عنوان مقاله [English]
In recent years, many studies have been presented on the interpretation and modeling of new problems by basic models. One of the most widely used of these basic models is the Bin packing problem. Over time, the importance and power of this issue in modeling new problems becomes clearer. This paper also attempts to interpret and model ``An Ordering and assigning orders to supplier's
problem'' by using one of the generalizations of the bin packing problem. There are many generalizations about the bin packing problem. In this paper, for the first time, generalization of the bin packaging problem called "developed Variable size and cost bin packing problem" is modeled, which increases the flexibility of the model in solving current problems. Because the presented model is a bi-objective nonlinear programming type and NP-hard one to be solved in a reasonable time, a well-known multi-objective evolutionary algorithm, namely a Non-dominated Sorting Genetic Algorithm (NSGA-II), is proposed. To verify the obtained solution and evaluate the performance of the NSGA-II, the $rm varepsilon$-constraint method is developed in solving small-sized problems. In large-sized problems, the test problems are solved by the proposed NSGA-II. Then, the Pareto-optimal solutions are evaluated by mean ideal distance, diversification, and time metrics.