Inventory Management in Supply Chains Based on a Linear Discrete System with a Quadratic Quality Criterion

Purpose of research. To analyze theoretical studies of models and methods used in the theory of inventory management and directions of their practical implementation. To present the problem of optimal inventory management as a discrete control problem. Tasks of this type are formulated in cases where there is a need to form strategies of management of material and production inventories in supply chains, taking into account their organization at a certain time interval. To propose a method for solving the corresponding management problem.

Methods. As a basic model, we consider the process of inventory management in the warehouse, in which a certain balance between the products released from the warehouse into production, released for sale, as well as its residues, which form the inventory of the next period must be fulfilled. The process of inventory management in supply chains during the planning period is based on the procedure of finding the appropriate control action for a linear discrete controlled system with a quadratic quality index. Implementation of control uses the principle of feedback. The computer algebra system Wolfram Mathematica is chosen as a tool for implementing the control.

Results. Within the framework of studying the methods of finding the optimal control, two solution methods were singled out - the method of finding the optimal program control and the method of determining the optimal control according to the feedback principle. In the process of verification of the obtained solution, several model examples with different initial conditions were considered.

Conclusion. The results of testing the proposed discrete model showed that the feedback method makes it possible to quite efficiently solve the inventory management problem with different initial conditions, which is described by a system of difference equations.

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