Adjusted Hazard Rate Estimator Based on a Known Censoring Probability

In most reliability studies involving censoring, one assumes that censoring probabilities are unknown. We derive a nonparametric estimator for the survival function when information regarding censoring frequency is available. The estimator is constructed by adjusting the Nelson–Aalen estimator to incorporate censoring information. Our results indicate significant improvements can be achieved if available information regarding censoring is used. We compare this model to the Koziol–Green model, which is also based on a form of proportional hazards for the lifetime and censoring distributions. Two examples of survival data help to illustrate the differences in the estimation techniques

The dynamic lot-sizing problem with convex economic production costs and setups

In this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver–Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner–Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner–Whitin algorithm turns out to be the best heuristic

Bivariate Density Estimation with Randomly Truncated Data

In this study bivariate kernel density estimators are considered when a component is subject to random truncation. In bivariate truncation models one observes the i.i.d. samples from the triplets (T, Y, X) only if T[less-than-or-equals, slant]Y. In this set-up, Y is said to be left truncated by T and T is right truncated by Y. We consider the estimation of the bivariate density function of (Y, X) via nonparametric kernel methods where Y is the variable of interest and X a covariate. We establish an i.i.d. representation of the bivariate distribution function estimator and show that the remainder term achieves an improved order of O(n-1 ln n), which is desirable for density estimation purposes. Expressions are then provided for the bias and the variance of the estimators. Finally some simulation results are presented.bivariate distribution, truncation/censoring, kernel density estimators

Full and conditional likelihood approaches for hazard change-point estimation with truncated and censored data

Hazard function plays an important role in reliability and survival analysis. In some real life applications, abrupt changes in the hazard function may be observed and it is of interest to detect the location and the size of the change. Hazard models with a change-point are considered when the observations are subject to random left truncation and right censoring. For a piecewise constant hazard function with a single change-point, two estimation methods based on the maximum likelihood ideas are considered. The first method assumes parametric families of distributions for the censoring and truncation variables, whereas the second one is based on conditional likelihood approaches. A simulation study is carried out to illustrate the performances of the proposed estimators. The results indicate that the fully parametric method performs better especially for estimating the size of the change, however the difference between the two methods vanish as the sample size increases. It is also observed that the full likelihood approach is not robust to model misspecification.Hazard function Change-point Conditional likelihood Left truncated right censored data

On the (Q,r) policy for perishables with positive lead times and multiple outstanding orders

We consider an inventory system for perishables with fixed lifetimes, positive replenishment lead times and lost sales in the presence of non-negligible fixed ordering costs. The system is studied under the lotsize reorder level (Q, r) policy. An exact analysis of this system based on the stationary distribution of the remaining lifetime process is provided by Berk and Gürler (Oper Res 56(5):1238–1246, 2008) under the restriction that there is at most one outstanding order at any time (r< Q). In this work, we generalize their results to allow for more than one outstanding orders (r≥ Q). We provide the operating characteristics of the inventory system and construct the exact expected cost rate expression using a renewal theoretic approach. An illustrative numerical study indicates that allowing for multiple outstanding orders (r≥ Q) may result in significant savings in the expected cost rate, compared to the case with r< Q. In particular, when the fixed lifetimes are short and the ordering costs are low, expected costs can be reduced by more than half

An Exact Analysis on Age-based Control Policies for Perishable Inventories

We investigate the impact of effective lifetime of items in an age-based control policy for perishable inventories, a so-called (Q, r, T) policy, with positive lead time and fixed lifetime. The exact analysis of this control policy in the presence of a service level constraint is available in the literature under the restriction that the aging process of a batch begins when it is unpacked for consumption, and that at most one order can be outstanding at any time. In this work, we generalize those results to allow for more than one outstanding order and assume that the aging process of a batch starts since the time that it is ordered. Under this aging process, we derive the effective lifetime distribution of batches at the beginning of embedded cycles in an embedded Markov process. We provide the operating characteristic expressions and construct the cost rate function by the renewal reward theorem approach. We develop an exact algorithm by investigating the cost rate and service level constraint structures. The proposed policy considerably dominates its special two-parameter policies, which are time-dependent (Q, T) and stock-dependent (Q, r) policies. Numerical studies demonstrate that the aging process of items significantly influences the inventory policy performance. Moreover, allowing more than one outstanding order in the system reaps considerable cost savings, especially when the lifetime of items is short and the service level is high

On the (Q,r) policy for perishables with positive lead times and multiple outstanding orders

\u3cp\u3eWe consider an inventory system for perishables with fixed lifetimes, positive replenishment lead times and lost sales in the presence of non-negligible fixed ordering costs. The system is studied under the lotsize reorder level (Q, r) policy. An exact analysis of this system based on the stationary distribution of the remaining lifetime process is provided by Berk and Gürler (Oper Res 56(5):1238–1246, 2008) under the restriction that there is at most one outstanding order at any time (r&lt; Q). In this work, we generalize their results to allow for more than one outstanding orders (r≥ Q). We provide the operating characteristics of the inventory system and construct the exact expected cost rate expression using a renewal theoretic approach. An illustrative numerical study indicates that allowing for multiple outstanding orders (r≥ Q) may result in significant savings in the expected cost rate, compared to the case with r&lt; Q. In particular, when the fixed lifetimes are short and the ordering costs are low, expected costs can be reduced by more than half.\u3c/p\u3

Centralized and decentralized management of groundwater with multiple users

a b s t r a c t In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterso