The general optimal market area model

Market area models determine the optimal size of market for a facility. These models are grounded in classical location theory, and express the fundamental tradeoff between economies-of-scale from larger facilities and the higher costs of transport to more distant markets. The simpler market area models have been discovered and rediscovered, and applied and reapplied, in a number of different settings. We review the development and use of market area models, and formulate a General Optimal Market Area model that accommodates both economies-of-scale in facilities costs and economies-of-distance in transport costs as well as different market shapes and distance norms. Simple expressions are derived for both optimal market size and optimal average cost, and also the sensitivity of average cost to a non-optimal choice of size. The market area model is used to explore the implications of some recently proposed distance measures and to approximate a large discrete location model, and an extension to price-sensitive demands is provided.