Lower bounds for single-machine scheduling problems

This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP-hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.     

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.     

Should we be using cost of capital in calculating holding costs of consumable inventory?

The DOD directs the usage of 10% of item cost as the cost of capital in the calculation of inventory holding costs. This 10% cost is not totally justified and a complete review must be accomplished to bring this factor to a meaningful and more useful value. The current logic supporting a 10% cost of capital results in a continuing perturbation which forces the Air Force to operate in a less than efficient mode when using the economic order quantity for consumable purchases.     

On the number of games played in a best of (2n – 1) series

Let p(⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X_n, the number of games played in the series. It is shown that X_n is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on X_n is unique.     

Properties of a three-dimensional estimator

A large-scale simulation was conducted to investigate the statistical properties and the suitability of an estimator that estimates the coordinates of a three-dimensional source, according to the angles at which several observers view the source. The estimator uses a heuristical averaging method of estimates obtained from the solution of six two-dimensional problems that utilize line-to-point transformations. The estimator was found to be approximately unbiased with low standard deviations for normal error distributions. An effective and easy-to-use forecasting formula was developed to forecast the parameters of the distributions of the estimates. © 1994 John Wiley & Sons, Inc.     

Employment and utilization of engineers among defense contractors

Defense contractors retain engineers for two reasons. First, engineers work on current-period production contracts. Second, engineers conduct independent research and development (IR&D) and write bids and proposals (B&P) for future contracts. The amount of IR&D/B&P activity, however, understates the amount of effort devoted to learning that reduces the cost of future production. Even some engineers who work on current-period production may engage in learning, as a by-product of their efforts. This article develops and implements a model for estimating the volume of learning activity undertaken by four large manufacturers of military aircraft. © 1994 John Wiley & Sons, Inc.     

Estimating moments of the minimum order statistic from normal populations—a bayesian approach

Let Yⁱ ∽ N(θⁱ, σ), i = 1, …, p, be independently distributed, where θⁱ and σ are unknown. A Bayesian approach is used to estimate the first two moments of the minimum order statistic, W = min (Y¹, …, Y^p). In order to compute the Bayes estimates, one has to evaluate the predictive densities of the Yⁱ's conditional on past data. Although the required predictive densities are complicated in form, an efficient algorithm to calculate them has been developed and given in the article. An application of the Bayesian method in a continuous-review control model with multiple suppliers is discussed. © 1994 John Wiley & Sons, Inc.     

Mean residual life of coherent systems consisting of multiple types of dependent components

Mean residual life is a useful dynamic characteristic to study reliability of a system. It has been widely considered in the literature not only for single unit systems but also for coherent systems. This article is concerned with the study of mean residual life for a coherent system that consists of multiple types of dependent components. In particular, the survival signature based generalized mixture representation is obtained for the survival function of a coherent system and it is used to evaluate the mean residual life function. Furthermore, two mean residual life functions under different conditional events on components’ lifetimes are also defined and studied.     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.