Over the past decades, a large number of methods have been developed to solve the urban problem associated with the distribution of goods. These solutions usually supplement or completely change the urban freight system. However, there is a problem associated with the evaluation of the proposed solution, since in the most of cases, the solution found had no analogues in the past and, accordingly, there is no real experience of their use. This fact makes it weaker to evaluate the results of applying the solution in real life, since in a multidimensional environment, together with the multi-parameter character of logistic assessments, its application can lead to negative results, in particular, if not all aspects have been carefully taken into account. To avoid such situations, it is proposed to use modelling as a tool for evaluating the proposed solution before applying it as well as sup-porting the decision-making process. Various models were developed to derive the way of logistic evaluation and they can be grouped in different ways, mostly according to the goals they fulfil. For example, Hicks grouped the models based on their profitability into simulation models, optimization models and simulation-optimization models [8]. And Taniguchi, in turn, categorized them in optimization models and simulation models [9].
Optimization processes are connected with the search for the best solution from a variety of alternative options in accordance with the goals to be achieved. For instance, such
a model has been used to find solutions for the problems of the minimization of total costs [10]. The aim of the simulation models is the replication of a working system for a total and profound understanding of processes. Then after the correction and validation, a model can be used as a testing tool for various scenarios as well as verification of opti-mization. Often, simulation models replace optimization since they can be interpreted as so-called ”test machines” that by trial and error try out all possible scenarios and choose the best from them. According to the [9] simulation methods can be grouped in system dynamics, multi-agent systems and traffic simulation [11].
In this research, various simulation models are considered, and their implementation is illustrated by using a real case.
2 BACKGROUND
2.1 Systems dynamics
System dynamics is a simulation modelling approach which focuses on the internal struc-ture and feastruc-tures of the system [11]. Originally it was developed in the 1950s as a tool for corporate managers which helps them better understand industrial processes. The be-ginning of the field of the system dynamics is associated with the development of hand simulations of the stock-flow-feedback structure of the General Electric plants. Based on the results obtained by hand calculations J. W. Forrester showed that the instability of the company employment was caused by internal processes of the company and not by exter-nal forces as it was initially supposed. Further, the process of simulation was modernized into the computer modelling which entailed the appearance of computer languages for such kind of modelling. Moreover, the fields of application of the system dynamics ap-proach were increased to the modelling of world dynamics and urban dynamics [12].
The examples of such modelling are the models of the world socio-economic system WORLD1, WORLD2 and WORLD3, each of which is an improved version of the previ-ous [12]. The last one was originally created by D. Meadows, who was one of the Jay W.
Forrester’s former PhD students, in collaboration with his associates and it was published in [13]. The purpose of the WORLD3 model is to identify which kind of the behaviour modes is the most characteristic of the population of the globe and material’s outputs un-der different conditions and to determine such policies which rather may lead to a stable behaviour mode. Considered in the modelling time parameters start from 1900 and cover two centuries. The period 1900-1970 is used as a test of the reliability of the model by comparing its behaviour with real historical trends. The model consists of five interacting sectors (capital, nonrenewable resources, agriculture, pollution, population) and it is pre-sented as a set of equations which are formulated in a format of the simulation language DYNAMO [14].
The main goal of the system dynamics is to consider complex real-world systems as a set of special ”building blocks”, for better understanding the system behaviour over time and use this knowledge to design and implement more efficient policy [12].
In terms of system dynamics, systems can be divided into the ”open” and ”closed”. The outputs of the ”open” systems respond to the inputs but don’t influence them. In the sys-tems of the second type they do both and such kind of syssys-tems is more common in the real world. The main ”building blocks” of system dynamics are stocks and flows, which can be outflows and inflows. One of the key task for modelling is to identify what are stocks and what are flows in the system. Stocks have four main characteristics which determine
the system behaviour. They have a memory, change the time shape of flows, decouple flows and create delays. The last property, in some sense, the interpretation of the fact that in real life, events do not occur instantly and there is often a gap between cause and effect. Fairly often the stocks and flows are the part of the of another ”building blocks” -feedback loops. The -feedback loops, which control closed systems, can be of two types:
positive and negative. In positive loops, some actions create the result which in its turn generates more actions which continue to provide more results. Thus, positive loops make a system unstable and force it to leave the current state. And negative loop has opposite effect, which force system to move toward or to keep at some state, stabilizing the system or, in some cases destabilizing and cause it to oscillate [12]. For the representation of the dynamics casual loop diagrams and stock-and-flow diagrams are often used [15].