We deal here with the Linear Arrangement Problem (LAP) on interval graphs, any interval graph being given here together with its representation as the intersection graph of some collection of intervals, and so with related precedence and inclusion relations. We first propose a lower bound LB, which happens to be tight in the case of unit interval graphs. Next, we introduce the restriction PCLAP of LAP which is obtained by requiring any feasible solution of LAP to be consistent with the precedence relation, and prove that PCLAP can be solved in polynomial time. Finally, we show both theoretically and experimentally that PCLAP solutions are a good approximation for LAP on interval graphs. Mathematics Subject Classification. 90C27.