Purpose. In the paper the question of the development of a methodological approach to the determination of logistics systems’ performance and grounding of the most effective goods’ delivery schemes, based on the theory of functions and sets of multiple objects, vector optimization approaches and discrete maximum principle for multi-stage processes (phase method) is considered. Methodology. To achieve the goals of the research, the model of logistic system represented by multiple object that defined by the structure and content. The object is represented by hybrid superposition, composed of sets, multi-sets, ordered sets (lists) and inhomogeneous sets (sequences, corteges), which at each stage of cargo delivery present sets of technological operations of their processing, choices and decisions algorithms. Multiple structure of objects is constructive three, consisting of the carrier, signatures and axiomatic. To determine the effective scheme of delivery, applied discrete maximum principle using vector optimization criterion. Findings. In this article, logistics system of delivery is presented in the form of a multi-stage (phase) of the process. Each stage reviews a plurality of discrete activities sets, which includes the possible technology cycles of operations in goods handling. At each stage of a multi-phase delivery process from the supplier to the consumer, these sets are different. Considered a model example solving the problem of vector optimization options for delivery of goods by the road in the international logistics system for the five-step process. Optimization performed on the basis of three indicators. Originality. In this paper, the choice of the most effective way of delivery goods produced using the theory of functions and sets of multiple objects, using the discrete maximum principle for multi-stage processes, based on the vector optimization criterion. At each of its stages are formed a plurality of valid solutions as discrete sets of technological cargo handling operations cycles. Practical value. The proposed approach to the modeling of logistic delivery goods systems on the basis of the theory of functions and sets of multiple objects, vector optimization approaches and discrete maximum principle for multi-stage processes (phase method) makes it possible to assess the efficiency of delivery in logistic system’s modeling. The choose the most effective delivery option, based on vector optimization criterion become more possible.