生产者对回收责任约束的参与意愿——强制性与自愿性的形成机理及驱动因素分析

绿色发展要求生产者承担回收、循环并再利用的延伸责任。政府通过合规计划约束生产者的行为,规制水平与获利驱动调控生产者的参与意愿而实现回收责任。本文以再制造作为废旧产品的价值恢复模式,导入了循环环节的环境成本,构建了基于经济效益和经济效益与环境效益相统一的生产者参与意愿决策模型,运用线性约束二次规划的K-T条件方法,确立了两种情境下的最优决策。研究结果给出了生产者强制性与自愿性的分型边界,分型边界受恢复价值和政府规制水平的联合驱动;评估了环境成本结构对强制性/自愿性的分型边界、效益的影响。     

Pricing with markups in industries with increasing marginal costs

We study a game that models a market in which heterogeneous producers of perfect substitutes make pricing decisions in a first stage, followed by consumers that select a producer that sells at lowest price. As opposed to Cournot or Bertrand competition, producers select prices using a supply function that maps prices to production levels. Solutions of this type of models are normally referred to as supply function equilibria. We consider a market where producers’ convex costs functions are proportional to each other, depending on the efficiency of each particular producer. We provide necessary and sufficient conditions for the existence of an equilibrium that uses simple supply functions that replicate the cost structure. We then specialize the model to monomial cost functions with exponent \(q>0\) , which allows us to reinterpret the simple supply functions as a markup applied to the production cost. We prove that an equilibrium for the markups exists if and only if the number of producers in the market is strictly larger than \(1+q\) , and if an equilibrium exists, it is unique. The main result for monomials is that the equilibrium nearly minimizes the total production cost when the market is competitive. The result holds because when there is enough competition, markups are bounded, thus preventing prices to be significantly distorted from costs. Focusing on the case of linear unit-cost functions on the production quantities, we characterize the equilibrium accurately and refine the previous result to establish an almost tight bound on the worst-case inefficiency of equilibria. Finally, we derive explicitly the producers’ best response for series-parallel networks with linear unit-cost functions, extending our previous result to more general topologies. We prove that a unique equilibrium exists if and only if the network that captures the market structure is 3-edge-connected. For non-series-parallel markets, we provide an example that does not admit an equilibrium on markups.     

Detecting copositivity of a symmetric matrix by an adaptive ellipsoid-based approximation scheme

It is co-NP-complete to decide whether a given matrix is copositive or not. In this paper, this decision problem is transformed into a quadratic programming problem, which can be approximated by solving a sequence of linear conic programming problems defined on the dual cone of the cone of nonnegative quadratic functions over the union of a collection of ellipsoids. Using linear matrix inequalities (LMI) representations, each corresponding problem in the sequence can be solved via semidefinite programming. In order to speed up the convergence of the approximation sequence and to relieve the computational effort of solving linear conic programming problems, an adaptive approximation scheme is adopted to refine the union of ellipsoids. The lower and upper bounds of the transformed quadratic programming problem are used to determine the copositivity of the given matrix.     

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.     

Evolving a three-world framework for solving algebraic equations in the light of what a student has met before

In this paper we consider data from a study in which students shift from linear to quadratic equations in ways that do not conform to established theoretical frameworks. In solving linear equations, the students did not exhibit the ‘didactic cut’ of Filloy and Rojano (1989) or the subtleties arising from conceiving an equation as a balance (Vlassis, 2002). Instead they used ‘procedural embodiments’, shifting terms around with added ‘rules’ to obtain the correct answer (Lima & Tall, 2008). Faced with quadratic equations, the students learn to apply the formula with little success. The interpretation of this data requires earlier theories to be seen within a more comprehensive framework that places them in an evolving context. We use the developing framework of three worlds of mathematics (Tall, 2004, Tall, 2013), based fundamentally on human perceptions and actions and their consequences, at each stage taking into account the experiences that students have ‘met-before’ (Lima and Tall, 2008, McGowen and Tall, 2010). These experiences may be supportive in new contexts, encouraging pleasurable generalization, or problematic, causing confusion and even mathematical anxiety. We consider how this framework explains and predicts the observed data, how it evolves from earlier theories, and how it gives insights that have both theoretical and practical consequences.     

消费者偏好、市场准入与产品安全水平:基于双寡头两阶段博弈模型分析

考虑消费者产品安全偏好和产品安全水平等因素,针对采取不同产品安全战略的两个寡头制造商,建立了两阶段博弈模型:第一阶段为两制造商选择各自的产品安全度水平,第二阶段为两产品制造商确定各自的产品价格。通过数值仿真重点讨论了消费者产品安全偏好支付系数和产品安全市场准入值两参数变化带来的影响。结果表明:消费者安全偏好支付系数提高时,两制造商利润均增加;产品安全准入值提高时,低价战略采取者的利润下降;主动安全战略采取者利润增加。所得结论对于产品安全管理中政府及不同类型制造商的决策具有参考价值和指导意义。     

Equilibria in a competitive model arising from linear production situations with a common-pool resource

In this paper we deal with linear production situations in which there is a limited common-pool resource, managed by an external agent. The profit that a producer can attain depends on the amount of common-pool resource obtained through a certain procedure. We contemplate a competitive process among the producers and study the corresponding non-cooperative games, describing their (strict) Nash equilibria in pure strategies. It is shown that strict Nash equilibria form a subset of strong Nash equilibria, which in turn form a proper subset of Nash equilibria.     

A signal-recovery system: asymptotic properties,and construction of an infinite-volume process

We consider a linear sequence of ‘nodes’, each of which can be in state 0 (‘off’) or 1 (‘on’). Signals from outside are sent to the rightmost node and travel instantaneously as far as possible to the left along nodes which are ‘on’. These nodes are immediately switched off, and become on again after a recovery time. The recovery times are independent exponentially distributed random variables. We present results for finite systems and use some of these results to construct an infinite-volume process (with signals ‘coming from infinity’), which has some peculiar properties. This construction is related to a question by Aldous and we hope that it sheds some light on, and stimulates further investigation of, that question.     

Recovery decisions of a producer in a legislative disposal fee environment

The main objectives of the environmental legislation originating from extended producer responsibility (EPR) principle are to lead producers to undertake recovery initiatives for their end-of-use products and to promote environmentally desirable product design. It is still controversial whether current implementations of EPR principle are effective in attaining these objectives. This study seeks to answer the following questions: (1) What is the impact of EPR legislation on the product recovery decisions of producers? (2) How do the redesign opportunities (i.e., design for disassembly) affect the willingness of producers for product recovery? (3) How do the investment needs to start recovery practices and the reluctance of producers to allocate sufficient funds for this purpose affect the optimal recovery decisions? We use stylized economic models to represent the implementation in practice and solving our models we obtain closed form and numerical solutions that help us to see the impact of various parameters on the optimal decisions of a producer. Our findings indicate that redesign opportunities encourage producers for more recovery, however the reluctance of producers to cover the initial investments may substantially reduce the effectiveness of the legislation and the recovery amounts.     

Day-ahead market bidding for a Nordic hydropower producer: taking the Elbas market into account

In many power markets around the world the energy generation decisions result from two-sided auctions in which producing and consuming agents submit their price-quantity bids. The determination of optimal bids in power markets is a complicated task that has to be undertaken every day. In the present work, we propose an optimization model for a price-taker hydropower producer in Nord Pool that takes into account the uncertainty in market prices and both production and physical trading aspects. The day-ahead bidding takes place a day before the actual operation and energy delivery. After this round of bidding, but before actual operation, some adjustments in the dispatched power (accepted bids) have to be done, due to uncertainty in prices, inflow and load. Such adjustments can be done in the Elbas market, which allows for trading physical electricity up to one hour before the operation hour. This paper uses stochastic programming to determine the optimal bidding strategy and the impact of the possibility to participate in the Elbas. ARMAX and GARCH techniques are used to generate realistic market price scenarios taking into account both day-ahead price and Elbas price uncertainty. The results show that considering Elbas when bidding in the day-ahead market does not significantly impact neither the profit nor the recommended bids of a typical hydro producer.     

A very simple SQCQP method for a class of smooth convex constrained minimization problems with nice convergence results

We introduce a new and very simple algorithm for a class of smooth convex constrained minimization problems which is an iterative scheme related to sequential quadratically constrained quadratic programming methods, called sequential simple quadratic method (SSQM). The computational simplicity of SSQM, which uses first-order information, makes it suitable for large scale problems. Theoretical results under standard assumptions are given proving that the whole sequence built by the algorithm converges to a solution and becomes feasible after a finite number of iterations. When in addition the objective function is strongly convex then asymptotic linear rate of convergence is established.     

Some generalizations of the criss-cross method for quadratic programming

Three generalizations of the criss-cross method for quadratic programming are presented here. Tucker’s, Cottle’s and Dantzig’s principal pivoting methods are specialized as diagonal and exchange pivots for the linear complementarity problem obtained from a convex quadratic program

A finite criss-cross method, based on least-index resolution, is constructed for solving the LCP. In proving finiteness, orthogonality properties of pivot tableaus and positive semidefiniteness of quadratic matrices are used

In the last section some special cases and two further variants of the quadratic criss-cross method are discussed. If the matrix of the LCP has full rank, then a surprisingly simple algorithm follows, which coincides with Murty’s ‘Bard type schema’ in the P matrix case     

An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs

We present an exact formula for the radius of robust feasibility of uncertain linear programs with a compact and convex uncertainty set. The radius of robust feasibility provides a value for the maximal ‘size’ of an uncertainty set under which robust feasibility of the uncertain linear program can be guaranteed. By considering spectrahedral uncertainty sets, we obtain numerically tractable radius formulas for commonly used uncertainty sets of robust optimization, such as ellipsoids, balls, polytopes and boxes. In these cases, we show that the radius of robust feasibility can be found by solving a linearly constrained convex quadratic program or a minimax linear program. The results are illustrated by calculating the radius of robust feasibility of uncertain linear programs for several different uncertainty sets.     

On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity

We consider a model of pay-as-clear electricity market based on a Equilibrium Problem with Complementarity Constraints approach where the producers are playing a noncooperative game parameterized by the decisions of regulator of the market (ISO). In the proposed approach the bids are assumed to be convex quadratic functions of the production quantity. The demand is endogenously determined. The ISO problem aims to maximize the total welfare of the market. The demand being elastic, this total welfare take into account at the same time the willingness to pay of the aggregated consumer, as well as the cost of transactions. The market clearing will determine the market price in a pay-as-clear way. An explicit formula for the optimal solution of the ISO problem is obtained and the optimal price is proved to be unique. We also state some conditions for the existence of equilibria for this electricity market with elastic demand. Some numerical experiments on a simplified market model are also provided.     

On best quadratic triangle inequalities

Contrary to published results, it is shown that there do not exist ‘strongest’ (or ‘best possible’) homogeneous quadratic polynomial triangle inequalities of the form $$q(R,r) \leqslant s^2 \leqslant Q(R,r)$$ without further restrictions. Also, several best inequalities for symmetric functions of three positive variables are considered.     

On a class of quadratic programs

This paper considers a class of quadratic programs where the constraints ae linear and the objective is a product of two linear functions. Assuming the two linear factors to be non-negative, maximization and minimization cases are considered. Each case is analyzed with the help of a bicriteria linear program obtained by replacing the quadratic objective with the two linear functions. Global minimum (maximum) is attained at an efficient extreme point (efficient point) of the feasible set in the solution space and corresponds to an efficient extreme point (efficient point) of the feasible set in the bicriteria space. Utilizing this fact and certain other properties, two finite algorithms, including validations are given for solving the respective problems. Each of these, essentially, consists of solving a sequence of linear programs. Finally, a method is provided for relaxing the non-negativity assumption on the two linear factors of the objective function.     

The augmented system variant of IPMs in two-stage stochastic linear programming computation

The application of interior point methods (IPM) to solve the deterministic equivalent of two-stage stochastic linear programming problems is a known and natural idea. Experiments have proved that among the interior point methods, the augmented system approach gives the best performance on these problems. However, most of their implementations encounter numerical difficulties in certain cases, which can result in loss of efficiency. We present a new approach for the decomposition of the augmented system, which ‘automatically’ exploits the special behavior of the problems. We show that the suggested approach can be implemented in a fast and numerically robust way by solving a number of large-scale two-stage stochastic linear programming problems. The comparison of our solver with fo1aug, which is considered as a state-of-the-art augmented system implementation of interior point methods, is also given.     

A unifying approach to solve a class of rank-three programs involving linear and quadratic functions

The aim of this paper is two-fold. First, the so-called ‘optimal level solutions’ method is described in a new unifying framework with the aim to provide an algorithmic scheme able to approach various different classes of problems. Then, the ‘optimal level solutions’ method is used to solve a class of low-rank programmes involving linear and quadratic functions and having a polyhedral feasible region. In particular, the considered class of programmes covers, among all, rank-three d.c., multiplicative and fractional programmes. Some optimality conditions are used to improve the performance of the proposed algorithm.     

On the stratification of a class of specially structured matrices

We consider specially structured matrices representing optimization problems with quadratic objective functions and (finitely many) affine linear equality constraints in an n-dimensional Euclidean space. The class of all such matrices will be subdivided into subsets [‘strata’], reflecting the features of the underlying optimization problems. From a differential-topological point of view, this subdivision turns out to be very satisfactory: Our strata are smooth manifolds, constituting a so-called Whitney Regular Stratification, and their dimensions can be explicitly determined. We indicate how, due to Thom's Transversality Theory, this setting leads to some fundamental results on smooth one-parameter families of linear-quadratic optimization problems with (finitely many) equality and inequality constraints.     

On the quality of heuristic solutions to a 19 × 19 quadratic assignment problem

Recently Murtagh et al. communicated the best (?) known solution to a 19 × 19 quadratic assignment problem, presented and solved earlier by Elshafei. Their approaches are based on the application of quadratic programming and on the construction of a good initial solution respectively. Their solutions are confronted with one better solution obtained by Lashkari and Jaisingh by means of linear assignment approximations, and many better solutions obtained by the present author through the application of exchange heuristics. The results stress the nonconvex character of the problem, and show the rather misleading nature of the concept: ‘good initial solution’. The quality of initial and final solution prove to be rather weakly (or even negatively!) correlated. A simple, but broad and randomized search results in significantly, better solutions, while simple statistical aids provide an estimate of the quality of these solutions. Finally we make remarks concerning some practical issues.