Expected Value Model Research Articles

A belief degree-based uncertain scheme for a bi-objective two-stage green supply chain network design problem with direct shipment

In the lack of historical data for an uncertain event, the belief degree-based uncertainty becomes more applicable than other types of uncertainty like fuzzy theory, stochastic programming, etc. This study focuses on an uncertain bi-objective two-stage supply chain network design problem. The problem consists of plants, depots, and customers with cost and environmental impacts (CO2 emission) where direct shipment between plants and customers is allowed. As such network could be designed for the first time in a geographical region, such problem is modeled in a belief degree-based uncertain environment. This is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts and direct shipment. Three approaches of expected value model, chance-constrained model, and their combination are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by two multi-objective optimization approaches of goal programming (GP) and global criterion method (GCM). An extensive computational study with various test problems is performed to study the performance of the crisp models and the solution approaches. As result, the obtained crisp formulations are highly sensitive to the changes in the cost parameters’ values, and the GP performs better than the GCM from the solution quality point of view.

Only child, parental educational expectation, self-expectation and science literacy in Zhuang adolescents in China: A serial mediation model

The impact of only-child policy on Chinese children's development has been widely studied, leaving those from ethnic minority groups unexplored. This study investigated the possible mediating factors in the relationship between Singleton (only-child or not) status and science literacy in Zhuang adolescents, the largest ethnic minority group in China. Altogether 527 Zhuang students (Female = 263; aged from 13 to 17) were surveyed and tested with PISA Science (2008). The path and mediation analysis have confirmed that Parental Educational Expectation (PEE) and Self-Educational Expectation (SEE) acted as the serial mediators between Singleton and Science Literacy. This model indicates that Singleton causes a higher PEE, which is associated with a higher SEE, and eventually results in a higher Science Literacy. This finding implies that the Expectancy Value Model might be cross-cultural and universal, and highlight the importance of fostering a positive educational expectation to promote science literacy in adolescents.

Uncertain Single-Machine Scheduling with Deterioration and Learning Effect

A single-machine scheduling problem with deterioration and learning effect is studied in the present paper. The processing time and due date are considered uncertain variables due to lack of historical data. The aim is to minimize the makespan, total completion time, total weight completion time, and maximum lateness under an uncertain environment. To address the problem in an uncertain environment, the expected value model and pessimistic value model are developed. These models can be converted into equivalent models based on the inverse distribution method. It is proved that the corresponding dispatching rules can solve the problem optimally under different objective criteria. Finally, sensitivity analysis is used to illustrate the effectiveness of these rules.

Uncertain location–allocation decisions for a bi‐objective two‐stage supply chain network design problem with environmental impacts

AbstractIn the cases that the historical data of an uncertain event is not available, belief degree‐based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi‐objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree‐based uncertainty theory. This article is almost the first study on belief degree‐based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance‐constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi‐objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.

Explaining Secondary Students’ Career Intentions for Technology and Engineering Jobs Using an Expectancy-Value Model

This research presents an empirical model based on expectancy-value theory to explain students’ attitudes towards science-based technology. The question is how students’ attitudes are connected with their aspirations for a career in the technology and engineering fields. There is a high demand for technology professionals, but students’ interest in such careers is low. The context of this study is a cooperation project involving local industry and Swiss secondary schools that aims to foster students’ interest in science-based technology. We conducted a mix-methods study with a sample of 337 students in secondary school (grades 7-9) and 12 science teachers. Based on the questionnaire data, we created a structural equation model to analyse the relationships between students’ expectancy-value attitudes and career interests. Context variables, such as gender, parents’ professions, and having a workshop at home complement the model. With the help of the data collected in the teacher interviews, the results were validated and elaborated. The findings indicate students’ attitudes and interest in science-based technology were rather low in general, and as expected, they were significantly lower for girls. Our 2-factor empirical model showed a stronger focus on application than on theory. Self-concept and values were predictors of career interests, but not of interest in applied science. Context variables also played a significant role. Triangulation of the data helped validate the measured constructs. In conclusion, our results indicate that school science lessons might not offer sufficient experiences in applied science to secondary school students. Interest in a career in the technology and engineering fields can be triggered by integrating more engineering experiences in the science classroom.

Youth Female Ice Hockey Players’ Enjoyment and Commitment to Sport

The purpose of this study was to identify sport-specific predictors of youth female athletes’ sport commitment and sport enjoyment. Based on the expectancy-value model, athletic identity and gender stereotypes were hypothesized to predict sport commitment and sport enjoyment in ice hockey, which has a masculine gender association. Participants consisted of 130 (89.2% Caucasian) youth female ice hockey players (Mage = 11.7, SD = 2.6). They completed measures of athletic identity; personal gender beliefs; perceived gender beliefs of parents, teammates, siblings, and the general population; and two outcome measures: sport commitment and sport enjoyment. The prediction model for sport commitment was significant, F(7, 122) = 9.56, p < .001, and accounted for 35.4% of the variance. The prediction model for sport enjoyment was also significant, F(7, 122) = 2.25, p < .01, and accounted for 11.5% of the variance. Overall, youth female ice hockey players held pro-feminine beliefs about competence and values of girls in hockey. Participants’ personal gender beliefs correlated moderately with perceived gender beliefs of their (socializers) parents, teammates, and the general population (r = .54–.56), suggesting youth female ice hockey players’ pro-feminine beliefs might be informed by these social influences. However, two multiple mediation analyses found no support for the hypotheses that personally held stereotypes mediated the link between all four socially based gender stereotypes and enjoyment and commitment.

Stochastic Dispatching of Wind Power Considering Errors of Power Prediction

Aiming at the stochastic dispatch problem brought by wind power, the expected model of wind power considering the errors of power prediction is established according to stochastic programming theory. And the calculation steps based on Monte Carlo stochastic simulation and genetic algorithm are proposed. An IEEE 30-bus example with wind farms is given to verify the feasibility and effectiveness of the method. The result shows that the stochastic dispatch method based expected value model can quantify the uncertainty caused by the prediction error of wind power well and optimize the expected value of wind power accommodation. It plays a positive role in improving dispatching level and promoting wind power accommodation.

Professional Learning Communities: Bridging the Technology Integration Gap Through Effective Professional Development

ABSTRACT While technology is prevalent in American classrooms, meaningful technology integration remains an issue, indicating a lack of effective professional development. Unlike the typical workshop model, professional learning communities (PLCs) utilize teacher-centered approaches to professional development. Kolb’s experiential learning theory, Bandura’s self-efficacy theory, and the expectancy-value model work together to provide the theoretical foundation supporting professional development through PLCs. This article proposes a plan for transformative technology integration using a PLC model for professional development.

VALIDATION OF THE MALAY-TRANSLATED EXPECTANCY VALUE MODEL QUESTIONNAIRE AND MULTI-DIMENSIONAL SPORTSPERSONSHIP ORIENTATIONS SCALE AMONG MALAYSIAN ADOLESCENCE FIELD HOCKEY PLAYERS

This study presents an overview of Malaysian adolescent field hockey players’ expectancy beliefs, subjective values and sportspersonship attitude. We aimed to translate and validate two questionnaires i.e., Expectancy Value Model Questionnaire (EVMQ) and Multi-dimensional Sportspersonship Orientations Scale (MSOS) to Malay language. The EVMQ and MSOS were translated into the Malay language using the back translation method. A total of 230 respondents (15.40 ± 2.17 years) were recruited for this study. The result of analyses are EVMQ-M (M = 5.38 ± .95) and MSOS-M (M = 3.64 ± .40) respectively. Content validity was checked by experts in the fields for content conformity and culture bias whereas face validity was confirmed by ten participants. Both questionnaires showed high internal consistency (reliability); EVMQ-M (α = .94) and MSOS-M (α = .82). Data fits were checked using the Structural Equation Model; EVMQ-M (χ² (df = 39) = 84.07, CFI = .97, GFI = .94, TLI = .95, RMSEA = .07, ChiSq/df = 2.16) and MSOS-M (χ² (df = 146) = 321.76, CFI = .92, GFI = .87, TLI = .90, RMSEA = .07, ChiSq/df = 2.20) also showed good construct validity. The translated Malay version EVMQ-M and the MSOS-M are reliable and valid instruments to assess Malaysian adolescent field hockey players.

Determining the Optimal Location of Vehicle Inspection Facilities Under Uncertainty via New Optimization Approaches

This study addresses the problem of optimally locating vehicle inspection facilities under uncertain customer demand and varying velocity considering regional constraints. The objective is to simultaneously minimize the transportation time of all customers and their transportation cost, while ensuring consumers to reach their desired destinations within their expected time and cost. We study two variants of the problem: vehicle inspection location with complete probability distributions of customer demand and vehicle velocity, and that with partial information of customer demand and vehicle velocity, i.e., only the supports and means of the stochastic variables are known. For the former problem, an expected value model and a chance-constrained program are first formulated. Then based on explored problem properties, the expected value program is equivalently reformulated as a deterministic non-linear program. To efficiently deal with the chance-constrained program, a sample average approximation (SAA)-based approach is proposed. For the latter one, we develop a new distribution-free model. Computational results for benchmark examples demonstrate that: i) for the former, the proposed deterministic program reformulation-based approach and SAA algorithm outperform the state-of-the-art approaches; ii) for the latter, the proposed distribution-free model can effectively deal with the problem with partial demand and velocity information.

Rough-interval in a two-stage solid transportation problems and its solution

The paper attempts a study on two stage formulation of a cost minimisation solid transportation problem, where the parameters are considered as rough interval form. A rough interval is based on approximation space and hence the solution of the proposed model obtained with the help of approximation theory. In order to solve the expected value model has been derived and the corresponding deterministic model so obtained is solved with LINGO 13.0 optimisation solver. Finally, the methodology and model is illustrated by simple numerical example at the last.

Rough-interval in a two-stage solid transportation problems and its solution

The paper attempts a study on two stage formulation of a cost minimisation solid transportation problem, where the parameters are considered as rough interval form. A rough interval is based on approximation space and hence the solution of the proposed model obtained with the help of approximation theory. In order to solve the expected value model has been derived and the corresponding deterministic model so obtained is solved with LINGO 13.0 optimisation solver. Finally, the methodology and model is illustrated by simple numerical example at the last.

Elementary Physical Education: Cost is Personal and Social

BACKGROUND Although expectancy-value models of motivation have been applied to understanding children’s physical activity in a variety of contexts, the construct of cost has received relatively less attention. In the present study, perceived cost for engaging in mandatory physical education (P.E.) classes is explored. In particular, we examine different dimensions to cost as well as how cost may be related to children’s competence beliefs and values, perceived autonomy-support, and P.E. engagement. METHODS Two hundred fifty-eight fifth-graders were surveyed in their P.E. classes. Children responded to items assessing cost, competence beliefs, intrinsic value, and attainment value for P.E., as well as perceived autonomy-support of the P.E. teacher. RESULTS Two distinct types of cost were identified through factor analysis: personal discomfort cost and social cost. Personal discomfort cost was negatively related to competence beliefs and values, engagement in P.E., and perceived autonomy-support. CONCLUSIONS Perceived cost appears to be a useful way to understand why some children may be less engaged in P.E. classes. P.E. teachers may be able to mitigate cost by engaging in tactics that are autonomy-supportive in nature, such as providing children with choices and rationales for activities.

Compensation mechanism of delayed distribution based on interest balance

ABSTRACT In view of the problem of delayed delivery, this paper propose a compensation mechanism for user to protect the rights and interests of consumers. Based on the stochastic programming model with the lowest cost, this paper discusses the situation that the requirement of vehicle distriution are not met in the distribution cycle. Firstly, the stochastic programming model is transformed into the expected value model to solve the randomness of residual and demand. Secondly, according to the balance of interest of logistics enterprises and consumers, combining the cost function of timely delivery and delayed delivery, the analytical method is used to obtain the specific expressions of the two functions and compare them to determine the relationship between cost and penalty. Finally, combining with the case of commodity distribution, the compensation mechanism to balance the interests of logistics enterprises and consumers is obtained.

Exploring the Effect of Perceived Teacher Support on Multiple Creativity Tasks: Based on the Expectancy–Value Model of Achievement Motivation

AbstractThe present study explores the effect of perceived teacher support on three forms of thinking related to creativity. Tests of convergent thinking (by means of the Remote Associates Test), insight thinking (explored through a brain‐teaser test), and divergent thinking (by means of a verbal creativity test) were given to 512 middle school students in China, along with assessments of their perceived teacher support and creative self‐efficacy. The results of this study indicate that perceived teacher support positively predicts convergent thinking and insight thinking, with creative self‐efficacy playing a partial mediating role between perceived teacher support and convergent thinking. However, no significant relationships were found between perceived teacher support and divergent thinking. The findings partly lend support to the expectancy–value model of achievement motivation that teacher’s behavior influences student performance through self‐belief pathway.

Uncertain interval programming model for multi-objective multi-item fixed charge solid transportation problem with budget constraint and safety measure

This paper presents uncertain interval programming models for multi-objective multi-item fixed charge solid transportation problem with budget constraint and safety measure (MOMIFCSTPBCSM). The human languages usually involve imperfect or unknown information and are in the lack of certainty, and often, it is impossible to exactly describe an existing state or a future outcome. In using the probability theory, we must have enough historical information to estimate the probability distributions and in the case of fuzzy theory, we must have a trustworthy membership function, which is not easy to do. Thus, we often estimate the degree of belief with some hesitation that each condition may occur. To deal with such a situation, the uncertain interval theory may be very useful. Based on these facts, the parameters of the formulated problem are chosen as uncertain intervals. We consider unit transportation costs, fixed charges, transportation times, deterioration of items, supplies at origins, demands at destinations, conveyance capacities, budget at each destination, selling prices and purchasing costs, and we assume the safety factor and the desired safety measure are interval uncertain parameters. To formulate the proposed MOMIFCSTPBCSM, we use interval theory and uncertain programming techniques to develop two different models: an Expected Value Model and a Chance-Constrained Model. The equivalent deterministic models are formulated and solved using a linear weighted method, a fuzzy programming method and the goal programming method.

Predicting Minimal Residual Disease in Acute Myeloid Leukemia through Stochastic Modeling of Clonality

Background. Relapse affects about 50% of AML patients who achieved remission after treatment, and the prognosis of relapsed AML is poor. Current evidence has shown that in many patients, mutations giving rise to relapse are already present at diagnosis and remain in small numbers in remission, defined as the minimal residual disease (MRD) [1]. Chemoresistant clones contributing to relapse of the disease arise from minimal residual disease (MRD) rather than resulting from newly acquired mutations during or after chemotherapy. MRD is the presence of measurable leukemic cells using non-morphologic assays. It is considered a strong predictor of relapse. The dynamics of clones comprising MRD is poorly understood and is considered influenced by a form of Darwinian selection.Methods. We propose a stochastic model based on a multitype (multi-clone) age-dependent Markov branching process to study how random events in MRD contribute to the heterogeneity in response to treatment in a cohort of six patients from The Cancer Genome Atlas database with whole genome sequencing data at two time points. Because human bone marrow cell counts are too large for direct stochastic simulation methods to be effective, we developed a hybrid numerical algorithm combining stochastic Gillespie-type and tau-leaping algorithms, and a deterministic differential equation solver, which uses much less computer time than a "straight Gillespie algorithm". Results. We developed a stochastic model of clonal evolution based on a multitype (multi-clone) age-dependent Markov branching process model of cell proliferation. In brief, we consider the critical time interval between diagnosis and initial relapse of AML that includes cytotoxic chemotherapy, chemotherapy-induced myelosuppression and decrease in leukemic cells, non-leukemic marrow recovery, and growth of the leukemic clones due to refractory or relapsed disease. Underlying our model are assumptions regarding the structure of growth, differentiation, and competition of the normal and leukemic clones. Our model reflects the stochasticity inherent when leukemic clones are near depletion after chemotherapy, which we hypothesize strongly contributes to the interpatient heterogeneity in treatment response. The parameters are estimated by fitting the expected-value model to the patient's clinical data. The available data at diagnosis includes patient's weight, percent cellularity, white blood cell count, percentage of blasts in both peripheral blood and bone marrow, and percentage of normal neutrophils in the peripheral blood. Importantly, the time to relapse and percentage of blasts in bone marrow at relapse are available. The parameters fitted to the expected-value model offer an explanation of how a leukemic clone can escape chemotherapy and promote relapse. These clones have either high proliferation rates or high self-renewal rates. As a result, there is a range of different parameter combinations that can explain their ability to succeed. On the other hand, we also study the clones that have been eradicated by the time of relapse and conclude that these clones might be eliminated either because they are not competitive and therefore surrender to other clones, or they are simply killed by chemotherapy. Also, we checked if the parameters are biologically relevant by using the model to compute the corresponding clonal growth rates for each patient. That these values fit in the clinically observed range independently found in for patients with the NPM1 mutations [1], suggests that the model is consistent with clinical data. Conclusions. Our model offers a more accurate understanding of how relapse arises and which properties allow a leukemic clone to thrive in the Darwinian competition among leukemic and normal hematopoietic clones. The model suggests a quantitative relationship between MRD and time to relapse and therefore may aid clinicians in determining when and how to implement treatment changes to postpone or prevent the time to relapse. [1]Assessment of Minimal Residual Disease in Standard-Risk AML. N Engl J Med. 2016;374:422. Relationship between MRD and time to relapse for all patients. Estimates of MRD and time to relapse are mean values from 1000 stochastic simulations. Each color corresponds to a single patient; left triangles, circles, and right triangles correspond to three parameter sets. Simulated points are fitted with a sigmoidal Hill function. Figure Disclosures No relevant conflicts of interest to declare.

An environmental supply chain network under uncertainty

In the present study, a closed-loop supply chain network for production and recovery of button batteries is investigated under uncertainty. The environmental impact of button batteries is taken into account in the design of the supply chain network. Since there are many uncertainties in reality, the demand, cost and capacity are considered uncertain variables. To explore the impact of these uncertainties on the supply chain network, two multi-objective mixed integer programming models under uncertainty are developed, i.e., the expected value model and the chance-constrained model. The aim is to reduce the multiple environment effects on the total cost and weigh the pros and cons. A method based on life cycle assessment is proposed to evaluate the environment effects on the supply chain network. The two models can be converted into crisp models by the uncertainty theory. Lastly, numerical experiments are used to verify the feasibility of the proposed models and method.

Uncertain programming models for multi-objective shortest path problem with uncertain parameters

The shortest path problem is considered as one of the essential problems in network optimization with a wide range of real-world applications. Modelling such real-world applications involves various indeterminate phenomena which can be estimated through human beliefs. The uncertainty theory proposed by Liu (Uncertain theory, 2nd edn., Springer, Berlin, 2007) is widely regarded as a legitimate tool to deal with such uncertainty. This paper presents an uncertain multi-objective shortest path problem (UMSPP) for a weighted connected directed graph (WCDG), where every edge weight is associated with two uncertain parameters: cost and time. These parameters are represented as uncertain variables. Here, we have formulated the expected value model and chance-constrained model of the proposed UMSPP, and the corresponding deterministic transformation of these models is also presented. Subsequently, the deterministic models are solved with a classical multi-objective solution method, namely the global criterion method. Furthermore, two multi-objective genetic algorithms (MOGAs): nondominated sorting genetic algorithm II (NSGA-II) and multi-objective cross-generational elitist selection, heterogeneous recombination and cataclysmic mutation (MOCHC), are employed to solve these models. A suitable example is provided to illustrate the proposed model. Finally, the performance of MOGAs is compared for five randomly generated instances of UMSPP.

Uncertain random quadratic bottleneck assignment problem

Uncertain random expected value simulation is one of the most important techniques to solve uncertain random optimization problems where random variables coexist with uncertain variables. A general simulation algorithm is designed to estimate the uncertain random expected value. Furthermore, an uncertain random quadratic bottleneck assignment problem is proposed and an uncertain random expected value model is presented. An algorithm is designed to find a lower bound of the uncertain random quadratic bottleneck assignment problem.