On the convexity of step out–step in sequencing games

The main result of this paper is the convexity of step out-step in (SoSi) sequencing games, a class of relaxed sequencing games first analyzed by Musegaas et al. (Eur J Oper Res 246:894-906, 2015). The proof makes use of a polynomial time algorithm determining the value and an optimal processing order for an arbitrary coalition in a SoSi sequencing game. In particular, we use that in determining an optimal processing order of a coalition, the algorithm can start from the optimal processing order found for any subcoalition of smaller size and thus all information on such an optimal processing order can be used.