modelling integrated multi-item supplier selection with shipping frequencies

there are many benefits for coordination of multiple suppliers when single supplier cannot satisfy buyer demands.  in addition, buyer needs to purchase multiple items in a real supply chain. so, a model that satisfies these requests has many advantages. we extend the existing approaches in the literature that assume all suppliers need to be put on a common replenishment cycle and each supplier delivers exactly once in a cycle. more specifically, inspired by approaches that perform well for the economic lot scheduling problem, we assume an integer number of times a supplier can ship available items in an overall replenishment cycle. because of complexity issue, a new approach based on genetic algorithm is employed to solve the presented model. results depict that new model is more beneficial and practical.