This paper considered the multi-product multi-level multi-period capacitated lot-sizing and sequencing problem with setup carry-over and sequence-dependent family setup times and costs. A formulation of the problem was provided as a mixed-integer nonlinear programming model. To propose this formulation, first, the mixed-integer nonlinear of the problem was linearized and then it was converted to a mixed-integer linear program. To solve large-size instances of the problem, first, a lower bound was provided. The results confirmed the efficiency of the proposed model compared to previous models in terms of the runtime and the number of defined variables and constraints. Since multi-level, multi-period and multi-item capacitated lot-sizing problem is NP-hard and adding other factors such as family setups, setup carry over and sequence-dependent setups increases its complexity, in this paper, a genetic algorithm was applied in large-size dimensions and its results were compared with the proposed lower bound. The numerical results showed that there is no significant difference between the results of the proposed genetic algorithm and lower bound, and, so, the genetic algorithm had been able to approach the optimal solution.
