grouping constraint

An integrated optimization framework, including location assignment under grouping class-based storage policy and schedule of dual shuttle cranes, is offered by presenting a new optimization programming model. The objective functions, which are considered at this level, are the minimization of total costs and energy consumption. Scheduling of dual shuttle cranes among specified locations, which were determined in the upper-level, is conducted in the lower-level by considering time windows and balance constraints under multi-period planning conditions. A modified nested differential evolution-based algorithm is introduced to solve the proposed model because it is an Np-hard bi-level bi-objective optimization model. Eventually, with the intention of illustrating the validation of the presented optimization model and solution methodology, various numerical experiments are tailored, and different comparative numerical examples are provided based on two current algorithms in the literature. Sensitivity analyses illustrate that grouping class-based storage policy could be rendered superior planning of operations in both levels of the investigated problem.