STOCHASTIC COST-VOLUME-PROFIT ANALYSIS IN A COMPETITIVE OLIGOPOLY

Previous stochastic cost-volume-profit (CVP) models have assumed that the firm was operating under either perfect competition or monopolistic conditions. This paper presents a stochastic CVP model applicable to oligopolistic competition. Each firm is assumed to maximize a linear function of the expected value and the standard deviation of its random profits. The result is a game-theoretic model that is solved using the concept of a Nash equilibrium. The results of the model are used to examine a firm's competitive strength. The model can be easily modified to accommodate a measure of risk based on the capital asset pricing theory.     

一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟

由于经典的Black-Scholes期权定价模型的假设忽略了突发事件对资产价格的影响和"波动率微笑"对期权价值的影响而与实际情形往往存在偏差,因此学者们对Black-Scholes模型的改进则主要分别集中在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型等两个方面,然而却少见将这两种模型结合起来的研究。本文首先在带跳扩散过程的期权定价模型与具随机波动率的期权定价模型的研究工作的基础上,建立了一种同时带跳扩散过程和具随机波动率的美式期权定价模型,并通过伊藤引理推导出了资产价格、随机波动率和期权满足的偏微分方程;然后,利用特征函数法和傅里叶变换导出了资产价格的随机分布,进而通过马尔科夫链方法给出了基于跳扩散过程和随机波动率的美式期权的数值解;最后,运用已建立的带跳扩散过程和随机波动率的美式期权定价模型对高新技术企业项目投资的专利权价值进行实物期权定价评估的案例研究,并对跳扩散强度参数和随机波动率参数进行敏感性分析,研究结果表明:将项目收益跳扩散过程和市场环境随机波动率加入到专利权实物期权定价模型中,可以有效避免专利权的期权价值被高估。     

Strategic supply network planning with vendor selection under consideration of risk and demand uncertainty

We present a stochastic version of a three-layer supply network planning problem that includes the selection of vendors that must be equipped with company-specific tools. The configuration of a supply network must be determined by using demand forecasts for a long planning horizon to meet a given service level. The risk induced by the uncertain demand is explicitly considered by incorporating the conditional value at risk. The objective is to maximize the weighted sum of the expected net present value of discounted cash flows and the conditional value at risk. This would lead to a non-linear model formulation that is approximated by a mixed-integer linear model. This approximation is realized by a piecewise linearization of the expected backlogs and physical inventory as non-linear functions of cumulative production quantities. A two-stage stochastic programming approach is proposed. Our numerical analysis of generic test instances indicates that solving the linearized model formulation yields a robust and stable supply network configuration when demand is uncertain.     

Allocation of Returned Products among Different Recovery Options through an Opportunity Cost–Based Dynamic Approach*

In a make‐to‐order product recovery environment, we consider the allocation decision for returned products decision under stochastic demand of a firm with three options: refurbishing to resell, parts harvesting, and recycling. We formulate the problem as a multiperiod Markov decision process (MDP) and present a linear programming (LP) approximation that provides an upper bound on the optimal objective function value of the MDP model. We then present two solution approaches to the MDP using the LP solution: a static approach that uses the LP solution directly and a dynamic approach that adopts a revenue management perspective and employs bid‐price controls technique where the LP is resolved after each demand arrival. We calculate the bid prices based on the shadow price interpretation of the dual variables for the inventory constraints and accept a demand if the marginal value is higher than the bid price. Since the need for solving the LP at each demand arrival requires a very efficient solution procedure, we present a transportation problem formulation of the LP via variable redefinitions and develop a one‐pass optimal solution procedure for it. We carry out an extensive numerical analysis to compare the two approaches and find that the dynamic approach provides better performance in all of the tested scenarios. Furthermore, the solutions obtained are within 2% of the upper bound on the optimal objective function value of the MDP model.     

基于期权视角的海外市场拓展的双目标多项目多期优化随机机会约束模型

随着经济全球化趋势进程的加快,海外市场资源优化配置逐步成为理论研究和实务关注的热点,而已有研究却鲜有涉及海外目标市场开拓的资源配置问题。本文在对此问题进行分析的基础上,提出了基于期权度量的收益目标模型和基于信息熵度量的风险目标模型,构建了随机环境下基于现金流供需约束的双目标多项目多期优化0-1机会约束优化模型。在吸取NSGA-Ⅱ算法思想的基础上对DE算法进行了改进,设计了求解此类配置问题的Pareto解算法,比较了伸缩因子分别为固定数和随机数时差分算法的性能,得出后者算法性能稍微优于前者。     

基于改进粒子群优化方法的供应商优选与订货量分配模型

研究了随机性需求环境下的供应商优选与订货量分配问题,构建了以质量、成本、交货期3个准则为目标函数、以其他目标为约束条件的多目标随机约束规划模型;借助于加权法和罚函数法,将多目标随机约束规划模型转化为单目标优化模型;进而设计了带惯性因子和收缩因子的粒子群优化求解算法对所建模型进行求解,并与常用的遗传算法求解方法进行对比分析,实例验证了粒子群优化算法解决此类优化问题的可行性和有效性.     

A LINEAR PROGRAMMING MODEL OF RESOURCE ALLOCATION IN A UNIVERSITY*

This paper describes the application of a linear programming model to the process of resource allocation at Illinois State University. The model developed is a general model designed to assist academic administrators in allocating the scarce resources at their disposal. The model, and the assumptions upon which it is based, may be altered to suit the particular decision criteria of any particular academic institution. The linear programming model developed here maximizes an objective function which reflects the total net social profit realized by the university on its outputs to society. This objective function was maximized subject to a myriad of constraints which reflected the limitations of budget, space, and other scarce inputs. Further, the constraints reflect the joint interdependency of many parts of the university and the particular educational delivery system employed by a given department. The outputs of the model include the optimal mixture of academic outputs by the university, the optimal distribution and usage of inputs inside the university, and the shadow price of each input. While the linear programming model developed here is general and may be applied to any university, it was applied to Illinois State University in this paper. In the case of Illinois State University, the model recommended a substantial reduction in emphasis upon teacher education.     

资源约束下可打断项目组合选择模型研究

首先,本文在已有可打断项目组合选择模型的基础上,引入了消耗性资源和可更新资源约束,构建了一个更符合实际的新模型;其次,为了达到模型简化的目的,本文给出了资金约束的现值表示,并给出了理论证明;最后,利用GAMS对模型进行了算例分析。数值实验结果表明：1）资源约束下的项目打断有时可以给企业带来积极效益,这有别于已有的研究;2）在考虑资源约束的情况下,资源消耗少且同时收益高的项目应优先执行;3）当资源的供给量较少时,资源约束是决定项目选择的关键因素。此外,通过企业实际的案例对数值实验结果进行了验证。     

A multi-stage stochastic supply network design problem with financial decisions and risk management

In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.     

工期-质量协调均衡的项目导向型供应链跨组织激励

在假定项目型组织之间平等合作的基础上,从项目价值增值最大化角度,考虑工期-质量目标努力成本关系,构建并剖析工期-质量协调均衡的项目导向型供应链跨组织激励模型,并对模型进行数据模拟和算例分析。结果表明,不论工期-质量目标间努力成本是否存在线性关系,以调整不同控制目标的激励强度为协调手段,实施工期-质量协调激励策略不仅可实现项目导向型供应链项目价值增值的最大化,而且可实现合作双方净收益的帕累托改善,进而使得承包商在工期-质量目标上合理分配资源和努力水平,实现项目工期-质量目标间的协调均衡。     

Assessing Trade‐offs among Multiple Objectives for Humanitarian Aid Delivery Using Expert Preferences

Humanitarian aid agencies deliver emergency supplies and services to people affected by disasters. Scholars and practitioners have developed modeling approaches to support aid delivery planning, but they have used objective functions with little validation as to the trade‐offs among the multiple goals of aid delivery. We develop a method to value the performance of aid delivery plans based on expert preferences over five key attributes: the amount of cargo delivered, the prioritization of aid by commodity type, the prioritization of aid by delivery location, the speed of delivery, and the operational cost. Through a conjoint analysis survey, we measure the preferences of 18 experienced humanitarian logisticians. The survey results quantify the importance of each attribute and enable the development of a piecewise linear utility function that can be used as an objective function in optimization models. The results show that the amount of cargo delivered is the most valued objective and cost the least important. In addition, experts prioritize more vulnerable communities and more critical commodities, but not to the exclusion of others. With these insights and the experts’ utility functions, better humanitarian objective functions can be developed to enable better aid delivery in emergency response.     

An Integrated Methodology for Assessment and Selection of the Project Risk Response Actions

In a systematic process of project risk management, after risk assessment is implemented, the risk analysts encounter the phase of assessment and selection of the project risk response actions (RA). As indicated by many researchers, there are less systematic and well-developed solutions in the area of risk response assessment and selection. The present article introduces a methodology including a modeling approach with the objective of selecting a set of RA that minimizes the undesirable deviation from achieving the project scope. The developed objective function comprises the three key success criteria of a project, namely, time, quality, and cost. Our model integrates overall project management into the project risk response planning (P2RP). Furthermore, the proposed model stresses on an equivalent importance for both "risk" and "response." We believe that applying the proposed model helps the project risk analyst in most effective and efficient manner dealing with his or her complicated RA selection problems. The application of the proposed model was implemented in projects in the construction industry in which it showed tremendous time, cost, and quality improvements.     

基于DSM的复杂研发项目价值流优化

针对传统设计结构矩阵(DSM)优化研发项目的不足,本文采用基于价值要素的DSM价值流优化方法,提出了活动的"费用时间比"参数和返工因子DSM矩阵,以综合反映活动的费用、时间及返工风险等价值要素对复杂研发项目活动排序优化的影响。进一步,将活动的"费用时间比"参数和返工因子作为优化参数,构建了相应的DSM价值流优化目标函数。对某案例优化计算表明,与传统方法相比,采用本文提出的价值流优化方法能明显降低由于返工而引起的项目费用增加值。     

A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance

We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.     

Value‐Driven Creation of Functionality in Software Projects: Optimal Sequencing and Reuse

We study the problem of optimally sequencing the creation of elements in a software project to optimize a time‐weighted value objective. As elements are created, certain parts of the system (referred to as “groups”) become functional and provide value, even though the entire system has not been completed. The main tradeoff in the sequencing problem arises from elements that belong to multiple groups. On the one hand, creating groups with common elements early in the project reduces the effort required to build later functionality that uses these elements. On the other hand, the early creation of such groups can delay the release of some critical functionality. We formulate the element sequencing problem and propose a heuristic to solve it. This heuristic is compared against a lower bound developed for the problem. Next, we study a more general version of the element sequencing problem in which an element requires some effort to be made reusable. When a reusable element is used in another group, some more effort is needed to specialize the element to work as desired in that group. We study reuse decisions under a weighted completion time objective (i.e., the sum of the completion time of each group weighted by its value is minimized), and show how these decisions differ from those under a traditional makespan objective (i.e., only the final completion time of the project is minimized). A variety of analytical and numerical results are presented. The model is also implemented on data obtained from a real software project. A key finding of this work is that the optimal effort on reuse is never increased (typically lowered) when a weighted completion time objective is used. This finding has implications for managing reuse in projects in which user value influences the order in which functionality is created.     

A note on the facility location problem with stochastic demands

In this research note that the single source capacitated facility location problem with general stochastic identically distributed demands is studied. The demands considered are independent and identically distributed random variables with arbitrary distribution. The unified a priori solution for the locations of facilities and for the allocation of customers to the operating facilities is found. This solution minimizes the objective function which is the sum of the fixed costs and the value of one of two different recourse functions. For each case the recourse function is given in closed form and a deterministic equivalent formulation of the model is presented. Some numerical examples are also given.     

α-鲁棒随机截流选址问题的模型和算法

由于选址决策的长期性,相关参数会随着时间而变化,所以选址问题存在很多不确定因素。本文通过不同的情景来处理截流问题中流量的不确定性,并结合随机优化和鲁棒优化,提出α-鲁棒随机截流选址模型。该模型规定了在各情景下的相对后悔值不超过α的条件下,使截得的流量的期望值最大,该条件称为α-鲁棒约束。本文将该模型建立成为一个线性0-1整数规划,并给出了改进型贪婪算法和拉格朗日启发式算法。最后,本文使用这两种算法对不同规模的截流选址问题进行了研究。     

Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems

Genetic algorithm (GA) approach is developed for solving the P-model of chance constrained data envelopment analysis (CCDEA) problems, which include the concept of “Satisficing”. Problems here include cases in which inputs and outputs are stochastic, as well as cases in which only the outputs are stochastic. The basic solution technique for the above has so far been deriving “deterministic equivalents”, which is difficult for all stochastic parameters as there are no compact methods available. In the proposed approach, the stochastic objective function and chance constraints are directly used within the genetic process. The feasibility of chance constraints are checked by stochastic simulation techniques. A case of Indian banking sector has been presented to illustrate the above approach.     

Market segmentation: A multiple criteria approach combining preference analysis and segmentation decision

We propose a new multiple criteria decision aiding approach for market segmentation that integrates preference analysis and segmentation decision within a unified framework. The approach employs an additive value function as the preference model and requires consumers to provide pairwise comparisons of some products as the preference information. To analyze each consumer’s preferences, the approach applies the disaggregation paradigm and the stochastic multicriteria acceptability analysis to derive a set of value functions according to the preference information provided by each consumer. Then, each consumer’s preferences can be represented by the distribution of possible rankings of products and associated support degrees by applying the derived value functions. On the basis of preference analysis, a new metric is proposed to measure the similarity between preferences of different consumers, and a hierarchical clustering algorithm is developed to perform market segmentation. To help firms serve consumers from different segments with targeted marketing policies and appropriate products, the approach proposes to work out a representative value function and the univocal ranking of products for each consumer so that products that rank in the front of the list can be presented to her/him. Finally, an illustrative example of a market segmentation problem details the application of the proposed approach.     

考虑风险总关联的项目风险应对策略选择方法

本文针对考虑风险总关联的项目风险应对策略选择问题,首先结合MACBETH方法以及DEMATEL方法分析项目风险总关联;然后,在考虑项目管理者风险态度的基础上,以最大化项目管理者期望效用为目标构建考虑风险总关联的项目风险应对策略选择优化模型;最后,通过实际案例分析验证所提方法和模型的可行性与有效性,并比较分析了不同关联作用对风险应对决策的影响。结果表明：1）存在使项目管理者期望效用达到最大的最优项目风险应对预算;2）项目管理者的风险态度和对风险关联的关注程度对风险应对策略的选择和项目管理者的期望效用均有影响,在实际项目风险应对决策中均应予以考虑;3）在项目风险应对策略选择过程中,项目管理者不仅要考虑风险之间的直接关联还要重视风险之间的间接关联,而风险之间的积极关联则可以忽略。