Optimization of Crude Oil Transportation by Using the Bin Packing Problem

In recent years, many papers 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 (BPP). One of the most widely used of these basic models is BPP, the use of which is increasing in various modeling. In this paper, while introducing a new generalization of the BPP called the developed VCSBPP, a "decision to transport crude oil by different modes of transport" problem is interpreted and modeled by the BPP for the first time. The proposed mathematical model has two objectives and answers the question of which method or combination of methods is used to transfer crude oil from the existing methods in order to reduce the risk in addition to the costs. Transportation methods are defined based on five criteria: "capacity", "coordination cost", "set-up cost", "transportation cost" and "risk cost". Because based on the literature, 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 goal programing 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 (MID), diversification, and time metrics.