Multi-agent single machine scheduling problem with transportation constraints

A multi-agent single machine scheduling problem with transportation constraints is studied. we assume that there are several independent agents placed in different geographical locations, each of them has several orders and each order includes different types of products. we use a simple and effective model to obtain maximum profit of the products. to have desired on-time deliveries, the minimization of the transportation costs and total tardiness costs are considered as objective functions. the main idea of this research is to develop a simple and integrated scheduling and transportation model which can be applied in many factories, chain stores, and so on. in order to solve this problem, a mixed integer linear programming (milp) model is presented. moreover, since solving large instances of the proposed milp model is very time-consuming, a heuristic algorithm is presented. implementing of two approaches on a variety of datasets show that the heuristic algorithm can provide good-quality solutions in very short time.