Rapidly changing business environment requires new approaches and methods for supporting management systems in all types of companies. Modern companies doing business use e-commerce systems by default. One of the key areas of e-commerce systems is logistics and the supply chain. The optimal way to ensure the success of logistics and supply chains is to use the methods of modeling and simulation based on appropriate models and especially its mathematical representation. In this paper, authors highlight the customer-oriented model of the e-commerce system and deal with logistic optimization and simulations. As an example, a sample logistic structure which requires the adequate control approach is presented. This is realized by means of heuristic algorithms which are responsible for meeting the set criterion. Moreover, the criteria to either maximize the production output or minimize the lost flow capacity of the logistic system or minimize the tool replacement criterion are introduced. Equations of state are given in order to represent the flow of material through the logistic system.