Complexity and approximation for scheduling problem for a torpedo

This paper considers a special case of the coupled‐tasks scheduling problem on monoprocessor. The general problems were analyzed in depth by Orman and Potts (1997). In this paper, we consider that all processing times are equal to 1, the gap has exact length L, we have precedence constraints, incompatibility constraints are introduced and the criterion is to minimize the scheduling length. We use this problem to study the problem of data acquisition and data treatment of a torpedo under the water. We show that this problem is NP‐complete and we propose an ρ‐approximation algorithm where $\rho \le \frac{(L+6)}{6}‐\frac{1}{2(L+2)}+\frac{(L+3)}{6n(L+2)}$ .