Pre-specified Limit Research Articles

OR software - ORSEP operations research software exchange program Edited by Professor H.W. Hamacher K_TREE/K_SUBGRAPH: A program package for minimal weighted K-cardinality trees and subgraphs

Given an undirected defining graph for the k-Cardinality Tree Problem (KCTP), an associated directed graph involving two additional vertices is introduced in this paper and gives rise to two compact reformulations of the problem. For the first one, connectivity of feasible solutions is enforced through multicommodity flows while, for the other, lifted Miller–Tucker–Zemlin constraints are used. Comparing the two reformulations, much stronger Linear Programming relaxation bounds are obtained from the first one, albeit at much higher CPU times. However, a Branch-and-Bound algorithm based on the second reformulation proved much more effective and managed to obtain, for the first time, optimality certificates for a large number of KCTP instances from the literature. Additionally, for some instances where optimality could not be proven within the given pre-specified CPU time limit, new best upper bounds were generated. Finally, a Lagrangian heuristic based on the first reformulation was also implemented and proved capable of generating feasible KCTP solutions comparable in quality with the best overall results obtained by metaheuristic based heuristics found in the literature. For our test cases, Lagrangian upper bounds are no more than 3.8% away from the best upper bounds known. Additionally, several new best upper bounds and optimality certificates were obtained by the heuristic. Corresponding Lagrangian heuristic CPU times, however, are typically higher than those associated with their competitors.

Optimal dispatching of an infinite capacity shuttle with compound poisson arrivals: Control at a single terminal

We consider the optimal control of an infinite capacity shuttle which transports passengers between two terminals. Passengers arrive at each of two terminals according to independent compound Poisson processes. The travel time from one terminal to the other one is a random variable following an arbitrary distribution. The dispatcher can hold the shuttle at only one of the terminals. Thus, when the shuttle is dispatched at terminal 1, it transports all the passengers waiting at terminal 1 to terminal 2 and instantaneously picks up the passengers at terminal 2 and returns to terminal 1. Assuming that the dispatcher has complete information about the number of passengers waiting at each terminal, we consider the following control limit policy: dispatch the shuttle if, and only if, the total number of passengers waiting at both terminals is at least as large as some prespecified control limit, m. In this paper, under a linear cost structure, we provide an explicit expression for the expected cost per unit time as a function of the control value, m, and present a simple and efficient method for computing the optimal control value.

Sampling for Confidence

Abstract A stopping rule for the process of sequential sampling inspection of finite lots is obtained which, with confidence 1—α, guarantees a prespecified upper confidence limit on the number of defective items in the uninspected portion of the lot. Usual assumptions of “control” are not invoked here and, in that sense, the plans are called nonparametric.