Note: Pairwise rearrangements in reliability structures

Boland, Proschan, and Tong [2] used the notion of criticality of nodes in a coherent system to study the optimal component arrangement of reliability structures. They also provided a sufficient minimal cut (path) based criterion for verifying the criticality ordering of two nodes. We develop a necessary and sufficient condition for two nodes to be comparable and provide specific examples illustrating our result's applicability. As a corollary, certain optimal arrangement properties of well-known systems are derived. © 1994 John Wiley & Sons, Inc.     

Discount pricing policies for inventories subject to declining demand

Until only recently, the mechanism behind determining item price has been ignored and the discount price taken as a given in quantity-discount inventory decision problems. Inventory subject to declining demand further complicates both pricing and replenishment decisions. This article provides the vendor with the means for optimally determining both the discount price and replenishment order frequency for all buyers in the system in an environment of declining demand. In the multiple-buyer case, we provide an efficient algorithm for classifying buyers into homogeneous subgroups to further enhance joint cost savings among all system participants.     

Reserve forces and the transformation of British military organisation: soldiers,citizens and society

In recent years, there has been a sharp growth in political and sociological interest in the British military. Set against the backdrop of the armed forces’ increasing presence in everyday life, alongside the organizations’ ongoing restructuring, the current paper focuses on the MoD’s problematic attempts to recruit 30,000 reservists by 2020; what has become known as the Future Reserves 2020 programme (FR2020). We argue that these changes are driven in part by the need to cut costs in defence. However, we also suggest that they are a reflection of the changing nature of modern military organisation, and the manner in which armed forces engage with the societies of which they are a part, and with the citizens that make up that society. We locate FR2020 programme in the context of a wider narrative about the changing nature of military organisation in contemporary western democracies, identifying structural, circumstantial and normative reasons for change. We also examine the specific challenges of implementing FR2020 in practice, including issues of recruitment and retention, integration and support, and relations with families and employers, drawing on the experience of comparator countries to do so. We conclude by considering the implications of these changes, both for the future of UK armed forces, and for the evolving nature of military-society relations in Britain.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.     

Pseudo-monotonic interval programming

A pseudo-monotonic interval program is a problem of maximizing f(x) subject to x ε X = {x ε Rⁿ | a < Ax < b, a, b ε R^m} where f is a pseudomonotonic function on X, the set defined by the linear interval constraints. In this paper, an algorithm to solve the above program is proposed. The algorithm is based on solving a finite number of linear interval programs whose solutions techniques are well known. These optimal solutions then yield an optimal solution of the proposed pseudo-monotonic interval program.     

A parallel sequencing algorithm for minimizing total cost

The problem of sequencing jobs on parallel processors when jobs have different available times, due dates, penalty costs and waiting costs is considered. The processors are identical and are available when the earliest job becomes available and continuously thereafter. There is a processor cost during the period when the processor is available for processing jobs. The proposed algorithm finds the sequence (or sequences) with minimum total cost (sum of waiting, penalty and processor costs.). A proof of the algorithm and numerical results are given.     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

On the optimal allocation of crewmen aboard a warship

In the temporarily isolated situation in which a warship finds itself during a mission. not only spare parts, but also “spare” crewmen in various categories of specialization must he on board. Mathematical models for the probabilities of mission survival for personnel and for personnel and materiel jointly are proposed. A practical example is worked out: the optimal allocation of spare crewmen to different categories of specialization is calculated.