Mathematical models for ordering complex assemblies (called outsourcing) are analyzed based on collaborations and relationships among agents. This paper deals with the analysis of factors affecting changes in formations of outsourcing among firms by using mathematical modeling. We assume that firms face credit constraints and supports by another outside agent with a certain cost of labor usage in productions. Then, we indicate that the wealth of firm agent bears chaotic fluctuation depending on the rate of collaboration among agents. The model is extended to multi-agent systems where the relations of collaboration is represented by a network. And, it is found that due to the firm agents' behaviors seeking cheaper labor prices induce a fluctuation in wealth process. Furthermore, by considering the deterministic decision on pricing, we utilize the control (suppression) scheme for the fluctuations.