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Cross-border relocation of the production lines of Hong Kong companies to the Pearl River Delta Region (PRDR) of China relocates the pollution source geographically. In contextualizing corporate social responsibility (CSR), more and better collaborations on environmental management between Hong-Kong-based companies and their supply chains within Hong Kong and the PRDR are needed. Using a qualitative approach, this research identifi es and examines nine concerned business supply chain partnership cases. Stakeholders perceived that partnership is a good tool for improving corporate environmental management. However, although it has become more active since 2002, partnership is not yet popular. More time and support are needed to develop it. Businesses should take further steps to benefi t themselves and the environment. Based on the fi rst-hand experiences and opinions of interviewees, this paper analyzes and presents recent partnership activities; their drivers and barriers; factors in their successes; and the possible roles of government and business associations in fostering partnership development.

Abstract. In this paper we study the distribution of C (A) and log C (A), where C (A) is a condition number for the linear conic system Ax ≤ 0, x = 0, with A ∈ R n×m . For Gaussian matrices A we develop both upper and lower bounds on the decay rates of the distribution tails of C (A), showing that P [C (A) ≥ t] ∼ c/t for large t, where c is a factor that depends only on the problem dimensions (m, n). Using these bounds, we derive moment estimates for C (A) and log C (A) and prove various limit theorems for the cases where m and/or n are large. Combined with condition number based complexity analyses, our results yield tail information on the distribution of running times for interior-point or relaxation methods designed to solve the feasibility problem Ax ≤ 0, x = 0.

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In recent years, several condition numbers were defined for a variety of linear programming problems based upon relative distances to illposedness. In this paper we provide a unifying view of some of these condition numbers. To do so, we introduce yet another linear programming problem and show that its distance to ill-posedness naturally captures the most commonly used distances to ill-posedness.