Inventory Control and Scheduling of Multiple Products in a Common Facility*

Consider a set of chemical products to be produced in a single facility. Each product has its own unique reaction time (which is assumed to be independent of its batch size), as well as other cost and demand values. In this paper, we address the problem of determining the optimal number of batches, batch sizes, and an accompanying production schedule for these products in the single facility that will minimize the total cost. Two different algorithms have been developed for this problem, the performances of which are contrasted with classical cyclic production schedules. Finally, some guidelines for the application of these methods to real-life problems are outlined.     

Nonparametric estimation of transition probabilities in a non-Markov illness–death model

In this paper we consider nonparametric estimation of transition probabilities for multi-state models. Specifically, we focus on the illness-death or disability model. The main novelty of the proposed estimators is that they do not rely on the Markov assumption, typically assumed to hold in a multi-state model. We investigate the asymptotic properties of the introduced estimators, such as their consistency and their convergence to a normal law. Simulations demonstrate that the new estimators may outperform Aalen–Johansen estimators (the classical nonparametric tool for estimating the transition probabilities) in non-Markov situation. An illustration through real data analysis is included.     

压强和温度对薄膜折射率的影响模型

基于膜分子和气相分子在沉积时竞争的观点,得到压强和温度对薄膜折射率影响的理论模型.模型的研究表明,薄膜折射率随真空压强的增加而降低;并随沉积温度的增加而增加.在不同真空压强和不同沉积温度下制备了氧化锆薄膜,计算了样品的折射率,结果显示的规律和理论模型的规律基本一致.     

Unit root tests: the autoregressive approach in comparison with the periodogram regression

In Monte Carlo sudies we investigate unit root tests in line with Dickey/Fuller (1979). In case of positively autocorrelated MA(1) residuals their experimental power is extremely poor. Next we compare different versions of periodogram regression suggested in the literature. Their experimental behaviour is investigated with fractionally integrated processes. It is demonstrated how unit root tests may be based on periodogram regression. There is simulation evidence that those tests may do better in terms of power than the autoregressive tests, especially when testing ARMA(1,1) series against a linear time trend.     

Hellinger distances and α-entropy in a one-parameter class of density functions

Hellinger distances are considered as measures of distance between density functions, and an inequality concerning different Hellinger distances is proved. Distance measures based on the α-entropy are proposed, and their relationship to a Hellinger distance is shown. Furthermore explicit expressions for the distance measures examined are derived in a one—parameter class of density functions, including Weibull, Gamma, and Maxwell distributions.     

Multivariate boundary kernels and a continuous least squares principle

Whereas there are many references on univariate boundary kernels, the construction of boundary kernels for multivariate density and curve estimation has not been investigated in detail. The use of multivariate boundary kernels ensures global consistency of multivariate kernel estimates as measured by the integrated mean-squared error or sup-norm deviation for functions with compact support. We develop a class of boundary kernels which work for any support, regardless of the complexity of its boundary. Our construction yields a boundary kernel for each point in the boundary region where the function is to be estimated. These boundary kernels provide a natural continuation of non-negative kernels used in the interior onto the boundary. They are obtained as solutions of the same kernel-generating variational problem which also produces the kernel function used in the interior as its solution. We discuss the numerical implementation of the proposed boundary kernels and their relationship to locally weighted least squares. Along the way we establish a continuous least squares principle and a continuous analogue of the Gauss–Markov theorem.     

Demography of Indian aging, 2001-2051

India is the second largest country in the world, with 72 million elderly persons above 60 years of age as of 2001, compared to China's 127 million. One of the objectives of this paper is to assess the emerging scenario of elderly for the first half of the 21st century. According to projections, the elderly in the age group 60 and above is expected to increase from 71 million in 2001 to 179 million in 2031, and further to 301 million in 2051; in the case of those 70 years and older, they are projected to increase from 27 million in 2001 to 132 million in 2051. Among the elderly persons 80 and above, they are likely to improve their numbers from 5.4 million in 2021 to 32.0 million in 2051. The increasing number and proportion of elderly will have a direct impact on the demand for health services and pension and social security payments. Mobilizing resources for geriatric care and providing sufficient maintenance for the elderly will emerge as a major responsibility for heath-care providers and pension economists.