Minimizing the sum of absolute lateness in single-machine and multimachine scheduling

Kanet addressed the problem of scheduling n jobs on one machine so as to minimize the sum of absolute lateness under a restrictive assumption on their common due date. This article extends the results to the problem of scheduling n jobs on m parallel identical processors in order to minimize the sum of absolute lateness. Also, a heuristic algorithm for a more general version with no restriction on the common due date, for the problem of n-job single-machine scheduling is presented and its performance is reported.     

An efficient heuristic for the multi-item newsboy problem with a single constraint

This article treats the problem of determining optimal and approximately optimal order quantities for a multiple-item inventory system subject to a single constraint on space or budget. Although this problem can be solved by the usual method of Lagrange multipliers, we wish to consider a more efficient scheme that requires fewer computations. We provide calculations that compare and contrast four approximation techniques. In particular, we have discovered a method that yields a direct algebraic expression of the problem parameters for allocation and achieves an expected profit within 90% of the optimal in about 90% of the cases tested.     

An acceptance life test for high-reliability products

This article introduces a replacement life-test procedure for the exponential failure rate: Failure-free operation of a unit for at least t_k consecutive time units is designated a “success”; the acceptance test is passed if and only if the first success is encountered before k unit failures have been recorded. Test plans are presented and the test is compared with the usual time-truncated test and to the truncated sequential probability ratio test. It is shown that this new test has smaller expected test time than the time truncated test when the true failure rate is small relative to the null hypothesized failure rate. Consistency and unbiasedness are proved and methods for making inferences on failure rate are described.     

A note on the constrained shortest-path problem

The subject of this note is the validity of the algorithm described by Aneja and Nair to solve the constrained shortest-path problem.     

On the moments of gamma order statistics

A recurrence relation between the moments of order statistics from the gamma distribution having an integer parameter r is obtained. It is shown that if the negative moments of orders -(r?1), …, ?1 of the smallest order statistic in random samples of size n are known, then one can obtain all the moments. Tables of negative moments for r = 2 (1) 5 are also given.     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

Optimal project compression with due-dated events

The paper proposes an algorithm for the determination of the solution of the activities to be shortened and the amount by which they are to be shortened in order to minimize the total cost of project completion. This cost involves a linear penalty for tardienss of a set of key events and a linear cost of activity compression from its normal duration. The procedure is a generalization of the work of Fulkerson.     

Steady state waiting time in a multicenter job shop

This paper analyzes the waiting-time distribution of a specific job as it moves through a job-shop with multiple centers and exponential service times. The movement of the job through the shop is governed by a Markovian transition matrix and ends with the job's exit from the shop.     

Return policies for an inventory system with positive and negative demands

We consider a single item inventory system with positive and negative stock fluctuations. Items can be purchased from a central stock, n items can be returned for a cost R + rn, and a linear inventory carrying cost is charged. It is shown that for minimizing the asymptotic cost rate when returns are a significant fraction of stock usage, a two-critical-number policy (a,b) is optimal, where b is the trigger level for returns and b – a is the return quantity. The values for a and b are found, as well as the operating characteristics of the system. We also consider the optimal return decision to make at time zero and show that it is partially determined by a and b.