Complexity and approximation for scheduling problem for a torpedo

► Special case of the coupled-tasks scheduling problem on mono-processor. ► All processing times are equal to 1, and the gap has exact length L. ► Introduction of incompatibility constraints, and precedence constraints with treatment tasks. ► This problem is NP-complete and we propose an ρ-approximation algorithm where ρ⩽(L+6)6-12(L+2)+(L+3)6n(L+2).