Construction of mathematical models of controlled supply chains considering flows delays

Abstract

The problem of construction of mathematical models of controlled supply chains under the condition of an uncertain external demand with the presence of restrictions on the state and control, as well as transport delays, is considered. Using the model of the discrete delay a discrete model of supply chains with the controlled flows delays is received. On the basis of that model the "expanded" model without delays and a "moment" model, where the delay is equal to zero, are built. The proposed approach makes it possible to formulate the task of checking the conditions of existence and the task of forming the strategy of the inventory control in the supply chain, which guarantees the full and timely satisfaction of the external demand as a linear programming task. The first of them is solved in off-line mode before starting the process of control, and the second one is solved in on-line mode for each discrete instant of time. As an example, a problem of the analysis and synthesis of strategy of supplies control is consider for a three-tier supply chain, containing five knots.