Optimal list order under partial memory constraints

Abstract

Suppose that we are given a set of n elements which are to be arranged in some order. At each unit of time a request is made to retrieve one of these elements — the ith being requested with probability Pi. We show that the rule which always moves the requested element one closer to the front of the line minimizes the average position of the element requested among a wide class of rules for all probability vectors of the form P 1 = p, P 2= · ·· = Pn = (1 – p)/(n − 1). We also consider the above problem when the decision-maker is allowed to utilize such rules as ‘only make a change if the same element has been requested k times in a row', and show that as k approaches infinity we can do as well as if we knew the values of the Pi.