Computational Principles of Choicegroup Generation for Selective Menus

A computational procedure is presented to explore and formulate the quantitative relations between the preference distribution of a population for menu items and a corresponding set of optimum choice-groups on a selective menu schedule. The investigation is limited to the decision rules applicable for the determination of a single choice group, and it is carried out in two stages. First, it is shown that for any preference matrix a unique process of choicegroup augmentation exists with the properties that the augmented choicegroup will provide a maximum increase in population preferences along with the probability estimates of selections. Second, it is shown that if the preference matrix is updated in the function of time and predicted selections, a multistage process of chociegroup generation can determine a sequence of choicegroups with optimal properties of concerning the size or preference contribution involved. A computer program which operates on these principles is attached, and is used for column generating functions of constrained optimization models of selective menu scheduling.