Positioning and pricing a product line

A central problem in marketing is: how should the firm position (reposition) and price a line of related (substitute) products in order to maximize profits (or welfare). The authors formulate this problem faced by a monopolist as a mathematical program, outline how to obtain the market data from a sample of customers, discuss what cost data are relevant, and suggest a heuristic algorithm to solve the problem. The output of the process is a list of products to offer, their prices, and the customer segments which purchase each product. Heuristics for solving the problem are suggested. The heuristics are evaluated on a set of simulated problems, and compared to the optimal solutions. The heuristics perform well when compared to all feasible solutions on a set of small simulated problems. The authors also discuss the application of the procedure to a ‘real life’ sized problem.