A note on demand functions with uncertainty

Demand functions with “additive” and “multiplicative” uncertainty can fail to satisfy the “Slutsky symmetry” conditions required for demand to be based on utility maximization. This makes welfare analysis infeasible, which is important in many applications. Additive uncertainty can also generate negative demand realizations, and this can create non-trivial analytical problems.     

Nature plays with dice – terrorists do not: Allocating resources to counter strategic versus probabilistic risks

Probabilistic uncertainty is caused by “chance”, whereas strategic uncertainty is caused by an adverse interested party. Using linear impact functions, the problems of allocating a limited resource to defend sites that face either probabilistic risk or strategic risk are formulated as optimization problems that are solved explicitly. The resulting optimal policies differ – under probabilistic risk, the optimal policy is to focus the investment of resources on priority sites where they yield the highest impact, while under strategic risk, the best policy is to spread the resources so as to decrease the potential damage level of the most vulnerable site(s). Neither solution coincides with the commonly practiced proportionality allocation scheme.     

Using the K5Connected Cognition Diagram to analyze teachers’ communication and understanding of regions in three-dimensional space

This paper reports on a study that introduces and applies the K₅Connected Cognition Diagram as a lens to explore video data showing teachers’ interactions related to the partitioning of regions by axes in a three-dimensional geometric space. The study considers “semiotic bundles” ( Arzarello, 2006), introduces “semiotic connections,” and discusses the fundamental role each plays in developing individual understanding and communication with peers. While all teachers solved the problem posed, many failed to make or verbalize connections between the types of semiotic resources introduced during their discussions.     

The economics of social computing: Some preliminary findings on healthcare organizations

Large-scale organizations have used social computing platforms for various purposes. This research focuses on how hospitals utilize these platforms to attract potential customers (which represents the “extensivity” of a social computing platform) and generate interests in specific topics (which represents the “intensivity” of a platform). Specifically, we examine the effects of size of a hospital (or “size”) and the time that the social computing platform has been in existence (or “time”) on extensivity and intensivity. Our findings show that time is a significant variable on both dimensions; whereas size affects intensivity under certain conditions. We discuss the implications of these findings, and set the stage for future research.     

Theory of integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of “natural disposability” and “natural divisibility”. We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.     

MIP models for resource-constrained project scheduling with flexible resource profiles

This paper addresses the resource-constrained project scheduling problem with flexible resource profiles (FRCPSP). Such a problem often arises in many real-world applications, in which the resource usage of an activity is not merely constant, but can be adjusted from period to period. The FRCPSP is, therefore, to simultaneously determine the start time, the resource profile, and the duration of each activity in order to minimize the makespan, subject to precedence relationships, limited availability of multiple resources, and restrictions on resource profiles. We propose four discrete-time model formulations and compare their model efficiency in terms of solution quality and computational times. Both preprocessing and priority-based heuristic methods are also applied to compute both upper and lower bounds of the makespan. Our comparative results show significant dominance of one of the models, the so-called “variable-intensity-based” model, in both solution quality and runtimes.     

Characterizations of the optimal stable allocation mechanism

The stable allocation problem is the generalization of (0,1)-matching problems to the allocation of real numbers (hours or quantities) between two separate sets of agents. The same unique-optimal matching (for one set of agents) is characterized by each of three properties: “efficiency”, “monotonicity”, and “strategy-proofness”.     

The affect heuristic

This paper introduces a theoretical framework that describes the importance of affect in guiding judgments and decisions. As used here, “affect” means the specific quality of “goodness” or “badness” (i) experienced as a feeling state (with or without consciousness) and (ii) demarcating a positive or negative quality of a stimulus. Affective responses occur rapidly and automatically—note how quickly you sense the feelings associated with the stimulus word “treasure” or the word “hate”. We argue that reliance on such feelings can be characterized as “the affect heuristic”. In this paper we trace the development of the affect heuristic across a variety of research paths followed by ourselves and many others. We also discuss some of the important practical implications resulting from ways that this heuristic impacts our daily lives.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

Inventory sharing via circular unidirectional chaining

This research studies the performance of circular unidirectional chaining – a “lean” configuration of lateral inventory sharing among retailers or warehouses – and compares its performance to that of no pooling and complete pooling in terms of expected costs and optimal order quantities. Each retailer faces uncertain demand, and we wish to minimize procurement, shortage and transshipment costs. In a circular unidirectional chain all retailers are connected in a closed loop, so that each retailer can cooperate with exactly two others as follows: receive units (if needed?available) from the left “neighbor” and send units (if needed?available) to the right, and a retailer who receives units from one neighbor is not allowed to send any units to its other neighbor. If the chain consists of at least three nodes and demands across nodes are i.i.d., its performance turns out to be independent of the number of nodes. The optimal stocking is therefore solved analytically. Analytical comparative statics with respect to cost parameters and demand distributions are provided. We also examine thoroughly the cases of uniform demand distribution (analytically) and normal demand distribution (numerically). In the uniform case with free transshipment, a unidirectional chain can save up to 1/3 of the expected cost of separate newsvendors caused by uncertainty. For three nodes, the advantage of complete pooling over unidirectional chaining does not exceed 19%.     

基于非平稳性度量的彩票数据实证分析

非平稳性度量是衡量时间序列平稳程度的方法.利用非平稳度量,给出了C检验,并结合非平稳性度量值,对我国体彩"排列五"、"七星彩"及美国亚利桑那州的博彩"Pick3"的历史数据进行分析,发现博彩各数位上整数"0~9"出现都拥有稳定的概率,但并不是以等概率1/10出现,其分布与i.i.d均匀分布稍有差异,其中"七星彩"均匀性最好,"Pick3"的均匀性次之,"排列五"均匀性稍差.     

Robust portfolio selection involving options under a “ marginal+joint ” ellipsoidal uncertainty set

In typical robust portfolio selection problems, one mainly finds portfolios with the worst-case return under a given uncertainty set, in which asset returns can be realized. A too large uncertainty set will lead to a too conservative robust portfolio. However, if the given uncertainty set is not large enough, the realized returns of resulting portfolios will be outside of the uncertainty set when an extreme event such as market crash or a large shock of asset returns occurs. The goal of this paper is to propose robust portfolio selection models under so-called “ marginal+joint” ellipsoidal uncertainty set and to test the performance of the proposed models. A robust portfolio selection model under a “marginal + joint” ellipsoidal uncertainty set is proposed at first. The model has the advantages of models under the separable uncertainty set and the joint ellipsoidal uncertainty set, and relaxes the requirements on the uncertainty set. Then, one more robust portfolio selection model with option protection is presented by combining options into the proposed robust portfolio selection model. Convex programming approximations with second-order cone and linear matrix inequalities constraints to both models are derived. The proposed robust portfolio selection model with options can hedge risks and generates robust portfolios with well wealth growth rate when an extreme event occurs. Tests on real data of the Chinese stock market and simulated options confirm the property of both the models. Test results show that (1) under the “ marginal+joint” uncertainty set, the wealth growth rate and diversification of robust portfolios generated from the first proposed robust portfolio model (without options) are better and greater than those generated from Goldfarb and Iyengar’s model, and (2) the robust portfolio selection model with options outperforms the robust portfolio selection model without options when some extreme event occurs.     

Additive conjoint measurement with ordered categories

Conjoint measurement studies binary relations defined on product sets and investigates the existence and uniqueness of, usually additive, numerical representations of such relations. It has proved to be quite a powerful tool to analyze and compare MCDM techniques designed to build a preference relation between multiattributed alternatives and has been an inspiring guide to many assessment protocols. The aim of this paper is to show that additive representations can be obtained on the basis of much poorer information than a preference relation. We will suppose here that the decision maker only specifies for each object if he/she finds it “attractive” (better than the status quo), “unattractive” (worse than the status quo) or “neutral” (equivalent to the status quo). We show how to build an additive representation, with tight uniqueness properties, using such an ordered partition of the set of objects. On a theoretical level, this paper shows that classical results of additive conjoint measurement can be extended to cover the case of ordered partitions and wishes to be a contribution to the growing literature on the foundations of sorting techniques in MCDM. On a more practical level, our results suggest an assessment strategy of an additive model on the basis of an ordered partition.     

Safety and waste considerations in donated blood screening

We study an important problem faced by Blood Centers, of selecting screening tests for donated blood to reduce the risk of “transfusion-transmitted infectious diseases” (TTIs), including the human immunodeficiency virus (HIV), hepatitis viruses, human T-cell lymphotropic virus, syphilis, West Nile Virus, and Chagas’ Disease. This decision has a significant impact on health care quality in both developed and developing countries. The budget-constrained decision-maker needs to construct a portfolio of screening tests, from a set of available tests, each with given efficacy (sensitivity and specificity) and cost, to administer to each unit of donated blood so as to minimize the “risk” of a TTI for blood classified as “infection-free.” While doing this, it is critical, for a viable blood system, that the decision-maker does not falsely (i.e., through screening error) discard too much of the infection-free blood (“waste”). We construct mathematical models of this decision problem, considering the various objective functions (minimization of the TTI risk or the weighted TTI risk) and various constraints (on budget and wasted blood) relevant in practice. Our work generates insights on the test selection problem. We show, for example, that a reduction in risk does not necessarily come at the expense of an increase in waste. This underscores the importance of considering these different metrics in decision-making through an optimization-based model. Our work also highlights the importance of generating region-specific testing schemes that explicitly take into account the regional prevalence and co-infection rates, along with the impacts of the infections on the society and individuals.     

The inequality-satisfiability problem

We define a generalization of the satisfiability problem (SAT) where each “clause” is an or-list of inequalities in n variables. This problem is NP-complete even when containing only two inequalities per “clause”, but solvable in polynomial time when either the number of variables or the number of “clauses” is fixed.     

A theory of motivation and satisfaction with application to decision support

The paper deals with optimization of allocation of human resources among different activities. It is assumed that an individual is characterized by a risk averse and constant return to scale utility function of two variables: motivation to perform and reward following the performance. The individual is trying to maximize the utility by the best allocation of his time resources among the activities and by selecting the best portfolio of activities. Motivations are regarded, generally, as the product of the individual's preferences (i.e. subjective choice probabilities), productivities of time, output prices, performance and access probabilities, etc., while the rewards are profits or salaries connected with each activity. Satisfaction is defined as the maximum of utility attained for the optimum allocation and selection strategies. It is shown that for the given equitable reward rate, the optimum allocation and portfolio selection strategies can be derived explicitly and the derivation does not require the explicit knowledge of the individual's utility function.     

Coloring by two-way independent sets

The paper stems from an attempt to investigate a somewhat mysterious phenomenon: conditions which suffice for the existence of a “large” set satisfying certain conditions (e.g., a large independent set in a graph) often suffice (or at least are conjectured to suffice) for the existence of a covering of the ground set by few sets satisfying these conditions (in the example of independent sets in a graph this means that the graph has small chromatic number). We consider two conjectures of this type, on coloring by sets which are “two-way independent”, in the sense of belonging to a matroid and at the same time being independent in a graph sharing its ground set with the matroid. We prove these conjectures for matroids of rank 2. We also consider dual conjectures, on packing bases of a matroid, which are independent in a given graph.     

Solving the puzzles of structural efficiency

Since the concept of “structural efficiency” first appeared in Farrell [Farrell, M.J., 1957. The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, Part III 120, 253–281], attempts have been made to derive measures for the performance of a group of production units (often referred to an industry with many firms). Many empirical studies used the technical efficiency of an average unit to measure the structural efficiency of a group, but researchers have been puzzled by the discrepancies between the average of individual efficiency scores and the performance of the group as a whole. In this paper, we point out that the “shadow price model” provides a useful framework for understanding the economic meaning of the structural efficiency as well as its components. By recognizing these components, the puzzles related to the inconsistencies between the individual and group performance can be solved readily.     

Production decisions under joint price and production uncertainty

While production decisions in the presence of price uncertainty have been extensively studied, this is not so for the case in which the level of production is itself uncertain. In this paper,we provide a decision analysis under multiplicative production uncertainty, both with and without price uncertainty. We depict equilibrium and obtain comparative statics results with the aid of a diagram based on the difference between expected price and marginal cost. Comparative statics results are obtained for the model with production uncertainty alone and also for simultaneous price and production uncertainty (including two special cases). We first derive results based on the Arrow–Pratt coefficients of risk aversion, and then supplement these with the Ross measure of relative risk aversion, since this proves useful in the presence of multiple sources of uncertainty. We find that increases in risk (both price and production) or input prices reduce expected output. However, expected output supply is an increasing function of (expected) price only for “low” levels of risk aversion, and in general the relationship is ambiguous.     

Modeling technology adoptions for sustainable development under increasing returns,uncertainty, and heterogeneous agents

This paper presents a stylized model of technology adoptions for sustainable development under the three potentially most important “stylized facts”: increasing returns to adoption, uncertainty, and heterogeneous agents following diverse technology development and adoption strategies. The stylized model deals with three technologies and two heterogeneous agents: a risk-taking one and a risk-averse one. Interactions between the two agents include trade in resources and goods, and technological spillover (free riding and technology trade). With the two heterogeneous agents, we run optimizations to minimize their aggregated costs in order to find out what rational behaviors are under different assumptions if the two agents are somehow cooperative. By considering uncertain carbon taxes, the model also addresses environmental issues as potential driving forces for technology adoptions.