Project Based Learning in Preschool

According to the Buck Institute for Education (n.d.), Project Based Learning (PBL) engages learners in problem-solving, deeper learning, and building community connections. PBL with preschool aged learners is often seen as not possible. For community members, preschoolers are often seen as babies and need support. For educators, there is concern about how research and independent learning will work with emergent readers and writers (Lev et al., 2020). Through the work of Lev et al. (2020), early childhood educators are discovering how PBL can be implemented in a preschool setting. When implementing a new approach in classrooms it is important to have a process to reflect and make adjustments to affect change. This case study action research is in the beginning stages and can provide insight into the process, pitfalls, and successes that such an approach can have in a preschool setting where children attend four days a week for three hours. Questions included are how do we plan the PBL while honoring child-driven interests and how do we document the learning of our children. During the summer the leadership team of the LAB preschool participated in training via an online platform. From the platform the team chose an established unit, Creating Our Classroom Community, as the starting point for the Fall semester (Lev et al., n.d). Using the Plan- Do-Study-Act (PDSA) protocol throughout the semester, adjustments were made as the PBL was being implemented. The data showed that teachers needed ample time to collaborate, problem solve together, specifically plan to update the PBL boards in the classroom to become consistent and the need to further investigate how to use anchor charts with preschool children. The data from the PDSA is now informing the implementation of a second PBL for the spring semester

A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty. To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed

Introduction to the special issue : management science in the fight against Covid-19

At the time of writing of this Editorial in April 2021, Covid-19 continues to ravage our planet, with an official global death toll now exceeding three million, and a horrendous legacy of economic and human damage. The roll-out of vaccination has given hope that we will soon reach the end of this chapter of history. However, it will take years for the world to overcome this calamity and many individuals whose health or livelihoods have been destroyed will never fully recover. This failure of the world to effectively respond to the challenge of Covid-19 is all the more bitter because the outbreak of a novel pathogen was entirely predictable; the spread, preventable; and the suffering, avoidable. The experience of different countries around the world shows that the ability to plan, and to execute plans in a disciplined fashion, can make all the difference between relative security and catastrophe. The challenge for Management Scientists is to show that our discipline can have a role – a critical role – as a part of this planning. Epidemiological models of disease dynamics have been prominent through this crisis but do not fully capture the constraints in the health system and cannot directly support many of the management decisions which have to be made as part of the response. As Management Scientists, our perspective and our modelling tools have the potential to address those shortcomings; but if our profession cannot demonstrate our ability to add value, others will do so in our place

Models and model value in stochastic programming

Finding optimal decisions often involves the consideration of certain random or unknown parameters. A standard approach is to replace the random parameters by the expectations and to solve a deterministic mathematical program. A second approach is to consider possible future scenarios and the decision that would be best under each of these scenarios. The question then becomes how to choose among these alternatives. Both approaches may produce solutions that are far from optimal in the stochastic programming model that explicitly includes the random parameters. In this paper, we illustrate this advantage of a stochastic program model through two examples that are representative of the range of problems considered in stochastic programming. The paper focuses on the relative value of the stochastic program solution over a deterministic problem solution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44253/1/10479_2005_Article_BF02031741.pd

A simple randomised algorithm for convex optimisation: Application to two-stage stochastic programming

We consider maximising a concave function over a convex set by a simple randomised algorithm. The strength of the algorithm is that it requires only approximate function evaluations for the concave function and a weak membership oracle for the convex set. Under smoothness conditions on the function and the feasible set, we show that our algorithm computes a near-optimal point in a number of operations which is bounded by a polynomial function of all relevant input parameters and the reciprocal of the desired precision, with high probability. As an application to which the features of our algorithm are particularly useful we study two-stage stochastic programming problems. These problems have the property that evaluation of the objective function is #P-hard under appropriate assumptions on the models. Therefore, as a tool within our randomised algorithm, we devise a fully polynomial randomised approximation scheme for these function evaluations, under appropriate assumptions on the models. Moreover, we deal with smoothing the feasible set, which in two-stage stochastic programming is a polyhedron

Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function

In this paper, we analyze a class of methods for minimizing a proper lower semicontinuous extended-valued convex function . Instead of the original objective function f , we employ a convex approximation f k + 1 at the k th iteration. Some global convergence rate estimates are obtained. We illustrate our approach by proposing (i) a new family of proximal point algorithms which possesses the global convergence rate estimate even it the iteration points are calculated approximately, where are the proximal parameters, and (ii) a variant proximal bundle method. Applications to stochastic programs are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45249/1/10957_2004_Article_417694.pd