First passage game

Appealing to the theory of stochastic games, a two-person, zero-sum first passage game, which may be viewed as a generalization of the first passage decision problem, is developed. In the first passage game, the players have stationary optional strategies and the values are unique and these can be computed using an algorithm for terminating stochastic games. It is also shown that the solution of a recurrence game is closely related to that of the first passage game. Finally, it is shown that a finite step stochastic game with nonstationary transition probabilities and payoffs can be converted to a first passage game whose solution yields a solution of the original finite step game. The first passage game so obtained has stationary transition probabilities and payoffs. Because of its special structure, the solution method reduces to a dynamic programming recursion in the context of games.     

The state and civil society in disaster response: post-tsunami experiences in Tamil Nadu

This paper, based on the report "The State and Civil Society in Disaster Response: An Analysis of the Tamil Nadu Tsunami Experience," (Srinivasan, Nagaraj, & Venkatesh, 2005) is essentially an empirical analysis of state and civil society responses in Tamil Nadu (India) to the tsunami of December 26, 2004. It examines interventions by state and non-state agencies, as well as people's experiences in the relief and rehabilitation phases to identify factors influencing both positive and negative outcomes of the tsunami response. Issues related to vulnerability and exclusion, equity, transparency and accountability in different sectors of disaster intervention are explored to highlight themes revolving around reach and efficacy of relief and recovery processes. These analyses bring out some interesting lessons with regard to the importance of institutional autonomy, non-politicized decision-making, and synergetic state-civil society interfaces in fostering inclusive, transparent and accountable rehabilitation processes. The roles played by institutional responsiveness and flexibility in shaping an effective disaster response also emerge very clearly from this study of the Tamil Nadu experience. Another crucial finding points to the need for detailed, reliable and disaggregated geo-demographic and socioeconomic records as a resource base for informing relief and rehabilitation interventions. The study draws extensively from the experiences and insights of people affected by, and involved in tsunami response, and from secondary knowledge resources available on the disaster.     

Value of and Interaction between Production Postponement and Information Sharing Strategies for Supply Chain Firms

We analyze the value of and interaction between production postponement and information sharing, which are two distinct strategies to reduce manufacturers’ uncertainty about demand. In both single‐level and two‐level supply chains, from the manufacturer's perspective, while information sharing is always valuable, production postponement can sometimes be detrimental. Furthermore, the value of production postponement is not merely driven by savings in inventory holding cost as postponement enables the manufacturer to avoid both excess and shortfall in production. We find that production postponement and information sharing strategies may substitute, complement, or conflict with each other, depending on the extent of the increase in the unit production cost when production is postponed. In a two‐level supply chain, from the retailer's perspective, information sharing and production postponement can be beneficial or detrimental. When information sharing is beneficial to the retailer, the retailer always shares her demand information with the manufacturer voluntarily. In addition, this voluntary information sharing is truthful because inflated or deflated demand information hurts the retailer through a higher wholesale price or a stock‐out. However, the retailer never shares her demand information voluntarily if the manufacturer has already adopted production postponement because production postponement and information sharing strategies always conflict with each other. Even when the retailer does not benefit from information sharing, we show that the manufacturer can always design an incentive mechanism to induce the retailer to share the demand information, irrespective of whether the manufacturer has already implemented production postponement or not. The above findings underscore the need for a careful assessment of demand uncertainty‐reduction strategies before the supply chain players embark upon them.     

Some problems in determining the number of acceptors needed in a family planning programme to achieve a specified reduction in the birth rate

Abstract The paper attempts to revive professional interest in a problem originally considered by Lee and Isbister and which has assumed added importance recently because of the increasing number of national family planning programmes that are being instituted, which require the determination of the number of acceptors needed in a family planning programme in order to achieve a specified reduction in the birth rate. The publication of subsequent papers on births averted by programmes, notably by Potter and Wolfers, each of whom had made some criticisms of the paper by Lee and Isbister, has tended to obscure the differences in the nature between the problem raised by Lee and Isbister, and that discussedby Potter or Wolfers. The paper tries to bring out these differences and points out one of the limitations of the estimates of births averted obtained by using either Potter's or Wolfers's methods, viz. the inability to determine the time period to which the birth reduction refers, thereby further complicating the issues involved in assessing the social and economic implications of births averted by a family planning programme. The paper also points out some of the unrecognizedtechnical considerations which arise in dealingwith the 'target-setting' problem raised by Lee and Isbister and suggeststhat stochasticmodel studies might offera clue for evolving practical methods for tackling this problem.     

Contracting Under Vendor Managed Inventory Systems Using Holding Cost Subsidies

Vendor managed inventory systems are becoming increasingly popular. An important issue in implementing a vendor managed inventory scheme is the contracting terms that dictate the ownership of the inventory and the responsibility of inventory replenishment decisions. Thus the performance of a vendor managed system crucially depends on these terms and on how inventory‐related costs are shared in a supply chain. We consider a system where a manufacturer supplies a single product to a retailer who faces random demand in a competitive market. The retailer incurs a fixed cost per order, inventory holding cost, and a penalty cost for a stockout (unsatisfied demand is back‐ordered). Further, the manufacturer incurs a penalty cost when there is a stockout at the retailer and a fixed replenishment cost. We assume that the players are rational and act noncooperatively. We compare the performance of retailer managed inventory systems, where the retailer places orders and makes replenishment decisions, with vendor managed inventory systems, wherein the vendor or manufacturer makes inventory and replenishment decisions. Specifically, in the vendor managed inventory system, we propose and evaluate holding cost subsidy‐type contracts on inventories offered by the retailer to improve system performance. We evaluate this contract in the context of three widely used inventory systems—deterministic economic order quantity, continuous review (Q, r) policies, and periodic review policies—and show when such contracts may improve channel performance.     

Robustness of tests for directional mean

In this paper we study the robustness of the likelihood ratio, circular mean and circular trimmed mean test functionals in the context of tests of hypotheses regarding the mean direction of circular normal and wrapped normal distributions. We compute the level and power breakdown properties of the three test functionals and compare them. We find that the circular trimmed mean test functional has the best robustness properties for both the above-mentioned distributions. The level and power properties of the test statistics corresponding to these functionals are also studied. Two examples with real data are given for illustration. We also consider the problem of testing the mean direction of the von-Mises–Fisher distribution on the unit sphere and explore the robustness properties of the spherical mean direction and likelihood ratio test functionals.     

Self‐consistent estimation of mean response functions and their derivatives

Many methods have been developed for the nonparametric estimation of a mean response function, but most of these methods do not lend themselves to simultaneous estimation of the mean response function and its derivatives. Recovering derivatives is important for analyzing human growth data, studying physical systems described by differential equations, and characterizing nanoparticles from scattering data. In this article the authors propose a new compound estimator that synthesizes information from numerous pointwise estimators indexed by a discrete set. Unlike spline and kernel smooths, the compound estimator is infinitely differentiable; unlike local regression smooths, the compound estimator is self‐consistent in that its derivatives estimate the derivatives of the mean response function. The authors show that the compound estimator and its derivatives can attain essentially optimal convergence rates in consistency. The authors also provide a filtration and extrapolation enhancement for finite samples, and the authors assess the empirical performance of the compound estimator and its derivatives via a simulation study and an application to real data. The Canadian Journal of Statistics 39: 280–299; 2011 © 2011 Statistical Society of Canada     

SB-robustness of directional mean for circular distributions

In this paper we study the robustness of the directional mean (a.k.a. circular mean) for different families of circular distributions. We show that the directional mean is robust in the sense of finite standardized gross error sensitivity (SB-robust) for the following families: (1) mixture of two circular normal distributions, (2) mixture of wrapped normal and circular normal distributions and (3) mixture of two wrapped normal distributions. We also show that the directional mean is not SB-robust for the family of all circular normal distributions with varying concentration parameter. We define the circular trimmed mean and prove that it is SB-robust for this family. In general the property of SB-robustness of an estimator at a family of probability distributions is dependent on the choice of the dispersion measure. We introduce the concept of equivalent dispersion measures and prove that if an estimator is SB-robust for one dispersion measure then it is SB-robust for all equivalent dispersion measures. Three different dispersion measures for circular distributions are considered and their equivalence studied.