits and the overall collaboration savings. The largest benefits can be achieved with an overbooking policy that prescribes which requests should be accepted by all carriers, based on the locations of both the request and the carriers’ depots.

Distributed energy storage participating in power trading mechanism for power system flexibility

In the paper of the participation of multiple types of market members, such as photovoltaics, wind power, and distributed energy storage, in market-based trading, the development of new power systems hinges on strengthening the adaptability of power systems to accommodate various types of market participants and improving their flexibility. The establishment of a modern power system also faced major challenges. Such as how to achieving collaborative operation between the main grid, regional distribution networks, and distributed power generation and consumption devices, and how to improving the flexibility of grid operation, and how to increasing device utilization, and reducing operating costs. In view of above-mentioned issues, this study proposed employing the traceability and anti-tampering features of blockchain technology tackle the issue of establishing mutual trust among different types of market participants and, considering the high volatility of new energy output, studies the configuration of a flexible power system in response to output deviations resulting from day-ahead forecasting-intraday operation (DAF-IDO). A market-based trading mechanism involving multiple types of market participants has been established to smooth out the deviation in output from different types of participants, improving the economic benefits of system operation. This study has made innovative contributions as follows: First, this study employed blockchain technology to enable the participation of various types of market participants in trading activities together. Second, this study proposed a method for determining DAF-IDO energy storage action deviations to allow regional distribution networks based on distribution network operators to quantitatively calculate their energy storage supply and demand, providing crucial methodological support for their participation in market trading in the future. Third, the study developed a trading mechanism based on combinatorial auctions for multiple types of market participants, and incorporated an valley compensation mechanism into the pricing mechanism to encourage active and autonomous participation of users, while also considering the economic benefits of all parties involved. Ultimately, numerical simulations were conducted to verify the feasibility and rationality of the trading mechanism, taking into account the DAF-IDO energy storage action deviations while multiple regional networks are participating.

Combinatorial Auction of Used Cars Considering Pro-Environment Attribute: A Social Welfare Perspective

Air pollution is becoming more and more serious as the number of vehicles increases. To address such problems, many cities have implemented many measures, including the circular economy mode, in which used cars with low carbon emission are becoming important in the sustainable transportation and carbon abatement. Considering multi-attribute demand, this study designed combinatorial auction mechanism for the bidders of automobile enterprises on an online used-car platform to achieve social welfare maximization. Two kinds of attributes were considered, namely, price attribute and non-price attributes; the latter particularly included the pro-environment attribute based on an analysis of complementarity and substitutability. Moreover, the mechanism was proved to satisfy individual rational condition and incentive compatibility condition. Numerical application showed that preference for the pro-environment attribute can better realize social welfare and respond to national energy conservation and emission reduction targets. As a result, from the social welfare perspective, the multi-attribute combinatorial auction can provide a reference for more fair and effective allocation of used cars to bidders and can promote both buyer’s utility and seller’s income.

Energy Storage Sharing for Multiple Services Provision: A Computable Combinatorial Auction Design

Given the profound integration of the sharing economy and the energy system, energy storage sharing is promoted as a viable solution to address the underutilization of energy storage and the challenges associated with cost recovery. While energy storage sharing offers various services for system operation, a significant question remains regarding the development of an optimal allocation model for shared energy storage in diverse application scenarios and the proposal of efficient solving algorithms. This paper presents the design of a computable combinatorial mechanism aimed at facilitating energy storage sharing. Leveraging the distinct characteristics of buyers and sellers engaged in energy storage sharing, we propose a combinatorial auction solving algorithm that prioritizes and incorporates the offers of shared energy storage, accounting for temporal variations in the value of energy resources. The numerical results demonstrate that the proposed solving algorithm achieves a computation time reduction of over 95%, adequately meeting the practical requirements of industrial applications. Importantly, the proposed method maintains a high level of computational accuracy, ranging from 92% to 98%, depending on the participants and application scenarios. Hopefully, our work is able to provide a useful reference for the further mechanism design for energy storage sharing.

Properties of bundle valuations in carrier collaboration

Combinatorial auctions are an important part of many frameworks for carrier collaboration in logistics. In the last years, many innovative auction mechanisms have been developed in the economic literature that could potentially be applied in this context and that could significantly simplify the process of determining efficient allocations of requests. These mechanisms rely on certain assumptions about the valuations of bidders. In this paper, we perform computational experiments to analyze to which extent these requirements are fulfilled for valuations derived from a simple logistics problem, the Traveling Salesman Problem. We find that bidders’ valuations typically violate even very elementary requirements, but that these violations affect only a limited number of request bundles. We further analyze whether these violations exhibit a consistent pattern across multiple carriers and check consistency if route lengths are calculated exactly or approximated.