a new bi-objective integrated vehicle transportation model considering simultaneous pick-up and split delivery

Nowadays, global competition causes that the companies are dealing with the issue of cost reduction besides increasing productivity in business network more than ever. because of that, today, both researchers and industrial practitioners are focusing on the supply chain network issues. in order to achieve the real word objectives, we attempt to improve the efficiency of a supply chain via not only considering simultaneous pick up and split delivery but also minimizing the total costs and maximizing the customer service in the form of multi-products and multi-period. in addition, to accumulate the data of parameters, a case study in a food industry in the north of iran has been utilized. eventually, the proposed mixed-integer linear programming model is addressed by a ε-constraint approach. finally, related results of this solution are analyzed and also is compared with simple vrp.