A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

A possibilistic aggregate production planning model for brass casting industry

This article discusses a possibilistic aggregate production planning (APP) model for blending problem in a brass factory; the problem computing optimal amounts of raw materials for the total production of several types of brass in a planning period. The model basically has a multi-blend model formulation in which demand quantities, percentages of the ingredient in some raw materials, cost coefficients, minimum and maximum procurement amounts are all imprecise and have triangular possibility distributions. A mathematical model and a solution algorithm are proposed for solving this model. In the proposed model, the Lai and Hwang's fuzzy ranking concept is relaxed by using ‘Either-or’ constraints. An application of the brass casting APP model to a brass factory demonstrates that the proposed model successfully solves the multi-blend problem for brass casting and determines the optimal raw material purchasing policies.     

Intersection Bounds: Estimation and Inference

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a median‐bias‐corrected estimator of such bounds as a by‐product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel‐based empirical processes by a sequence of “penultimate” Gaussian processes. These penultimate processes are generally not weakly convergent, and thus are non‐Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.     

Modeling Acute Rheumatic Fever

Acute rheumatic fever (ARF) is a major cause of heart disease, rare in developed countries, but of concern in New Zealand, where a unique feature is the prevalence of ARF among Maori and Pacific Island peoples. The incidence and prevalence of ARF in a population are modeled for the New Zealand case, where risks of contracting Group A Streptococcus or developing ARF are allowed to vary according to ethnicity, age, and ARF history. The critical parameter R₀ determines whether a disease will become epidemic or not. A proportional treatment protocol is the most effective at reducing ARF.     

混合整数分式多目标规划及其在企业计划管理中的应用

本文将修正的Dakin分枝定界法用于求解带有线性分式目标的混合整数多目标规划问题,提出了“弹性约束”的概念及其处理方法和交互型分枝定界的两步算法,并将其应用于实际问题中。     

"李约瑟难题"数学问题新解

著名数学史难题:"近代数学为什么没有在中国产生而在西方建立",是"李约瑟难题"的子问题,近三十年来,海内外学者在解释这一数学史难题时,提出了各种观点,但细究起来不难发现,很多观点均存在着不完备性;数学创新的严重缺失是"李约瑟难题"数学问题的部分谜底.     

论数学方法的教学

本文在数学方法论的指导下,论述数学方法与数学知识教学之间的关系,并阐述数学方法教学实施意见和注意点.对师专的中教法教学研究具有一定的帮助.     

整数快速开方

给出了一种在具有单字节乘除机器指令的单片机上进行任意字节整数开方的快速算法。与传统的算法相比,它完全避免了除法的迭代,从而开方速度提高了大约一倍左右。     

线性规划在有功静态安全域中的应用

提出了一种以直流潮流模型为基础,将构成显式安全域超长方体每个分量的上、下限作为待求变量,并选取发电机有功调节量总和最大为目标函数,将有功静态安全域的模型化成一个线性规划模型直接求解的新方法。文中附有算例,计算结果验证了该方法的有效性。     

A Parametric Approach for a Nonlinear Discrete Location Problem

A discrete location problem is formulated for the design of a postal service network. The cost objective of this problem includes a nonlinear concave component. A parametric integer programming algorithm is developed to find an approximate solution to the problem. The algorithm reduces the problem into a sequence of p-median problems and deals with the nonlinear cost by a node-replacement scheme. Preliminary computational results are presented.