Modeling Co-optimization of an Enterprise’s Production Capacity, Retail Sale and Advertising

The work deals with the development of one of the methods for simulating the logistics system of an enterprise. The aim of the article is using the approach developed by J. Forrester to build a simulation model, based on which it is possible to perform mathematical co-optimization of the production capacity, retail sale and advertising of an enterprise which produces a single product. The paper formulates a system of equations describing the logistics system of the enterprise. The model of logistical system offered by authors is original. This model has no analogues in the scientific literature. Article purpose is working out of a technique of the co-ordinated definition of optimum parametres of logistical system. Article develops a numerical method of the decision of an optimising problem which is based on system of the equations written down in shape with discrete time. The calculations of the time behavior of all rates of the logistics system (rate of production, rate of delivery), as well as the behavior of the inventory levels at the wholesale warehouse and retail are carried out. The optimization problem of determining the maximum economic efficiency is formulated and solved. In this case, production capacity and advertising costs are considered as variable parameters of the optimization problem. By numerical calculations, it is proved that there is a single point of maximum economic efficiency as a function of the planned capacity of the enterprise. Dependence on time of current profit of the enterprise is calculated and analysed.