Positioning and Pricing a Product Line

Abstract

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). We 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. While additional real world complexities, e.g., uncertainty about customer wants, product performance, and competitive response, are not modeled, we believe the system developed can serve as an important input into the decision process when new products are designed and priced. The methodology can be used as a part of a decision support system, where management specifies the number of products desired. The system suggests a few good solutions, together with the prices and customer segments served by each product. We use the standard assumption that the market is composed of different customer segments of various sizes, each containing homogeneous customers. Customers choose one brand only, the one that provides them with maximum value for the money. The firm faces both fixed and variable production and marketing costs for each product. Competition is either nonexistent, or assumed not to respond to the firm's moves. The information available to the firm is the sizes and preferences of the segments, based on a sample of customers, and the cost data. As an alternative to the traditional approach of estimating a parametric utility function, and aggregating customers into segments, we can also use the raw data as input, where each customer in the sample represents a segment. This, we believe, allows us to reduce the errors introduced in the process. 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. We also discuss the application of the procedure to a ‘real life' sized problem.product line, product positioning pricing, decision support, heuristics

Product Line Design and Production Technology

“…In a product line design setting, Dobson and Kalish (1988) consider product-specific variable and fixed costs. However, the model is static (so inventory is not modeled) and these costs are independent of other decision variables and demand volume.…”

“…Even with these simplifications their formulation leads to a complex mixed-integer program that must be solved numerically. While the goal in Dobson and Kalish (1988) is to develop solution methodology for practically sized problems, we limit the size of the problem to obtain analytical solutions that lend themselves to analysis and interpretations.…”

A Demand Estimation Procedure for Retail Assortment Optimization with Results from Implementations

“…Krieger (1987a,b, 1992), McBride and Zufryden (1988), Dobson and Kalish (1988) and Kohli and Sukumar (1990) extend this line of research. Belloni et al (2008) compare the performance of different heuristics for product line design and find that the greedy and the greedy-interchange heuristics perform extremely well.…”

Approximating the Revenue Maximization Problem with Sharp Demands

“…As several papers on this topic (see for instance [12,22,17,7,15]), we assume that, by means of market research or interaction with the consumers, the seller knows each customer's valuation for each item.…”

“…Pricing problems have been intensively studied in the literature, see e.g., [26,27,21,20,25,1,18] just to cite a few, both in the case in which the consumers' preferences are unknown (mechanism design [29,5]) and in the case of full information that we consider in this paper. In fact, our interest here is in maximizing the seller's profit assuming that consumers' preferences are gathered through market research or conjoint analysis [12,22,17,7,15]. From an algorithmic point of view, [17] is the first paper dealing with the problem of computing the envy-free pricing of maximum revenue.…”