Brand Switching and Mathematical Programming in Market Expansion

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Abstract
In a number of industries, product is sold through individual outlets under control of a company through lease or franchise. If these individual outlets are independent, in that sales in one have no influence on another, then the decision to add or subtract an outlet in a marketing area rests solely on investment and cost considerations. If, on the other hand, one outlet has an influence on another in terms of sales, then the decision to expand must take this influence into account. This paper suggests a method for planning expansion systematically and consistently when this influence, which is called market share, is present. The approach taken is that of mathematical programming where the objective function is nonlinear. The solution suggested here is one of iteration which has worked well for problems studied by the authors. A theoretical model, based on brand switching, is validated by experimental evidence and these results are then employed in the development of a long-term planning model.

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