Facets of the polytope of the asymmetric travelling salesman problem with replenishment arcs

The Asymmetric Travelling Salesman Problem with Replenishment Arcs (RATSP) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints.

In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

New insights in asymmetric tetraorganodistannoxane ladder formation. A NMR-spectroscopic and crystallographic study

The syntheses of the asymmetrically substituted tetraorganodistannoxanes [t-Bu₂(X)SnOSn(Y)(CH₂SiMe₃)₂1₂ (1, X = Y = OH; 2, X = Cl, Y = OH; 3, X = Y = Cl) are reported and their structures in solution and in the solid state are characterized by multinuclear NMR spectroscopy and single crystal X-ray analyses. In toluene, the tetrahydroxy-substituted derivative 1 is in equilibrium with the organotin oxides cyclo-[t-Bu₂Sn{OSn(CH₂SiMe₃)₂}₂O] (4), cyclo[(Me₃SiCH₂)₂Sn(OSnt-Bu₂)₂O] (5), and cyclo-(t-Bu₂SnO)₃, and some additional, undefined species containing pentacoordinated tin atoms. In contrast, the dihydroxydichloro-substituted derivative 2 is inert in solution.

Sequential technology adoption with asymmetric firms

We analyse the incentives and welfare implications of costly technology adoption in a two-period duopoly model where firms have different amounts of capital. We also extend our framework to an open economy set-up and examine the relationship between trade and technology adoption. Our findings are as follows. First, no monotone relationship exists between the threshold cost of adoption and capital shares. Second, an unequal distribution of capital, despite lessening competition, can increase total surplus. Third, trade generally encourages adoption of modern technology unless the share of capital for the adopters is too low.

Photo-catalysis of red wine stains using titanium dioxide sol-gel coatings on wool fabrics

This paper investigated the use of titanium dioxide sol-gel coatings to photo-catalyse red wine stains on wool fabrics. Coatings were produced by the hydrolysis and condensation of titanium butoxide (Ti(OC4H9)4) on the surface of wool fabrics after pad application. Coatings were partially converted to the anatase form of titanium dioxide by prolonged immersion in boiling water. The coating presence was confirmed using scanning electron microscopy, UVspectrophotometry and atomic force microscopy. Coated samples were measured for photo-catalytic activity by degrading red wine stains from the surface of the coated fabric. The level of photocatalysis was determined for each of the coating systems after 168 hours. Red wine stains were photo-catalysed and level of staining was reduced from the UV exposed surface of the coated wool fabric.

Examining the asymmetric behaviour of macroeconomic aggregates in Asian economies

The goal of this paper is to test for asymmetric behaviour of macroeconomic aggregates for three Asian economies; namely, Malaysia, Hong Kong and Korea. Whether macroeconomic aggregates can be characterised as asymmetric has important implications for policy-making and econometric modelling including forecasting. We examine two forms of asymmetries; specifically deepness, which arises when a detrended time series contains an asymmetric distribution, and steepness, which arises when the first difference of a series contains an asymmetric distribution. Overall, our findings suggest that for all three countries, the bulk of the series display asymmetry behaviour.

Are health expenditures and GDP characterized by asymmetric behaviour? Evidence from 11 OECD countries

In this article, we examine whether per-capita health expenditures and per-capita GDP for 11 OECD countries can be characterized by asymmetric behaviour. We achieve this goal by using the nonparametric Triples test suggested by Randles et al. (1980). We examine two forms of asymmetries, namely deepness and steepness. Our main finding is that for 6 out of 11 countries, namely for the USA, the UK, Japan, Spain, Finland and Iceland, either per-capita health expenditures or per-capita GDP are characterized by asymmetric behaviour. This finding to some extent casts doubt on those studies that model the relationship between health and GDP using unit-root and cointegration tests that assume symmetric disturbances.

Can the electricity market be characterised by asymmetric behaviour?

In this paper, we test for asymmetric behaviour of industrial and residential electricity demand for the G7 countries, using the entropy-based test for symmetry suggested by [Racine, J., and Maasoumi, E., 2007. A versatile and robust metric entropy test of time-reversibility, and other hypotheses. Journal of Econometrics 138(2), 547–567; Racine, J., and Maasoumi, E., 2008. A robust entropy-based test of asymmetry for discrete and continuous processes. Econometric Reviews 28, 246–261], the Triples test of [Randles, R., Flinger, M., Policello, G., and Wolfe, D., 1980. An asymptotically distribution-free test for symmetry versus asymmetry. Journal of the American Statistical Association 75, 168–172] and the [Bai, J., and Ng, S., 2001. A consistent test for conditional symmetry in time series models. Journal of Econometrics 103, 225–258] test for conditional symmetry. Using data that spans over three decades, we find overwhelming evidence of conditional symmetry of residential and industrial electricity consumption. This finding implies that the use of econometric tests based on linear data generating processes is credible.

Asymmetric recognition of good and bad news at Malaysian capital market : a pre and crisis analysis

The aim of this paper is to analyze the asymmetric recognition of good and bad news on reported earnings of Malaysian-listed firms. The study uses both descriptive and regression analyses to ascertain whether there is a contemporaneous relationship between news (good and bad) and reported earnings. The analysis is based on a sample of 150 firms listed on the Bursa Malaysia Index over a period of 10 years, from 1990 to 2000. Two regression models were adopted based on Basu (1997) and Giner and Rees (2001). The first model aims to capture asymmetric recognition of good and bad news into reported earnings while the latter model is developed to capture both asymmetric recognition of information shock and permanent earnings effect on contemporaneous earnings. The evidence from this study reported the steady increase in earnings per share till 1997. However, a drastic decline was observed for the period 1997 to 1999 because of Asian financial crisis. The findings from the regression model one suggested that the asymmetric recognition of good news was more prominent during the good time compare to bad time and vice versa. The findings from model two also suggested that autoregressive effect of permanent effect was very prominent both for crisis and non crisis periods.

Sources of liquidity commonality, asymmetric information and ownership structure in emerging markets : evidence from the Chinese stock market

Xinwei Zheng examines if common factors of liquidity can be determined by ownership structure measured by asymmetric information in an emerging market that has adopted an order-driven trading system. Using China as a case for the study, I select a broad sample of stocks from two separate Chinese stock exchanges to measure and
analyse the relationship. My empirical evidence seems significant and pervasive. These findings about the Chinese stock market provide useful pointers for understanding commonality in emerging economies and shed critical light
on a new dimension of the working of emerging markets.

The ascent of asymmetric risk in information security: an initial evaluation

Dramatic changes in the information security risk landscape over several decades have not yet been matched by similar changes in organizational information security which is still mainly based on a mindset that security is achieved through extensive preventive controls. As a result, maintenance cost of information security is increasing rapidly, but this increased expenditure has not really made an attack more difficult. The opposite seems to be true, information security attacks have become easier to perpetrate and appear more like information warfare tactics. At the same time, the damage caused by a successful attack has increased significantly and may sometimes become critical to an organization. In this paper we evaluate one particular extremely asymmetric risk where a strongly motivated attacker unleashes a prolonged attack on an organization with the aim to do maximum damage, and suggest that the probability of such an attack is increasing. We discuss how preventive controls are unlikely to ever be effective against such an attack and propose more advanced strategies that aim to limit the damage when such an attack occurs. One crucial lesson to be learned for those organizations that are dependant on their information security, such as critical infrastructure organizations, is the need to deny motivated attackers access to any information about the success of their attack. Successful deception in this area is likely to significantly reduce any potential escalation of the incident.

Directional water-transfer through fabrics induced by asymmetric wettability

Fabrics having an interesting unidirectional water-transfer effect have been prepared by a special coating technique to create a wettability gradient across the fabric thickness, and the treated fabrics also show considerably different breakthrough pressures on the two fabric sides.