An extension of set partitioning with application to scheduling problems

The well known problems of set covering, set partitioning and set packing are defined and their interrelationship is considered. A natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation. In addition, the extended model includes another type of set problem which can be of greater use in certain applications. The model forms the basis of a computer assisted bus crew scheduling system developed by the authors. The system is in regular use by Dublin City Services in the Republic of Ireland. Finally, the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model

A co-operative parallel heuristic for integer linear programming: Combining simulated annealing with branch & bound

This paper considers the exact approach of branch and bound (B&B) and the metaheuristic known as simulated annealing (SA) for processing integer programs (IP). We extend an existing SA implementation (GPSIMAN) for pure zero–one integer programs (PZIP) to process a wider class of IP models, namely mixed zero–one integer programs (MZIP). The extensions are based on depth-first B&B searches at different points within the SA framework. We refer to the resultant SA implementation as MIPSA. Furthermore, we have exploited the use of parallel computers by designing a co-operative parallel heuristic whereby concurrent executions of B&B and MIPSA, linked through a parallel computer, exchange information in order to influence their searches. Results reported for a wide range of models taken from a library of MIP benchmarks demonstrate the effectiveness of using a parallel computing approach which combines B&B with SA

Portfolio optimisation models and properties of return distributions

Mean-risk models have been widely used in portfolio optimisation. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is nondominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective function values. A model is proposed in which the aspiration points relate to ordered return outcomes of the portfolio return. The model is extended by additionally specifying reservation points, which act pre-emptively in the optimisation. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated

Cutting plane methods for general integer programming

Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method. In this method, linear constraints are added to the associated linear programming (LP) problem until an integer optimal solution is found. These constraints cut off part of the LP solution space but do not eliminate any feasible integer solution. In this report algorithms for solving IP due to Gomory and to Dantzig are presented. Two other cutting plane approaches and two extensions to Gomory's algorithm are also discussed. Although these methods are mathematically elegant they are known to have slow convergence and an explosive storage requirement. As a result cutting planes are generally not computationally successful

Computer assisted modelling of linear, integer and separable programming problems

For mathematical programming (MP) to have greater impact upon the decision making process, MP software systems must offer suitable support in terms of model communication and modelling techniques . In this paper modelling techniques that allow logical restrictions to be modelled in integer programming terms are described and their implications discussed. In addition it is demonstrated that many classes of non-linearities which are not variable separable may be reformulated in piecewise linear form. It is shown that analysis of bounds is necessary in the following three important contexts: model reduction, formulation of logical restrictions as 0-1 mixed integer programs and reformulation of nonlinear programs as variable separable programs, It is observed that as well as incorporating an interface between the modeller and the optimiser there is a need to make available to the modeller software facilities which support the modelling techniques described here

Star Scientists, Innovation and Regional and National Immigration

We follow the careers 1981-2004 of 5401 star scientists listed in ISI HighlyCitedSM as most highly cited by their peers. Their number in a US region or a top-25 science and technology (S&T) country significantly increases the probability of firm entry in the S&T field in which they are working. Stars rather than their disembodied discoveries are key for high-tech entry. Stars become more concentrated over time, moving disproportionately from areas with few peers in their discipline to many, except for a countercurrent of some foreign-born American stars returning home. High impact articles and university articles all tend to diffuse. America has 62 percent of the world’s stars as residents, primarily because of its research universities which produce them. Migration plays a significant role in some developing countries.

Local Academic Science Driving Organizational Change: The Adoption of Biotechnology by Japanese Firms

The local academic science base plays a dominant role in determining where and when biotechnology is adopted by existing firms or -- much more frequently -- exploited by new entrants in the U.S. In Japan this new dominant technology has almost exclusively been introduced through organizational change in existing firms. We show that for the U.S. and global pharmaceutical business -- biotechnology's most important application -- the performance enhancement associated with this organizational change is necessary for incumbent firms to remain competitive and, ultimately, to survive. Japan's sharply higher organizational change/new entry ratio compared to the U.S. during the biotech revolution is related to Japan's relatively compact geography and institutional differences between the higher-education and research funding systems, the venture capital and IPO markets, cultural characteristics and incentive systems which impact scientists' entrepreneurialism, and tort-liability exposures. Both local science base and pre-existing economic activity explained where and when Japanese firms adopted biotechnology, with the latter playing a somewhat larger role. De nova entry was determined similarly as if entry and organizational change are alternative ways of exploiting the scientific base with relative frequency reflecting underlying institutions. While similar processes are at work in Japan and America, stars in Japan induce entry or transformation of significantly fewer firms than in the U.S. and preexisting economic activity plays a greater role. We find no such significant difference for entry of keiretsu-member and nonmember firms within Japan.

Movement of Star Scientists and Engineers and High-Tech Firm Entry

This paper analyzes the effects of top nanoscale scientists on industry entry in the comparative context of 5 major areas of science and technology, extending the concept of star scientist to all areas of science and technology. The results for nanotechnology are replicated using the comprehensive list of firms from NanoBank.org that provide an alternative industry entry measure not available for other high-tech fields. We follow careers 1981-2004 for 5,401 stars as identified in ISIHighlyCited.comSM, using their publication history to locate them each year. The number of stars in a U.S. region or in one of the top-25 science and technology countries generally has a consistently significant and quantitatively large positive effect on the probability of firm entry in the same area of science and technology. Other measures of academic knowledge stocks have weaker and less consistent effects. Thus the stars themselves rather than their potentially disembodied discoveries play a key role in the formation or transformation of high-tech industries. We identify separate economic geography effects in poisson regressions for the 179 BEA-defined U.S. regions, but not for the 25 countries analysis. Stars become more concentrated over time, moving from areas with relatively few peers to those with many in their discipline. A counter-flow operating on the U.S. versus the other 24 countries is the tendency of foreign-born American stars to return to their homeland when it develops sufficient strength in their area of science and technology. In contrast high impact articles and university articles and patents all tend to diffuse, becoming more equally distributed over time.

Innovation, Competition and Welfare-Enhancing Monopoly

The basic competitive model with freely available technology is suited for static industries but misleading as applied to major innovative economies for which development of new technologies equals in magnitude around 10% of gross domestic investment. We distinguish free generic technology from proprietary technologies resulting from risky investment with uncertain outcome. The totality of possible outcomes drives the national innovation system and the returns to a particular successful technology cannot be compared to its own direct investment costs. Eureka moments are hardly ever self-enabling and incentives are required to motivate investment attempting to turn them into an innovation. The alternative to a valuable proprietary innovation is not the same innovation freely available but the unchanged generic technology. Growth is concentrated in any country at any time in a few firms in a few industries that are achieving metamorphic technological progress as a result of breakthrough innovations. So long as the entry and exit of firms using the generic technology sets the price in an industry, one or more price-taking firms can coexist with proprietary technologies yielding more or less substantial quasi-rents to the sunk development costs. Consumer welfare is increased if an innovator creates a proprietary technology such that the market equilibrium price is reduced and output increased. If the technological breakthrough is sufficiently large for the innovator to drive all generic producers out of the industry and increase output as a wealth-maximizing monopolist, consumer welfare is surely increased. After some time, the innovative technology will diffuse into an imitative generic technology. The best innovators develop a stream of innovations so that technological leaders can maintain their status as dominant firm or monopolist for extended periods of time despite lagged diffusion, and consumers benefit from this stream as well. The economics of an innovative nation are different from those of the no-growth stationary state which we teach and fall back on. We propose an ambitious agenda to integrate major research streams treating innovation as an object of economic analysis into our standard models.

Virtuous Circles of Productivity: Star Bioscientists and the Institutional Transformation of Industry

The most productive (`star') bioscientists possessed intellectual human capital of extraordinary scientific and pecuniary value for some 10-15 yrs after Cohen & Boyer's 1973 founding discovery for biotechnology. This extraordinary value was due to the union of still scarce knowledge of the new research techniques and genius to apply these techniques in valuable ways. As in other sciences, star bioscientists were particularly protective of their ideas in the early years of the revolution, tending to collaborate more within their own institution which slowed diffusion to other scientists. Therefore, close, bench-level working ties between stars and firm scientists were needed to accomplish commercialization of the breakthroughs. Where and when the star scientists were actively producing academic publications is a key determinant of where and when commercial firms began to use biotechnology. The extent of collaboration by a firm's scientists with stars is a powerful predictor of its success: for each 9 articles co-authored by an academic star and firm scientists about 3 more products in development, 1 more on the market and 1550 more employees are estimated. Such collaboration with firms, or employment, also results in significantly higher rates of citation to articles written with the firm. The U.S. scientific and economic infrastructure has been quite effective in fostering and commercializing the bioscientific revolution. To provide an indication of international competitiveness, we estimate stars' distribution, commercial involvement and migration across the top 10 countries in bioscience. These results let us inside the black box to see how scientific breakthroughs become economic growth and consider the implications for policy.