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A formulation of the traveling salesman problem with more than one salesman is offered. The particular formulation has computational advantages over other formulations. Experience is obtained with an exact branch and bound algorithm employing both upper and lower bounds (mean run time for 55 city problems is one minute). Due to the special formulation, certain subtours may satisfy the constraints, thus reducing the search. A very good initial tour and upper bound are employed. The determination of these as well as the pathology of the formulation and the algorithm are discussed. No increase in computation time over the one-salesman case is experienced.

A review of the literature from many disciplines reveals conceptual agreement that individuals choose among alternatives by comparing the attributes of the alternatives in a sequential process. Yet in almost all the published empirical work the model used is a simultaneous compensatory model such as regression, logit, or probit. The sequential choice modeling approach has been severely retarded by the lack of an algorithm to generate the sample statistics projectable to hold-out samples and populations. This paper attempts to fill this void by presenting a prototype aggregate hierarchical model, called HIARC, for analyzing individual choice decisions. HIARC can be viewed as a semi-order lexicographic model that empirically estimates a set of tolerances directly from the data. HIARC and logit are applied to the same empirical data set. While the predictive accuracy is about equal, the two approaches yield different types of diagnostic information and the set of individuals whose choice is correctly predicted by one method is substantially different from the set correctly predicted by the other method.marketing, marketing: buyer behavior, decision analysis: sequential

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