The combinatorial assignment problem involves allocating a set of objects with integral capacity to a set of agents with qualitative preferences over bundles of objects; the application we explore in this paper is course allocation to students. We investigate how to computationally implement an approach to this problem which uses approximate competitive equilibria to balance notions of ef?ciency, fairness, and incentives; participants are en- dowed with budgets of “funny money” and anonymous prices are set on objects. This is similar to the winner determination problem in combinatorial auctions (WDCA), except there is no numeraire with which to compare individual utilities, since the currency here has no value after the assignment. Despite the similarities between the problems, we show that the mixed integer programming (MIP) approach used in clearing WDCA cannot be tractably represented in this new context. We present a solution that uses tabu search to guide price determination, and MIPs to solve individual demand problems in parallel at each iteration. Our approach is the first to effectively clear large-scale markets of this kind in practice. Joint work with Eric Budish (HBS/Chicago Booth) and Tuomas Sandholm.