D. K. Manna

A use-rate based failure model for two-dimensional warranty

We consider the problem of constructing probability model for product failure instances indexed by two scales, namely, age and usage. This is an important element in the analysis of two-dimensional warranty for automobiles. Specifically, we deal with models that apply to components or parts. The motivation for the same is stressed, and a model is proposed. The key feature of this model is: how use-rate affects life. Some existing models are then analyzed in the light of this feature, and the results are presented. Numerical examples are also provided to illustrate the application of this model in calculating warranty cost.

Bounds for the position of the smallest job in completion time variance minimization

The problem of scheduling jobs on a single machine so as to minimize the variance of job completion times is considered. We develop bounds on the position of the smallest job in an optimal sequence, which is vital due to the fact that an optimal sequence is necessarily a V-shaped sequence. Results of numerical experimentation indicate that the bounds are very effective if the job processing times are homogeneous. Using these bounds, we develop a new heuristic method to solve the problem. Based on numerical investigation, it is shown that performance of this heuristic compares favorably with existing but older heuristics.

A note on calculating cost of two-dimensional warranty policy

We study the derivation of warranty cost under rectangular two-dimensional policy for both repairable as well as non-repairable product. Typically, two approaches are adopted, namely, one-dimensional (1D) and two-dimensional (2D). We show the difference in results obtained from the formulae under the two approaches through several examples. Merits of the formulae are then analyzed to identify the correct ones.

Pseudopolynomial algorithms for CTV minimization in single machine scheduling

Abstract The problem of scheduling jobs on a single machine so as to minimize completion time variance (CTV) is considered. In this article, we have derived two dominance criteria and used them in the development of a new pseudopolynomial algorithm. This algorithm is an implicit enumeration scheme based on a binary branching strategy, with larger jobs fixed at early stages, and is superior to those of De, Ghosh and Wells [1] and Kubiak [2] in terms of computational complexity. It is observed that this algorithm is very good when the job processing times are quite heterogeneous, while the algorithm of De, Ghosh and Wells [1] is excellent for homogeneous processing times. By making use of these contrasting merits, another pseudopolynomial algorithm is then proposed. Results of extensive numerical investigation on the performances of the algorithms are also reported.

Warranty cost estimation of a multi‐module product

This article deals with the problem of cost estimation for increased warranty time of a multi‐module product. The warranty policy of interest is two‐dimensional involving warranty limits on both age and usage of the product. Failure of the product is caused due to malfunctioning of its module(s). Warranty service is rendered through repair or replacement of the respective module(s). From the past data, it is observed that age and usage are highly correlated. Based on life (age) data, the joint life distribution of the modules is well described by multivariate exponential distribution of Marshall and Olkin. The same is utilized to estimate cost for desired warranty times by the method of simulation.

Effect of use‐rate on system life and failure models for 2D warranty

Purpose – The purpose of this paper is to characterise the failure model of a system that is covered by a two‐dimensional warranty, one dimension depicting time and the other usage. Specifically, the authors study the effect of use‐rate on system life when each constituent component life is described by an accelerated‐failure‐time (AFT) type model.Design/methodology/approach – The paper evaluates the effect of use‐rate on the expected failure time of a system having different internal configurations involving components. Firstly, the coherent structure as well as modules with redundant structures (standby and load‐sharing) are analysed, whereby component failures are assumed to be conditionally independent. Study systems of some basic configurations with a general dependence structure among component failure instances are also studied.Findings – The results strongly indicate that, irrespective of the internal component‐configuration of the system, the models should posses the property that the expected fa...

Common Due-Date Assignment and Scheduling on Single Machine with Exponential Processing Times

This article deals with the problem of common due-date assignment and scheduling on single machine with exponential processing times. The objective is to minimize the expected total cost associated with the due-date and earliness/tardiness of jobs. For large due-date cost, we have derived a closed-form solution, which is applicable to the general processing times as well. In the other case, it is shown that an optimal sequence lies among the V-shaped sequences, and an algorithm is developed for the derivation of optimal solution.

Minimization of Expected Variance of Completion Times on Single Machine for Stochastic Jobs

This article deals with the problem of scheduling jobs with random processing times on single machine in order to minimize the expected variance of job completion times. SutTicient conditions for the existence of V-shaped optimal sequences are derived separately for general and ordered job processing times. It is shown that when coefficient of variation of random processing times are bounded by a certain value, an optimal sequence is V-shaped. c, 1997 JohnWiley&sons, ln~.

A Marketing Decision Problem in Single-Period Stochastic Inventory Model

This article deals with a marketing decision problem in the classical single-period stochastic inventory model, where the level of marketing effort decides on the extent of demand. Specifically, it is assumed that mean demand is an increasing concave function of the level of marketing effort. The problem under consideration is optimal determination of both order quantity as well as level of marketing effort. Results are presented to describe the solution procedure for general demand distribution. Optimal decision rules are derived for some particular demand distributions.

A Note on Lower Bound for Completition Time Variance in Single Machine Scheduling

This paper is concerned with the single machine scheduling problem where the objective is to minimize the variance of the job completion times. A lower bound on minimum completion time variance given by De et al. (1992) is corrected using a simple proof. Computational results on the lower bound are also provided.