AbstractThe capacitated p‐median problem is the variation of the well‐known p‐median problem in which a demand is associated to each user, a capacity is associated to each candidate median, and the total demand of the users associated to the same median must not exceed its capacity. We present a branch‐and‐price algorithm, that exploits column generation, heuristics and branch‐and‐bound to compute optimal solutions. We compare our branch‐and‐price algorithm with other methods proposed so far, and we present computational results both on test instances taken from the literature and on random instances with different values of the ratio between the number of medians and the number of users. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 45(3), 125–142 2005