Optimality conditions for a bilevel matroid problem

In bilevel programming there are two decision makers, the leader and the follower, who act in a hierarchy. In this paper we deal with a weighted matroid problem where each of the decision makers has a different set of weights. The independent set of the matroid that is chosen by the follower determines the payoff to both the leader and the follower according to their different weights. The leader can increase his payoff by changing the weights of the follower, thus influencing the follower’s decision, but he has to pay a penalty for this. We want to find an optimum strategy for the leader. This is a bilevel programming problem with continuous variables in the upper level and a parametric weighted matroid problem in the lower level. We analyze the structure of the lower level problem. We use this structure to develop local optimality criteria for the bilevel problem that can be verified in polynomial time.     

线性二层决策问题的期望收益模型及算法

下层反应不唯一时 ,如何确定二层线性决策问题最优策略为一非确定型决策问题 .对此类问题 ,本文通过引入领导者对追随者合作程度的期望系数 ,提出期望收益模型 .利用双罚函数把该问题转换为一单层次优化问题 ,并提出一种求解问题的全局优化算法 .应用此模型分析二层线性问题可知 :对存在不确定性反应的二层决策问题 ,下层追随者与上层领导者的合作态度是领导者确定其最优策略的关键 ;对下层追随者而言 ,某些情况下 ,采取与领导者部分合作的态度对其自身收益的提高是合理的     

On linear bilevel problems with multiple objectives at the lower level

Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.     

A market regulation bilevel problem: A case study of the Mexican petrochemical industry

In this paper, a bilevel programming model is proposed to study a problem of market regulation through government intervention. One of the main characteristics of the problem herein analyzed is that the government monopolizes the raw material in one industry, and competes in another industry with private firms for the production of commodities. Under this scheme, the government controls a state-owned firm to balance the market; that is, to minimize the difference between the produced and demanded commodities. On the other hand, a regulatory organization that coordinates private firms aims to maximize the total profit by deciding the amount of raw material bought from the a state-owned firm. Two equivalent single-level reformulations are proposed to solve the problem. The first reformulation is based on the strong duality condition of the lower level and results in a continuous non-linear model. The second reformulation resorts to the complementarity slackness optimality constraints yielding a mixed-integer linear model. Additionally, three heuristic algorithms are designed to obtain good-quality solutions with low computational effort. In this problem, the feasible region of the dual problem associated to the follower is independent from the leader’s decision. Therefore, the proposed heuristics exploit this particular characteristic of the bilevel model. Moreover, the third heuristic hybridizes the other two algorithms to enhance its performance. Extensive computational experimentation is carried out to measure the efficiency of the proposed solution methodologies. A case study based on the Mexican petrochemical industry is presented. Additional instances generated from the case study are considered to validate the robustness of the proposed heuristic algorithms. Numerical results indicate that the hybrid algorithm outperforms the other two heuristics. However, all of them demonstrate to be good alternatives for solving the problem. Additionally, optimal solutions of all the instances are obtained by using good quality solutions (given by the hybrid algorithm) as initial solutions when solving the second reformulation via a general purpose solver.     

生产能力限制下价格Stackelberg博弈模型

生产能力限制条件下,同质产品市场中两企业以价格为决策变量进行Stackelberg竞争,采取有效配给规则。两企业对称情况下,生产能力较小时模型存在唯一的子博弈精炼纳什均衡,两企业销量达到自身生产能力,得到相同收益;生产能力较大时,追随企业匹配领头企业的价格,博弈存在后动优势。分析了领头企业生产能力大于追随企业的不对称情形,并给出相应均衡。算例分析表明,企业价格竞争的前提是充分大的供给能力,追随企业应在领头企业生产能力较大时进入市场。     

Decentralised bilevel model for shared inventory management

In this study, we consider the case of a large corporation that owns a warehouse and two concurrent chains. The company opted for shared inventory policy. The warehouse is looking into minimising its inventory cost and at the same time reducing the fluctuation of the personnel. The chains, independently, are trying to minimise their inventory costs. The warehouse plays the role of a leader in optimising its objectives and, as followers, the two chains try to satisfy their objectives. The problem is formulated into a decentralised nonlinear bilevel programming problem. We also consider the fuzziness of some parameters due to the imprecise available information. We propose the mathematical model and we solve it for our specific case.     

Transformational leadership and follower creativity: The mediating role of follower relational identification and the moderating role of leader creativity expectations

We examined follower relational identification with the leader as a mediator and follower perceptions of leader creativity expectations as a moderator in the relationship between transformational leadership and follower creativity. Using a sample of 420 leader–follower dyads from an energy company in mainland China, we found that follower relational identification with the leader mediates the transformational leadership–follower creativity relationship, and this mediating relationship is conditional on the moderator variable of follower perceptions of leader creativity expectations for the path from follower relational identification to follower creativity. These results contribute to the literature by clarifying why (through relational identification) and when (high creativity expectations set by the leader) transformational leadership is positively related to follower creativity.     

How follower traits and cultural values influence the effects of leadership

Follower traits and cultural values are important context variables that influence the effectiveness of leader behaviors. Understanding how these variables interact with leader behaviors has been an important scholarly pursuit for the past several decades. Yet, this research is dispersed, and there exist methodological and theoretical limitations within this line of inquiry. We seek to improve our collective understanding of the role of follower traits and cultural values in leadership behavior research. First, we provide a comprehensive review of the extant research on follower traits and cultural values as moderators of leader behaviors. Second, based on our review and analysis of prior research, we identify important patterns in the literature. Third, we highlight methodological shortcomings and solutions that should enhance the quality of future research in this area. We also offer up theoretical insights for future research that should increase our understanding of how follower traits influence leader behaviors.     

On the Global Convergence of Stochastic Fictitious Play

We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by appealing to techniques from stochastic approximation theory, which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process. The key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system. Our analyses of the other cases combine Lyapunov function arguments with a discrete choice theory result: that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities.     

Transfer of risk in the newsvendor model with discrete demand

In this paper we consider the transfer of risk in a newsvendor model with discrete demand. We view the newsvendor model as a leader/follower problem where the manufacturer (leader) decides the wholesale price and the retailer (follower) decides the quantity ordered. Taking a Pareto-optimal contract as a starting point, the manufacturer wishes to design a real option contract to enhance profits. A new real option contract is said to be feasible if both parties' expected profit is at least as great as in the original contract. When demand is discrete, there are usually infinite feasible contracts that yield maximum expected profits to the manufacturer. In the paper we show that either all, some or none of these real option contracts offer an improved position for the retailer.     

The impact of leader emotion display frequency on follower performance: Leader surface acting and mean emotion display as boundary conditions

Theory and evidence suggest leader emotion has an important influence on follower performance. However, we lack a theoretical framework to understand when the frequency of leader emotional displays may or may not explain significant variance in follower performance. To advance knowledge in this emerging line of research, we integrate Emotion As Social Information (EASI) theory with attribution theory to explore boundary conditions of the relationships of the frequencies of positive and negative leader emotional displays with follower performance. Results based on leaders and followers in three organizations show that leader surface acting acted as a boundary condition, neutralizing the effects of the frequencies of positive and negative leader emotional displays toward an individual follower on that follower's performance. In addition, higher frequency of negative emotional displays shown by the leader to all group members acted as a boundary condition, neutralizing the effect of the frequency of negative leader emotional displays toward an individual follower on that follower's performance. This work advances our understanding of the way the frequency of leader emotional displays may influence follower performance, introduces new types of contingency factors to the leader emotion area, and helps extend emotional labor theory to the leadership context.     

Reconsidering the accuracy of follower leadership ratings

Accurate behavioral measurement is essential to developing a science of leadership, yet accurate measurement has remained elusive. The use of follower reports of leader behavior creates challenges given that a large body of basic and applied research suggests that behavioral ratings reflect not only recall of actual behaviors, but also inferences based on semantic memory, which may vary among individuals. In this paper, we examine several explanations for rater effects that are associated with follower individual differences, contextual factors, and even research methods, such as the type of measure used, that may bias ratings of leader behavior. We also develop a conceptual model to illustrate these processes. Finally, we offer potential solutions to increase accuracy in follower reports of leader behavior.     

LINEAR PROGRAMMING WITH DISCRETE STOCHASTIC RESOURCES: AN ALTERNATIVE APPROACH ACCOUNTING FOR INFEASIBILITY*

In this paper an alternative to, or extension of, the chance-constrained method of stochastic programming is presented whereby an expected cost of infeasibility is included in the objective function. The problem is to select a solution to implement before the available resources are known where the adaption of a non-feasible solution to the resources available involves a system cost. While increasing the amount of computation required, the model enables the decision maker to more effectively trade off increased payoff for decreased likelihood of feasibility.     

Designing time-of-use tariffs in electricity retail markets using a bi-level model – Estimating bounds when the lower level problem cannot be exactly solved

Time-of-use tariffs are a pricing strategy for a product or service in which the supplier establishes time-differentiated prices. Dynamic (e.g., day-ahead) time-differentiated electricity prices can contribute to increase the retailer's profit, allow end-users to reduce the consumption costs and enhance grid efficiency.The electricity retailer and the consumer are hierarchically related. The interaction between them can be modeled by a bi-level (BL) optimization model – the retailer is the upper level decision maker and the consumer is the lower level decision maker. The retailer and the consumer have different and conflicting goals: the retailer establishes the pricing scheme to sell electricity to consumers to maximize his profit; the consumer reacts to these prices by determining the operation of the controllable loads in order to minimize the discomfort and the electricity bill.In this work, a BL optimization model incorporating shiftable, interruptible and thermostatic loads is proposed. The upper level problem is tackled by a particle swarm optimization algorithm while the lower level problem is solved by an exact mixed-integer programming solver. The inclusion of the thermostatic load in the lower level problem imposes a much higher computational burden. Therefore, it may not be possible to find the optimal lower level solution, and a sub-optimal lower level solution is infeasible to the BL problem. Considering a computational budget, this work proposes an approach to compute good quality estimates of bounds for the upper level objective function, providing the leader further information and allowing him to make sounder decisions in an adequate time frame.     

竞争环境下基于服务约束的轴-辐式海运网络优化研究

针对同一海运市场中不同的海运企业——领导者与跟随者在设计多分配的轴-辐式海运网络时引起的竞争问题,突破已往枢纽港口集合是给定的假设,将航线连接设计扩展为可存在多条,引入基于服务约束（服务质量\价格\时间）的吸引力模型来定量表示托运人的选择行为,建立了竞争环境下基于服务约束的轴-辐式海运网络优化问题的数学模型,利用NCP函数、凝聚函数和增广Lagrange乘子罚函数法对这一问题进行求解。算例仿真结果显示：（1）跟随者在托运人考虑单位服务价格时,即使不存在规模经济效应,跟随者也可通过建立合适的枢纽港口来获取一定的市场机会;（2）跟随者在存在较大规模经济效应时其利润最可观,因采用比例模型,在不存在规模经济效应下跟随者在领导者决定设计不同数量的枢纽港口时其利润不会统一收敛于某一定值;（3）跟随者在领导者仅设计1个枢纽港口时可通过建立大量的枢纽港口来争夺丰厚的利润,但对于港口集合 N={1,2,…,12} 的海运市场,领导者只需设计2个以上枢纽港口时跟随者的利润空间便会受到较大挤压。     

合作知识创新中基于Stackelberg博弈的资源共享决策模型

在跨组织的合作知识创新中,如何合理地分配和共享资源至关重要。本文研究了合作知识创新中的跨组织资源共享及合作维系的条件,采用博弈论方法,把合作知识创新看作是一个领导组织和多个从属组织的Stackel berg主从博弈决策模型,领导组织作为主方给出最优参与率策略,各跟随组织作为从方以总体投入以及参与率策略响应,求出了知识创新投入的均衡值、领导组织的参与、各跟随者的参与率以及创新的总体期望收益。文中指出,只有领导组织的边际收益和各从属组织边际收益之和保持最优比,合作才可能形成并有效维系。     

A MATHEMATICAL PROGRAMMING APPROACH TO SENSITIVITY ANALYSIS IN SINGLE-STAGE DECISION MAKING

This paper presents sensitivity analyses for a single-stage decision problem where an action which will maximize the expected payoff must be chosen from a finite number of actions given the states of nature, their probabilities, and the payoffs corresponding to each action and state of nature. Three types of sensitivity analysis are developed: (1) sensitivity analysis on the probabilities keeping the payoff numbers fixed, (2) sensitivity analysis on the payoffs keeping the probabilities fixed, and (3) joint sensitivity analysis on the payoffs and the probabilities. The approach is illustrated with an example. Quite often the sensitivity analysis can be conducted by solving an appropriate linear or quadratic programming problem.     

基于双层规划的反恐应急设施选址模型及算法

恐怖袭击常以人流密集地区的平民作为袭击目标，并存在突发性和随机性等特点，极易造成严重的袭击后果。通过反恐应急设施的合理布局可以缩短救援人员和物资的到达时间，从而减轻袭击后果。首先，对反恐应急设施选址问题进行描述，并将其构造为一类离散双层规划模型。其中，上层规划是关于政府选址的0-1规划问题，下层规划则是关于恐怖分子袭击目标选择的0-1规划问题。其次，结合模型和问题的特征设计算法，利用分支定界算法实现上层选址变量的隐枚举，同时通过下层问题的求解来确定上下界并判断是否满足分枝或剪枝的条件。最后，结合南疆地区的交通拓扑网络进行算例分析，结果证明有效的选址方案可以大大降低袭击损失。     

Leader distance: a review and a proposed theory

The concept of leader distance has been subsumed in a number of leadership theories; however, with few exceptions, leadership scholars have not expressly defined nor discussed leader distance, how distance is implicated in the legitimization of a leader, and how distance affects leader outcomes. We review available literature and demonstrate that integral to untangling the dynamics of the leadership influencing process is an understanding of leader–follower distance. We present distance in terms of three independent dimensions: leader–follower physical distance, perceived social distance, and perceived task interaction frequency. We discuss possible antecedents of leader–follower distance, including organizational and task characteristics, national culture, and leader/follower implicit motives. Finally, we use configural theory to present eight typologies (i.e., coexistence of a cluster or constellation of independent factors serving as a unit of analysis) of leader distance and propose an integrated cross-level model of leader distance, linking the distance typologies to leader outcomes at the individual and group levels of analysis.     

Blocking Rumor by Cut

In this paper, a rumor blocking problem is studied with an objective function which is neither submodular or supermodular. We will prove that this problem is NP-hard and give a data-dependent approximation with sandwich method. In addition, we show that every set function has a pair of monotone nondecreasing modular functions as upper bound and lower bound, respectively.