基于高斯分布的在线采购机制设计及竞争分析

依附于互联网电子商务的在线采购拍卖交易, 对传统的贝叶斯离线拍卖理论提出新的挑战, 因为面对不同时间点的投标, 采购电商必须即可决策出是否中标以及购买价格。鉴于此, 对于诸如石油、煤、粮食等无限可分商品的电子采购, 本文基于投标具有高斯分布特征设计了一种激励相容的在线采购策略, 演绎出在线采购的数学模型, 利用Runge-Kutta数值算法, 通过Matlab编程求解出采购电商在线定价策略的需求曲线及其对应的竞争比, 最后, 利用数值模拟, 将在线采购机制策略与纯竞争分析得到的在线采购策略比较, 结果显示利用了高斯分布信息的在线采购策略的竞争性能由于利用了投标的统计信息而得到了提高。     

Compact bidding languages and supplier selection for markets with economies of scale and scope

Combinatorial auctions have been used in procurement markets with economies of scope. Preference elicitation is already a problem in single-unit combinatorial auctions, but it becomes prohibitive even for small instances of multi-unit combinatorial auctions, as suppliers cannot be expected to enumerate a sufficient number of bids that would allow an auctioneer to find the efficient allocation. Auction design for markets with economies of scale and scope are much less well understood. They require more compact and yet expressive bidding languages, and the supplier selection typically is a hard computational problem. In this paper, we propose a compact bidding language to express the characteristics of a supplier’s cost function in markets with economies of scale and scope. Bidders in these auctions can specify various discounts and markups on overall spend on all items or selected item sets, and specify complex conditions for these pricing rules. We propose an optimization formulation to solve the resulting supplier selection problem and provide an extensive experimental evaluation. We also discuss the impact of different language features on the computational effort, on total spend, and the knowledge representation of the bids. Interestingly, while in most settings volume discount bids can lead to significant cost savings, some types of volume discount bids can be worse than split-award auctions in simple settings.     

Using a DEA-cross efficiency approach in public procurement tenders

The paper addresses the topic of supplier selection in public procurement. According to European directives, when tenders are awarded through the “Most Economically Advantageous Tender” (MEAT) criterion, the awarding committee has to decide the tender evaluation criteria of the presented bids in advance. The authors propose a decision making tool that is aimed at helping the awarding committee in this difficult task and, at the same time, maintaining a transparent procedure in accordance with governmental procurement regulations and requirements as well as guaranteeing fair and equal evaluation of all bids. In this regard, the decision problem of supplier selection is addressed by applying an extension of the DEA (data envelopment analysis) methodology. The cross-efficiency evaluation is used for selecting the best supplier among the eligible candidates. The proposed technique allows the evaluation of quantitative data related to vendor selection and keeps the transparency features requested by public procurement. In addition, all bids are equally assessed according to the same objectively defined weights without any subjective setting by the public officers. The effectiveness and efficiency of the approach is supported by a case study that pertains to the tender of an Italian public agency.     

Robust strategic bidding in auction-based markets

In this paper, we propose an alternative methodology for devising revenue-maximizing strategic bids under uncertainty in the competitors’ bidding strategy. We focus on markets endowed with a sealed-bid uniform-price auction with multiple divisible products. On recognizing that the bids of competitors may deviate from equilibrium and are of difficult statistical characterization, we proposed a two-stage robust optimization model with equilibrium constraints aiming to devise risk-averse strategic bids. The proposed model is a trilevel optimization problem that can be recast as a particular instance of a bilevel program with equilibrium constraints. Reformulation procedures are proposed to find a single-level equivalent formulation suitable for column-and-constraint generation (CCG) algorithm. Results show that even for the case in which an imprecision of 1% is observed on the rivals’ bids in the equilibrium point, the robust solution provides a significant risk reduction (of 79.9%) in out-of-sample tests. They also indicate that the best strategy against high levels of uncertainty on competitors’ bid approaches to a price-taker offer, i.e., bid maximum capacity at marginal cost.     

Optimal bidding in auctions of mixed populations of bidders

A mixed population of bidders consists of two asymmetric groups. Members of the first group are game-theoretic players, who maximize their expected profit and incorrectly believe that their opponents act similarly. The second group of bidders adopts an irrational strategy: they either choose their bids randomly following a given probability distribution, in a “naïve” form of bidding, or follow a decision-theoretic approach, maximizing their expected profit under the assumption that all other bids are random. In a sealed bid private-value procurement auction we examine the optimal strategy of a new player, who has perfect knowledge of the structure of the mixed bidder population and enters the auction. The optimal bid of the new bidder is derived when the cost and mark-up follow a uniform distribution in [0, 1]. The effect of the relative size of the group of game-theoretic bidders and the population size on the optimal bid price is established.     

Nonparametric identification and estimation of score auctions in multi-attribute procurement

Score auctions are used in procurement to incorporate other attributes beyond price. We establish nonparametric econometric identification of bidders' pseudotypes (a measure of bidder's private cost), when bids are evaluated using a preannounced quasi-linear score, calculated on the basis of the submitted levels of the attributes. Hence, we extend the standard nonparametric method for independent private costs sealed-bid, first price auctions, to multi-attribute quasi-linear score auctions. We illustrate the result with an application to scoring bid data.     

Comparing the Spanish and the discriminatory auction formats: A discrete model with private information

The Spanish Treasury is the only Treasury in the world that uses a hybrid system of discriminatory and uniform price auctions to sell government debt: winning bidders pay their bid price for each unit if this is lower than the weighted average price of winning bids (WAP), and pay the WAP otherwise. Following Gordy [Gordy, M., 1996. Multiple bids in a multiple-unit common-value auction. Board of Governors of the Federal Reserve System], we model the Spanish auction as a common value auction of multiple units with private information, allowing for multiple bids. Numerical analysis shows that bidders spread their bids more in the Spanish than in the discriminatory auction and bid higher for the first unit, and that the expected seller’s revenue is higher in the Spanish than in the discriminatory auction within a reasonable set of parameter values.     

On being balanced in an unbalanced world

This paper examines the case of a procurement auction for a single project, in which the breakdown of the winning bid into its component items determines the value of payments subsequently made to bidder as the work progresses. Unbalanced bidding, or bid skewing, involves the uneven distribution of mark-up among the component items in such a way as to attempt to derive increased benefit to the unbalancer but without involving any change in the total bid. One form of unbalanced bidding for example, termed Front Loading (FL), is thought to be widespread in practice. This involves overpricing the work items that occur early in the project and underpricing the work items that occur later in the project in order to enhance the bidder's cash flow. Naturally, auctioners attempt to protect themselves from the effects of unbalancing—typically reserving the right to reject a bid that has been detected as unbalanced. As a result, models have been developed to both unbalance bids and detect unbalanced bids but virtually nothing is known of their use, success or otherwise. This is of particular concern for the detection methods as, without testing, there is no way of knowing the extent to which unbalanced bids are remaining undetected or balanced bids are being falsely detected as unbalanced. This paper reports on a simulation study aimed at demonstrating the likely effects of unbalanced bid detection models in a deterministic environment involving FL unbalancing in a Texas DOT detection setting, in which bids are deemed to be unbalanced if an item exceeds a maximum (or fails to reach a minimum) ‘cut-off’ value determined by the Texas method. A proportion of bids are automatically and maximally unbalanced over a long series of simulated contract projects and the profits and detection rates of both the balancers and unbalancers are compared. The results show that, as expected, the balanced bids are often incorrectly detected as unbalanced, with the rate of (mis)detection increasing with the proportion of FL bidders in the auction. It is also shown that, while the profit for balanced bidders remains the same irrespective of the number of FL bidders involved, the FL bidder's profit increases with the greater proportion of FL bidders present in the auction. Sensitivity tests show the results to be generally robust, with (mis)detection rates increasing further when there are fewer bidders in the auction and when more data are averaged to determine the baseline value, but being smaller or larger with increased cut-off values and increased cost and estimate variability depending on the number of FL bidders involved. The FL bidder's expected benefit from unbalancing, on the other hand, increases, when there are fewer bidders in the auction. It also increases when the cut-off rate and discount rate is increased, when there is less variability in the costs and their estimates, and when less data are used in setting the baseline values.     

Multicriteria decision making on maintenance: Spares and contracts planning

The competitiveness of an industrial system is directly related to decision making in areas of product support logistics, such as the maintenance area. Multicriteria decision making takes into account various aspects associated with competitiveness of the system. This paper presents multicriteria decision models for two maintenance problems: repair contract selection and spares provisioning. In the repair contract problem the model incorporates consequences modelled through a multiattribute utility function. These consequences consist of contract cost and system performance, represented by the system interruption time. Two criteria (risk and cost) are combined through a multiattribute utility function in the spares provisioning decision model. This paper presents the formulation and derivations for both models and the numerical application illustrates the use of models including sensitivity analysis.     

Target market selection and marketing effort under uncertainty: The selective newsvendor

We consider a firm that markets, procures, and delivers a good with a single selling season in a number of different markets. The price for the good is market-dependent, and each market has an associated demand distribution, with parameters that depend on the amount of marketing effort applied. Given long procurement lead-times, the firm must decide which markets it will serve prior to procuring the good. We develop a profit maximizing model to address the firm’s integrated market selection, marketing effort, and procurement decisions. The model implicitly accounts for inventory pooling across markets, which reduces safety stock costs but increases model complexity. The resulting model is a nonlinear integer optimization problem, for which we develop specialized solution methods. For the case in which budget constraints exist, we provide a novel solution approach that uses a tailored branch-and-bound algorithm. Our approach solves a broad range of 3000 test instances in an average of less than 2 seconds, significantly outperforming a leading commercial global optimization solver.     

Newsvendor with multiple options of expediting

We consider a manufacturer facing single period inventory planning problem with uncertain demand and multiple options of expediting. The demand comes at a certain time in the future. The manufacturer may order the product in advance with a relatively low cost. She can order additional amount by expediting after the demand is realized. There are a number of expediting options, each of which corresponds to a certain delivery lead time and a unit procurement price. The unit procurement price is decreasing over delivery lead time. The selling price is also decreasing over time. In this paper, we assume that the manufacturer must deliver all products to the customer in a single shipment. The problem can be formulated as a profit maximization problem. We develop structural properties and show how the optimal solution can be identified efficiently. In addition, we compare our model with the classical newsvendor model and obtain a number of managerial insights.     

Application of multi-dimensional procurement auction in single-period inventory models

Procurement is one of the major activities in the Manufacturing Resource Planning (MRP II), which is closely coupled with inventory management. Any improvement in this area will have a direct impact on the performance of the entire supply chain. Auction mechanism can be a successful procurement method when there are several potential suppliers available. In this paper, we consider a single-period inventory model when the selection of the supplier is done through a reverse auction with bids consisting of several attributes, namely price, shortage quantity, and lead time. The multi-dimensionality of the bid increases the complexity of the underlying problem creating a need for an approach to determine an approximate optimal target level. This is needed for the initiation of the auction and the procurement process. Monte-Carlo simulation method was used to investigate the performance of the approximation. Simulation results show that the analytical method provides an acceptable approximation for the optimal target inventory level.     

Post-objective determination of weights of the evaluation factors in public procurement tenders

In public procurement tenders the awarding criterion of the most economically advantageous bid employs weights to aggregate the numerical scores assigned to each proposal with respect to different evaluation factors. Typically these weights are fixed and subjectively set in advance. Methods, which objectively determine the weights after the opening of the sealed bids on the basis of the most or least favorable weights for each proposal, are developed. Post-objective methods of weight determination are shown to enhance the integrity of the evaluation process and to limit corruption in a public tender. The connection of Data Envelopment Analysis, which has been extensively applied to measure supplier efficiency, with the developed methods, is explored. Average least and most favorable weights are derived and optimal bidding strategies in this setting are presented.     

Configurable offers and winner determination in multi-attribute auctions

The theory of procurement auctions traditionally assumes that the offered quantity and quality is fixed prior to source selection. Multi-attribute reverse auctions allow negotiation over price and qualitative attributes such as color, weight, or delivery time. They promise higher market efficiency through a more effective information exchange of buyer’s preferences and supplier’s offerings. This paper focuses on a number of winner determination problems in multi-attribute auctions. Previous work assumes that multi-attribute bids are described as attribute value pairs and that the entire demand is purchased from a single supplier. Our contribution is twofold: First, we will analyze the winner determination problem in case of multiple sourcing. Second, we will extend the concept of multi-attribute auctions to allow for configurable offers. Configurable offers enable suppliers to specify multiple values and price markups for each attribute. In addition, suppliers can define configuration and discount rules in form of propositional logic statements. These extensions provide suppliers with more flexibility in the specification of their bids and allow for an efficient information exchange among market participants. We will present MIP formulations for the resulting allocation problems and an implementation.     

蜂群算法求解支持模糊QoS约束的电子采购模型

基于Web的电子物流采购是电子商务的热点.通过将模糊量化的QoS约束加入到Web电子物流采购模型,构造一种带有QoS约束的Web电子物流采购模型,并设计一种改进的人工蜂群算法进行求解.模型基于现有Web采购系统的采购模式,融合了非功能性Web服务评价理论,着重将带QoS约束的电子物流采购选择过程与人工蜂群算法求解过程相结合,从而能快速准确地获得使整体利益最大的解.经仿真计算,验证了模型的有效性.     

Simple probability models for project contracting

There are two aspects to the process of price setting using sealed bids. The project owner is interested in deploying the contract mechanism that will secure reliable service at the cheapest cost. On the other hand, each contractor bidding for the project is interested in winning the contract but at a price that assures him a reasonable profit margin. We use a parsimonious stochastic model to compare and contrast some commonly used contracts from the point of view of the project owner. We show that if the bidders are risk neutral, a Fixed Price contract results in the smallest expected procurement cost for the project owner. We introduce and analyze Menu contracts and show that the expected price of a Menu contract lies in between the prices of the Fixed Price and Cost Plus contracts for the same project. We analyze how risk aversion and collusion, which we model using concepts of stochastic dependence, impacts the average winning bid price.     

On Heuristics for Solving Winner Determination Problem in Combinatorial Auctions

The winner determination problem (WDP) in combinatorial auctions is the problem of, given a finite set of combinatorial bids B, finding a feasible subset B of B with a maximum revenue. WDP is known to be equivalent to the maximum weight set packing problem, and hard to approximate by polynomial time algorithms. This paper proposes three heuristic bid ordering schemes for solving WDP; the first two schemes take into account the number of goods shared by conflicting bids, and the third one is based on a recursive application of such local heuristic functions. We conducted several experiments to evaluate the goodness of the proposed schemes. The result of experiments implies that the first two schemes are particularly effective to improve the performance of the resulting heuristic search procedures. More concretely, they are scalable compared with the conventional linear programming (LP) relaxation based schemes, and could quickly provide an optimum solution under optimization schemes such as the branch-and-bound method. In addition, they exhibit a good anytime performance competitive to the LP-based schemes, although it is sensitive to configurable parameters controlling the strength of contributions of bid conflicts to the resultant bid ordering schemes.     

Multiple unit auctions with economies and diseconomies of scale

This paper discusses multiple unit auctions for industrial procurement where the cost structures of suppliers capture economies and diseconomies of scale caused by the nature of the production cost and the opportunity value of suppliers’ capacities. The problem of winner determination and demand allocation is proven to be NP-complete. We propose a binary tree algorithm with bounds (BTB) which efficiently exploits the model’s optimality properties. BTB outperforms general integer optimization software in computational time, especially with existence of substantial economies and diseconomies of scale. The algorithm complexity is linear in demand volume. This property allows for efficient handling of high volume auctions and thus leads to increased benefit for the overall system. Under the assumption of the myopic best response strategies, we investigate the behavior of suppliers and price dynamics for iterative (multiple round) bidding with appropriate allocation and stopping rules. The allocation rules, featured by several tie breakers for multiple optimal solutions to the allocation model in each round, are proposed to induce suppliers’ dominant strategies and to improve the system’s performance.     

Graphical method for identifying high outliers in construction contract auctions

Construction contract auctions are characterised by (1) a heavy emphasis on the lowest bid, as that is which usually determines the winner of the auction, (2) anticipated high outliers due to the presence of uncompetitive bids, (3) very small samples, and (4) uncertainty of the appropriate underlying density function model of the bids. This paper describes a graphical method for simultaneously identifying outliers and density functions by first removing candidate (high) outliers and then examining the goodness-of-fit of the resulting reduced samples by comparing the reduced sample predictability (by the expected value of the lowest order statistic) of the lowest bid with that of the equivalent predictability by Monte Carlo simulations of one of the common density functions. When applied to a set of 1073 auctions, the results indicate the appropriateness of censored and reduced sample lognormal models for a wide range of cut-off values. These are compared with cut-off values used in practice and to identify potential improvements.     

带有风能的智能电网多周期买电策略研究

本文研究带有风能随机供给的智能电网中传统能源的多周期买电问题,假设存在一个能源运营商集中负责智能电网传统能源的购买和消费。通过构建并求解动态规划模型,找到能源运营商在风能供给不确定性下的传统能源最优多周期买电策略。在最优买电策略下,能源运营商只有在当期电价足够小时才购买传统能源,其买电量与风能分布、价格信息和时间信息有关。在实际数据的基础之上,提供详实的数值实验对比研究了本文的最优买电策略和其他两种策略(实践中只考虑风能估计的策略和放弃利用风能的策略)在最小化总成本方面的效果,并验证了本文的最优买电策略在真实风能数据中的鲁棒性。