Background: The integration, besides synergy and convergence, is regarded as a leading orientation in modern logistics. The connection of various participants within supply chains enables the integration of actions and allows to fulfill growing customers' demands in an effective and economically efficient way.  In times of a concept of the balanced development, growing interest in utilization of recycled material, connected with possibilities to consolidate  logistic activities, can be observed. According to the scientific literature (integration models) as well as practical business cases, supply chains of forward and backward type (two-directional) are the area of logistics of the intensive development.   

Material and methods: The paper presents the Authors' model and methodology of modeling of the integration of supply chains, which realizes the flows of forward and backward type (two-directions). The empirical material was obtained during modeling and simulation of processes in the environment of iGrafx Process 2013 for Six Sigma with the support of Minitab 17 (for planning of experiments).  The method of the verification of statistical hypotheses was used. As a first step, the correlation between the level of the integration and the global service level for the supply chain was conducted using the method of Pearson's coefficient. The test of relevance of correlation coefficient was conducted by the use of t-distribution method. Then the verification of statistical hypotheses was made, based on the method using the Z-statistics.

Results: The obtained results indicate clearly the strong relationship between the level of the integration of a supply chain and the obtained service level (values of Pearson's correlation coefficient and results of t-test). The detailed statistical researches of authors indicate that the increased level of the integration leads to the increase of the average value of service level coefficient (results of Z-statistics). Concluded, the analyze of the service level indicator shows its growth together with the growth of the integration level.

Conclusions: Based of integration aims, the integrated systems should have bigger possibility of activity. The possibility to obtain higher customer service level is one of postulated effects ("gains") of the integration of supply chains.  The results of Authors' researches confirmed such statement in quantitative way, and not only in a describing one. The conclusions from conducted researches encourage to integration activities within supply chains of forward and backward type.