Partial enumeration (PE) is presented as a method for treating large, linear model predictive control applications that are out of reach with available MPC methods. PE uses both a table storage method and online optimization to achieve this goal. Versions of PE are shown to be closed-loop stable. PE is applied to an industrial example with more than 250 states, 32 inputs, and a 25-sample control horizon. The performance is less than 0.01% suboptimal, with average speedup factors in the range of 80-220, and worst-case speedups in the range of 4.9-39.2, compared to an existing MPC method. Small tables with only 25-200 entries were used to obtain this performance, while full enumeration is intractable for this example. (c) 2007 Elsevier Ltd. All rights reserved.