Crowd behaviour is difficult to predict and might not be easy to translate. A number of mathematical and psychological models are proposed in the literature to investigate crowd behaviour. In this paper, we exploit mixed integer programming to model crowd behaviour with multiple time periods. This research improves upon methods by Breer et al. (2015) for determining the number of active agents and solving the problem of reducing this number by controlling reputations in a single period, under the added assumption of a reputation model of interactions (Granovetter, 1978). Thus, this paper goes on to extend the single period reputation control problem and solution to the case of multiple time periods. This class of problems requires a mixed integer program to be solved several times with a varying constraint and a varying number of variables. This model is then supported by a promising case study of queue management at airport security gates.