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The purpose of this paper is to explore students' mathematization through a flow of lessons using the Thailand Lesson Study Incorporated Open Approach (TLSOA) to improve the excellence of instruction.

A total of 16 Grade 4 students were selected because they have been taught using the TLSOA model for four years. Six Lesson Study (LS) team members participated, and two instruments were utilized, namely student worksheets, and field notes. An ethnographic research design was employed.

The results revealed that the students' mathematical ideas were developed from the real world to the mathematical world through a flow of lessons based on the four phases of the Open Approach (OA).

Firstly, the students demonstrated their ability to represent the real world independently when the teacher posed an open-ended problem. Secondly, the students demonstrated their ability to use semi-concrete aids to develop their ideas while self-learning. Thirdly, the students showed how they developed their ideas to solve the open-ended problem using relevant objects or related concepts as part of a whole-class discussion and comparison exercise. Finally, the students demonstrated their abilities to represent the mathematical world using numbers and symbols to communicate their ideas when they were required to make a summary by connecting their mathematical ideas.

This study adds new insight to the literature on students' mathematization using the TLSOA model.

Efficient management of earthmoving equipment is critical for decision-makers in construction engineering management. Thus, the purpose of this paper is to prudently identify, select, manage and optimize the associated decision variables (e.g. capacity, number and speed) for trucks and loaders equipment to minimize cost and time objectives.

This paper addresses an innovative multiobjective and multivariable mathematical optimization model to generate a Pareto-optimality set of solutions that offers insights of optimal tradeoffs between minimizing earthmoving activity’s cost and time. The proposed model has three major stages: first, define all related decision variables for trucks and loaders and detect all related constraints that affect the optimization model; second, derive the mathematical optimization model and apply the multiobjective genetic algorithms and classify all inputs and outputs related to the mathematical model; and third, model validation.

The efficiency of the proposed optimization model has been validated using a case study of earthmoving activities based on data collected from the real-world construction site. The outputs of the conducted optimization process promise the model’s originality and efficiency in generating optimal solutions for optimal time and cost objectives.

This model provides the decision-maker with an efficient tool to select the optimal design variables to minimize the activity's time and cost.

This paper aims to examine the integration of lateral transshipment and road vulnerability into the humanitarian relief chain in light of affected area priority to address equitable distribution and assess the impact of various parameters on the total average inflated distance traveled per relief item.

After identifying comprehensive critical criteria and subcriteria, a hybrid multi-criteria decision-making framework was applied to obtain the demand points’ weight and ranking in a real-life earthquake scenario. Direct shipment and lateral transshipment models were then presented and compared. The developed mathematical models are formulated as mixed-integer programming models, considering facility location, inventory prepositioning, road vulnerability and quantity of lateral transshipment.

The study found that the use of prioritization criteria and subcriteria, in conjunction with lateral transshipment and road vulnerability, resulted in a more equitable distribution of relief items by reducing the total average inflated distance traveled per relief item.

To the best of the authors’ knowledge, this study is one of the first research on equity in humanitarian response through prioritization of demand points. It also bridges the gap between two areas that are typically treated separately: multi-criteria decision-making and humanitarian logistics.

This is the first scholarly work in Shiraz focused on the equitable distribution system by prioritization of demand points and assigning relief items to them after the occurrence of a medium-scale earthquake scenario considering lateral transshipment in the upper echelon.

The paper clarifies how to prioritize demand points to promote equity in humanitarian logistics when the authors have faced multiple factors (i.e. location of relief distribution centers, inventory level, distance, lateral transshipment and road vulnerability) simultaneously.

This paper proposes a two-level supply chain including suppliers and manufacturers. The purpose of this paper is to design a resilient fuzzy risk-averse supply portfolio selection approach with lead-time sensitive manufacturers under partial and complete supply facility disruption in addition to the operational risk of imprecise demand to minimize the mean-risk costs. This problem is analyzed for a risk-averse decision maker, and the authors use the conditional value-at-risk (CVaR) as a risk measure, which has particular applications in financial engineering.

The methodology of the current research includes two phases of conceptual model and mathematical model. In the conceptual model phase, a new supply portfolio selection problem is presented under disruption and operational risks for lead-time sensitive manufacturers and considers resilience strategies for risk-averse decision makers. In the mathematical model phase, the stages of risk-averse two-stage fuzzy-stochastic programming model are formulated according to the above conceptual model, which minimizes the mean-CVaR costs.

In this paper, several computational experiments were conducted with sensitivity analysis by GAMS (General algebraic modeling system) software to determine the efficiency and significance of the developed model. Results show that the sensitivity of manufacturers to the lead time as well as the occurrence of disruption and operational risks, significantly affect the structure of the supply portfolio selection; hence, manufacturers should be taken into account in the design of this problem.

The study proposes a new two-stage fuzzy-stochastic scenario-based mathematical programming model for the resilient supply portfolio selection for risk-averse decision-makers under disruption and operational risks. This model assumes that the manufacturers are sensitive to lead time, so the demand of manufacturers depends on the suppliers who provide them with services. To manage risks, this model also considers proactive (supplier fortification, pre-positioned emergency inventory) and reactive (revision of allocation decisions) resilience strategies.

The site layout has a significant impact on the efficiency of construction operations. Planning an effective site layout partly involves identifying and positioning temporary facilities such as tower cranes and areas on the jobsite for materials storage. This study proposes an approach to optimizing the type and location of the tower crane and material supply point on construction sites.

The problem is formulated into an integer linear programming (ILP) model considering the total cost of material transportation as the objective function and site conditions as constraints. The efficacy of the approach is demonstrated by finding the optimum site layout for a numerical example. The proposed model is validated and verified using two methods.

Results indicate that the proposed model successfully identifies the type and location of the tower crane and the location of material supply point, leading to approximately 20% cost reduction compared with when such features of a site layout are decided solely based on experience and educated guesses of the construction manager.

The primary contribution of this study is to present a modified linear mathematical model for site layout optimization that exhibits improved performance compared with previous models. The type and location of the tower crane and the material supply point as decision variables are extracted directly from solving the proposed model. The proposed model will help enhance time and cost efficiency on construction sites.

This paper proposed a bi-level mathematical model for location, routing and allocation of medical centers to distribution depots during the COVID-19 pandemic outbreak. The developed model has two players including interdictor (COVID-19) and fortifier (government). Accordingly, the aim of the first player (COVID-19) is to maximize system costs and causing further damage to the system. The goal of the second player (government) is to minimize the costs of location, routing and allocation due to budget limitations.

The approach of evolutionary games with environmental feedbacks was used to develop the proposed model. Moreover, the game continues until the desired demand is satisfied. The Lagrangian relaxation method was applied to solve the proposed model.

Empirical results illustrate that with increasing demand, the values of the objective functions of the interdictor and fortifier models have increased. Also, with the raising fixed cost of the established depot, the values of the objective functions of the interdictor and fortifier models have raised. In this regard, the number of established depots in the second scenario (COVID-19 wave) is more than the first scenario (normal COVID-19 conditions).

The results of the current research can be useful for hospitals, governments, Disaster Relief Organization, Red Crescent, the Ministry of Health, etc. One of the limitations of the research is the lack of access to accurate information about transportation costs. Moreover, in this study, only the information of drivers and experts about transportation costs has been considered. In order to implement the presented solution approach for the real case study, high RAM and CPU hardware facilities and software facilities are required, which are the limitations of the proposed paper.

The main contributions of the current research are considering evolutionary games with environmental feedbacks during the COVID-19 pandemic outbreak and location, routing and allocation of the medical centers to the distribution depots during the COVID-19 outbreak. A real case study is illustrated, where the Lagrangian relaxation method is employed to solve the problem.

The airlines cancel their flights frequently because of factors that they do not have any control over. Spare aircraft can potentially address some of the issues caused by cancelled flights. This paper aims to offer an exploratory study into the financial and operational viabilities of spare aircraft for airlines.

Mathematical models are proposed to evaluate the financial and operational metrics under different scenarios. The models are applied to Delta, Spirit and Southwest Airlines with different business models. All data are extracted from US Bureau of Transport Statistics, Cirium Diio Mi and CAPA databases. The IBM Cplex solver was used to execute the binary linear program models.

The research revealed that factors such as airline network size, hub and spoke structure and average weekly flight cancellations are crucial in establishing the need for spare aircraft. For the number of weekly cancellations, there exist break-even values that reasonably justify spare aircraft.

Models can be customized and applied to other modes of transportations.

This study is the first to consider the use of spare aircraft in airlines from both financial and operational perspectives within the scope of the mathematical model. The analyses identify financial break-even points for a number of spare aircraft and their home base locations for three airlines. Operational utilization of spare aircraft is studied and contrasted with financial metrics.

Most projects are facing delays, and accelerating the pace of project progress is a necessity. Project managers are responsible for completing the project on time with minimum cost and with maximum quality. This study provides a trade-off between time, cost, and quality objectives to optimize project scheduling.

The current paper presents a new resource-constrained multi-mode time–cost–quality trade-off project scheduling model with lags under finish-to-start relations. To be more realistic, crashing and overlapping techniques are utilized. To handle uncertainty, which is a source of project complexity, interval-valued fuzzy sets are adopted on several parameters. In addition, a new hybrid solution approach is developed to cope with interval-valued fuzzy mathematical model that is based on different alpha-levels and compensatory methods. To find the compatible solution among conflicting objectives, an arithmetical average method is provided as a compensatory approach.

The interval-valued fuzzy sets approach proposed in this paper is denoted to be scalable, efficient, generalizable and practical in project environments. The results demonstrated that the crashing and overlapping techniques improve time–cost–quality trade-off project scheduling model. Also, interval-valued fuzzy sets can properly manage expressions of the uncertainty of projects which are realistic and practical. The proposed mathematical model is validated by solving a medium-sized dataset an adopted case study. In addition, with a sensitivity analysis approach, the solutions are compared and the model performance is confirmed.

This paper introduces a new continuous-based, resource-constrained, and multi-mode model with crashing and overlapping techniques simultaneously. In addition, a new hybrid compensatory solution approach is extended based on different alpha-levels to handle interval-valued fuzzy multi-objective mathematical model of project scheduling with influential uncertain parameters.

This paper deals with the combined management and design of a sustainable pharmaceutical supply chain network with considering recycling.

This paper first utilizes the analytical hierarchy process to select and rank green manufacturers. Second, the authors proposed a multi-objective nonlinear mathematical model to design a sustainable pharmaceutical supply chain network. The proposed model has been linearized and solved using the LP-metric method using GAMS software.

A real case study has been conducted in Iran. The results show that environmental and social issues can be improved while minimizing total costs.

Given the criticality and importance of drugs in human health and the importance of recycling in today's world, proper management and design of a sustainable drug supply chain are necessary. This study pays special attention to environmental issues by utilizing multi-criteria decision approaches and customer satisfaction.

The purpose of this study is to present a general review that provides an overview of the concept of sustainability and the effectiveness of mathematics curricula in courses where deeper work on economic and environmental sustainability has become central.

A qualitative methodology consisting of a review based on a pre-defined systematic method was used to exhaustively search and identify the most relevant answers to the research question: What is the role of mathematics to sustainability? To facilitate answering such a broad question, several concrete questions were formulated. Answers from published and unpublished documents were analysed. The quality of the extracted data was assessed, and the results were synthesized.

It was concluded that, on the one hand, the discipline of mathematics has much to contribute to solving the problems of sustainability; on the other hand, new mathematics is appearing stimulated by new challenges.

This work presents social implications in an innovative way. It allows for an increase in educational sustainability by bringing the academic community closer to the business world and the challenges of society and, furthermore, by having a major impact on the motivation of teachers and students to develop cooperative work within university institutions.

The originality is based on an a priori analysis for the construction and implementation of didactic tools for university teacher training in the area of mathematics within the framework of sustainable development, both economically and environmentally.