A note on a paper by W. Szwarc

In this note the authors call for a change of the optimality criteria given by Theorem 3 in section 5 of the paper of W. Szwarc “On Some Sequencing Problems” in NRLQ Vol. 15, No. 2 [2]. Further, two cases of the three machine problem, namely, (i) ≦ and (ii) ≦ are considered, and procedures for obtaining optimal sequences in these cases are given. In these cases the three-machine problem is solved by solving n (the number of jobs) two-machine problems.     

Determining the most vital link in a flow network

The most vital link in a single commodity flow network is that are whose removal results in the greatest reduction in the value of the maximal flow in the network between a source node and a sink node. This paper develops an iterative labeling algorithm to determine the most vital link in the network. A necessary condition for an are to be the most vital link is established and is employed to decrease the number of ares which must be considered.     

Reviews

Douglas S. Derrer, We Are All the Target: A Handbook of Terrorism Avoidance and Hostage Survival. Annapolis, MD: US Naval Institute Press, 1992. Pp. x+135, notes, index. $14.95. ISBN 01–55750–150–5

Ian Knight, Zulu: Isandlwana and Rorke's Drift, 22–23 January 1879. London: Windrow & Greene, 1992. Pp.136, 150 illus., incl 8 colour plates, maps, biblio. £35. ISBN 1–872004–23–7

Ian Knight, By the Orders of the Great White Queen: Campaigning in Zululand through the Eyes of the British Soldiers, 1879. London: Greenhill Books and Novato: Presidio Press, 1992. Pp. 272, 17 illus., 1 map. £18.95. ISBN 1–85367–122–3

Manfried Rauchensteiner and Erwin A. Schmidl (eds.), Formen des Krieges: vom Mittelalter zum ‘Low‐intensity’ Conflict’. Graz : Verlag Styria, 1991. Pp.208. DM35. ISBN 3–22–12139–7

Harold J. Kearsley, Maritime Power and the Twenty‐First Century. Dartmouth: Dartmouth Publishing Company, Limited, 1992. Pp.xv + 203, 13 diagrams, index. £32.50. ISBN 1–85521–288–9     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

India's Evolving Nuclear Posture

This article analyzes India's nuclear doctrine, finding it to be critically flawed and inimical to strategic stability in South Asia. In pursuing an ambitious triad of nuclear forces, India is straying from the sensible course it charted after going overtly nuclear in 1998. In doing so, it is exacerbating the triangular nuclear dilemma stemming from India's simultaneous rivalries with China and Pakistan. Strategic instability is compounded by India's pursuit of conventional “proactive strategy options,” which have the potential to lead to uncontrollable nuclear escalation on the subcontinent. New Delhi should reaffirm and redefine its doctrine of minimum credible nuclear deterrence, based on small nuclear forces with sufficient redundancy and diversity to deter a first strike by either China or Pakistan. It should also reinvigorate its nuclear diplomacy and assume a leadership role in the evolving global nuclear weapon regime.     

Multiple subset sum with inclusive assignment set restrictions

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011