Geometric Properties of Partial Sums of Univalent Functions

The $n$th partial sum of an analytic function $f(z)=z+\sum_{k=2}^\infty a_k z^k$ is the polynomial $f_n(z):=z+\sum_{k=2}^n a_k z^k$. A survey of the univalence and other geometric properties of the $n$th partial sum of univalent functions as well as other related functions including those of starlike, convex and close-to-convex functions are presented

Tuberculosis Control in developing countries: A Generalized Community Health Worker Based Model

Tuberculosis is a major health care burden in developing countries. World Health Organization (WHO) has been assisting developing countries through their respective Governments to control this curable disease. The Amsterdam declaration aims to control tuberculosis globally by the year 2005. The TBC project implementation experiences are varied across countries both on cure and detection rates. The government initiatives are complemented by the non government organizations involvement at the operational level. The BRAC model in Bangladesh involves the NGOs in an extensive and cohesive way. This paper documents the BRAC model for TBC in Bangladesh. We introduce the concept of value chain, in the context of TBC. Based on the value chain concept, the logic for the effectiveness of the BRAC model is discussed. An improved version of the Bangladesh delivery model is proposed. We hope the model proposed in this work would draw the attention of policy planners, and help them to control TB in their respective countries.

Vision 2020: The Role and Scope of Operations Research Models

In this theme article, we summarize the broad characteristics of Vision 2020 (a document which outlines the transformation process related to evolution of India as a developed nation by 2020) as envisaged by Dr. A.P.J. Abdul Kalam. We discuss the enabling role of our discipline related to this critical national (social) transformation process. This theme article is organized in three segments. The first segment, which is drawn heavily based on the published work by Dr. A.P.J. Abdul Kalam introduces the salient features of Vision 2020 and a road map related to realizing this national dream. The second segment sketches the evolution of operations research as a scientific discipline in the international and Indian context. The third and final segment of the article relate OR tools and techniques that can facilitate the planning and implementation of several projects / activities / policies in the overall context of Vision 2020.

Dynamic pore collapse in viscoplastic materials

Dynamic pore collapse in porous materials is studied by analyzing the finite deformation of an elastic/viscoplastic spherical shell under impulsive pressure loading. Effects of dynamic loading rate, pore size, initial porosity, strain-i-ate sensitivity, strain hardening, thermal softening, and mass density of the matrix material on the pore collapse process are examined and results are compared with those from quasistatic analyses of both rate-independent and rate-dependent matrix materials. Dynamic (inertia) effects are found to be significant or even dominant in certain shock wave consolidation conditions. An approximate method is proposed to incorporate dynamic effects into quasistatic pore-collapse relations of viscoplastic matrix materials. Implications of results of current study are discussed in terms of understanding the processes of shock wave consolidation of powders

A Finite Horizon Inventory Model: An Operational Framework

We present a simulation based decision support system to decide the inventory ordering policy in the context of a single commodity, multi pack, and finite horizon situation. The multiple objectives include (a) Minimizing the end of the season inventory, (b) Maximizing the operating profit, (c) Minimizing the peak working capital requirements during the season. Stochastic demand and positive lead time add to the complexity of the problem context. In addition multiple partners in the supply chain with distinct and conflicting set of objectives necessitate the need for a formal approach. The motivation for this model is based on a real life situation. The model addresses the decision choices faced by the distributor in a specific logistics chain. In this chain, a typical distributor has to balance between the stochastic nature of the demand and the attractive nature of financial incentives (order quantity based) proposed by the manufacturer. The problem can be formulated as a multi-period dynamic programming problem with stochastic demand with an objective to optimize the expected operating profit, subject to specific constraints on working capital requirement, service level, order fill rate and end of the season inventory. Such a formulation is hard to solve and does not lend itself to analyze several ordering policies. Based on simulation experiments, we propose an ordering policy which optimizes the overall objectives of supply chain partners and hence demonstrated the possibility of jointly managing the uncertain demand by supply chain partners. The model is simple and easy to use. It is implemented by using spreadsheet. It provides adequate flexibility to conduct what-if analysis. The model has a potential to be useful in a wide range of situations.