Models for collective decision making in industry

When actions are taken by individual managers within a firm to enhance certain performance criteria they may be found to have an adverse effect on other criteria. Changes in pricing policies and promotional activity, modifications in product design, increased mechanisation of production processes or operations, etc., are just examples of actions which in general do not have equally desirable consequences on the most commonly pursued objectives within the company, such as that of reducing unit costs, or those of increasing turnover, market share, profit levels and return on capital employed.In this paper simple models are developed and analysed, each enabling the user to assess explicitly the effects on the unit cost; the revenue and the profit of combined changes imposed on the system by management decisions or by external factors. It is suggested that these models be used as a basis for discussion by the managers involved with a view to reaching a consensus as to the desirable decisions that should be taken.     

To charge or not to charge?

Discussions on the success or failure of OR practice tend to focus on specific case studies which often highlight major dilemmas that face OR professionals: Model robustness, simplicity vs complexity, optimising vs satisficing, conflict between criteria, who is the ‘client’?, and so on. But above all, the following issues predominate: Should OR be concerned with tactical or strategic problems? Where should it be placed in the organisational structure and who should it report to? These issues inevitably raise the questions of accountability, coupled with that of charging for OR services. It is this issue in particular, whether to charge or not to charge for OR services, that the paper seeks to explore.     

Models for use in Negotiations on Pay and Working Conditions

In this paper we develop three inter-related models, based on value added concepts, that can form the starting point for discussions on pay and working conditions at the plant level. The first model considers the factors that contribute to an increase in the added value (such as prices, sales volume and material productivity) and provides a relationship between relative changes in the values of these factors and the resulting relative change in the added value. In the second model the increase in the added value is assumed to be shared between the labourforce (through increased wages) and the management (who require funds to cover all other costs and make provision for profit); the relative change in wages is decomposed further to take into consideration the effect on the average employee's pay of possible changes in the labour productivity and/or the size of the workforce. The two models are then combined to produce the third model with a view to rewarding labour and management in proportion to each one's contribution towards improving the operational efficiency of the plant.All three models are simple and versatile enough to allow:

1. a)
   The use of alternative assumptions and functional relationships to reflect differing views of the negotiators;
    
2. b)
   sensitivity analyses to identify the most crucial assumptions and estimates that are likely to affect the results; and
    
3. c)
   further disaggregation to incorporate additional variables and a more detailed breakdown of the added value, wage rates or working hours, if this is thought to be desirable.
    

It is recommended that such models be developed, discussed and analysed by the negotiators themselves in an attempt to make them highlight the issues, arguments and important characteristics pertaining in each individual case. The models could then provide the basis of a common communication language leading to a better understanding of each other's position and, hopefully, to less conflict.     

The Role of Management Science

Many of the arguments that are found in the literature on the theme "O.R./M.S. in crisis" stem not just from alternative definitions of O.R./M.S., but from differences in strongly held views about its scope and role in organisations, and these are then reflected in the vehemence with which certain definitions are defended or criticised. It is when the hopes and aspirations of O.R./M.S. are compared with what is being achieved in practice, that we realise the degree to which O.R./M.S. has failed to live up to its original promise. In most organisations, O.R. analysts are expected and are happy to act as technicians and not as advisers, so that technique orientation and concern with tactical problems are constantly reinforced. In addition, managers in various functions have become aware of the potential contribution of analytical modelling in their own spheres and have begun to recruit analysts direct, resulting in the possible fragmentation of O.R. and the loss of its unique identity. The responsibilities of O.R./M.S. obviously relate not only to its organisational status, but also to an examination of and an identification with organisational goals. Many O.R. analysts are plainly more comfortable when these goals are clearly defined for them, an attitude which people from other professions will readily endorse, but if O.R./M.S. has any aspirations to get involved in strategic problems, it will have to pose questions about the validity and appropriateness of organisational goals and try to influence the formulation of problems accordingly.     

Towards molecular computers that operate in a biological environment

Even though electronic computers are the only computer species we are accustomed to, the mathematical notion of a programmable computer has nothing to do with electronics. In fact, Alan Turing’s notional computer [L.M. Turing, On computable numbers, with an application to the entcheidungsproblem, Proc. Lond. Math. Soc. 42 (1936) 230-265], which marked in 1936 the birth of modern computer science and still stands at its heart, has greater similarity to natural biomolecular machines such as the ribosome and polymerases than to electronic computers. This similarity led to the investigation of DNA-based computers [C.H. Bennett, The thermodynamics of computation — Review, Int. J. Theoret. Phys. 21 (1982) 905-940; A.M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024]. Although parallelism, sequence specific hybridization and storage capacity, inherent to DNA and RNA molecules, can be exploited in molecular computers to solve complex mathematical problems [Q. Ouyang, et al., DNA solution of the maximal clique problem, Science 278 (1997) 446-449; R.J. Lipton, DNA solution of hard computational problems, Science 268 (1995) 542-545; R.S. Braich, et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Science 296 (2002) 499-502; Liu Q., et al., DNA computing on surfaces, Nature 403 (2000) 175-179; D. Faulhammer, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci. USA 97 (2000) 1385-1389; C. Mao, et al., Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature 407 (2000) 493-496; A.J. Ruben, et al., The past, present and future of molecular computing, Nat. Rev. Mol. Cell. Biol. 1 (2000) 69-72], we believe that the more significant potential of molecular computers lies in their ability to interact directly with a biochemical environment such as the bloodstream and living cells. From this perspective, even simple molecular computations may have important consequences when performed in a proper context. We envision that molecular computers that operate in a biological environment can be the basis of “smart drugs”, which are potent drugs that activate only if certain environmental conditions hold. These conditions could include abnormalities in the molecular composition of the biological environment that are indicative of a particular disease. Here we review the research direction that set this vision and attempts to realize it.     

Quitting games – An example

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r _S ⁱ, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon. Received: October 2001     

A model with a measurable which does not carry a normal measure

We construct a model of ZF in which there is a measurable cardinal but there is no normal ultrafilter over it.