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.     

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.     

Some branch-and-bound procedures for fixed-cost transportation problems

In this article we present three properties that will improve the performance of branch-and-bound algorithms for fixed-cost transportation problems. By applying Lagrangian relaxation we show that one can develop stronger up and down penalties than those traditionally used and also develop a strengthened penalty for nonbasic variables. We also show that it is possible to “look ahead” of a particular node and determine the solution at the next node without actually calculating it. We present computational evidence by comparing our developments with existing procedures.     

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.     

Design of a process control scheme for defects per 100 units based on aoql

A process control scheme is developed in which decisions as to the frequency of sampling are made based upon the choice of an Average Outgoing Quality Limit. The scheme utilizes plotted points on a U-control chart for defects and the theory of runs to determine when to switch among Reduced, Normal, Tightened, and 100 percent inspection. The scheme is formulated as a semi-Markov process to derive steady stale equations for the probabilities of being in Reduced, Normal, Tightened, or 100 percent inspection and for Average Outgoing Quality and Average Fraction Inspected. The resulting system and the computer programs used to derive it are discussed.     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.