Competitive strategies: a cognitive choice model

A theory of competition between firms in heterogeneous markets is formulated using a psychological model of choice, the heteroscedastic form of the Thurstone random strength model. Market shares are defined in terms of random variables which portray individual variation in perceived utility. The analysis focuses on the relationship between market shares and utility variances. Besides the general theory of competition two special cases are analyzed, each of which can be identified without precise knowledge of the utility parameters. The conclusions tend to support conventional marketing wisdom but emphasize that the degree of dominance of the market leader is a significant factor in its competitive strategy. Short and long-run analyses of the model are presented, and it is shown that the best policy for a particular firm in the short run remains optimal in the presence of competitors' reactions, but it may no longer be effective. The paper concludes with some comments on statistical implementation.     

On additive and multiplicative damage models and the characterizations of linear and logarithmic exponential families

Rao (1963) has formulated a damage model which we call an additive damage model. A suitable damage model, which we call a multiplicative damage model, has been considered by Krishnaji (1970) for income-related problems. In these models, an original observation is subjected to damage, e.g., death or under-reporting, according to a specified probability law. Within the framework of an additive damage model, with a special form of damage, characterizations of the linear and logarithmic exponential families are formulated using regression properties of the damaged part on the undamaged part. The characterizations of the gamma and Pareto distributions that have been found of some use in the theory of income distributions, are obtained as special cases. Similar results are investigated within the framework of the multiplicative damage model.     

Allocation of research and development funds: A zero-one goal programming approach

The research and development project selection process is one of the most difficult and important problems faced by management. It is typically complicated by indivisibility of projects and multiple and conflicting objectives, in addition to limitations on funding, facilities, and qualified researchers. In this paper a case example involving a high technology electrical equipment manufacturer is developed to illustrate this problem using zero—one goal programming to accommodate indivisibility of projects in addition to multiple and conflicting goals. The model presented is an attempt to provide managers with a robust tool for allocating scarce resources among research and development projects.     

THE USE OF CORRELATION IN LARGE SAMPLES

The asymptotic relative efficiency of Kendall's and Spearman's coefficients of rank correlation are considered for samples from a bivariate normal distribution and comments are made on the calculation of their variances. For large samples it is suggested that one should use mean values of the coefficients calculated by splitting the sample into a fairly large number of smaller samples. This reduces the amount of calculation required and the asymptotic relative efficiency of this procedure is found both for ρ= 0 and ρ≠ 0.     

Output planning for material requirements under uncertainty

This paper considers a production planning and control system requiring that, for each work station, a time-phased series of input and output values be estimated. It is assumed that the projected input levels can vary significantly across time periods and that anticipated output levels can be determined by management, subject to limits specified by available manpower and subcontracting. The actual input and output levels for each period depart from the planned levels according to a probability distribution determined empirically. An approach is presented that allows management to evaluate a chosen set of output levels to determine the probability that sufficient amounts of work will be available at a work station each period.