A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets

We study a location problem that involves a weighted sum of distances to closed convex sets. As several of the weights might be negative, traditional solution methods of convex optimization are not applicable. After obtaining some existence theorems, we introduce a simple, but effective, algorithm for solving the problem. Our method is based on the Pham Dinh - Le Thi algorithm for d.c. programming and a generalized version of the Weiszfeld algorithm, which works well for convex location problems

Research paper: firm dynamics and productivity growth in Australian manufacturing and business services, Oct 2014

This paper examines the productivity of firms in manufacturing and business services, particularly the contribution of entry and exit to aggregate productivity growth. Abstract Competitive markets foster the reallocation of inputs where resources are channelled from less competitive to more competitive firms, and hence increase aggregate productivity. The turnover of firms entering and exiting industries is part of this competitive process as entrants vie for market shares and exiters cease consuming inputs. There is a large body of theoretical and empirical work on firm dynamics, yet to date very few large scale studies have been conducted in Australia due to limited access to firm-level data. This study uses a large panel of businesses, drawn from administrative data provided to the Australian Bureau of Statistics (ABS), which allows us to track firms over the nine years from 2002–03 to 2010–11. Using this comprehensive panel we examine the productivity of firms in manufacturing and business services and, in particular measure the contribution of entry and exit to aggregate productivity growth. We find that exiting firms not only have low productivity relative to established firms in the year prior to exit, but the productivity gap is observed many years before they depart the market. Entrants grow most rapidly in their second year of operation, but after five years are still ten per cent below the productivity level of established firms. At the division level, the main driver of productivity growth is continuing firms, and the net impact of firm turnover is relatively modest. However, among the studied industries, net entry can be significant – a fact masked by the higher level of aggregation. Over the nine year period, entry lowered aggregate productivity growth by 13 per cent in manufacturing and 23 per cent in business services as entrants were less productive than continuing firms. In contrast, exiting firms raised productivity by 12 per cent in manufacturing, and 23 per cent in business services