MODELING OF OPTIMAL CREDIT STRATEGY OF A PHARMACEUTICAL PRODUCT DISTRIBUTOR WITH DELAY

The activities of pharmaceutical products distribution companies are multifaceted. They establish contacts with producers and consumers, determine the range of prices of medicines, do promotions, hold stocks of pharmaceuticals and take risks in their further selling. Therefore, the usage of mathematical models to research into ways of optimizing the management of pharmaceutical products distribution companies considering payments is of great current interest. The purpose of the paper is to present a model of optimal credit strategy of a distribution company on the pharmaceutical products market considering late delivery. In the mathematical terms, the given problem is the one of optimal control, where a number of pharmaceutical products act as a phase trajectory and the amount of credit granted to a distribution company is a control. To tackle the problem sufficient optimality conditions are used. It is established that the model of optimal credit strategy of a distributor with the delay has two modes of crediting (full and no credit) and the optimal mode. The structure of the optimal process for the given model is also described.