CONSISTENT AND INCONSISTENT RULES IN COMPETITIVE FACILITY CHOICE

Competitive facility location models are based on the assumption that customers select a facility to patronize according to some rule involv ing the distance to the facility. A customer prefers facility A over f acility B if the distance to facility A is shorter than some function of the distance to facility B. We define a consistency property of a s election rule. A selection rule is consistent if the selection of a fa cility remains unchanged along the shortest route to that facility: na mely the rule cannot indicate a preference for a different facility wh ile en route to the selected one. Otherwise, the rule is inconsistent. We prove that under mild conditions, the only consistent rule is the one based on an additive function of the distance, a function which is the sum of the distance and a constant. All other rules, such as a pr oduct of the distance and a constant (a multiplicative function), are inconsistent.