Scenario for applying the duality theory when planning production in the industry

The task of drawing up an optimal production plan for an enterprise with limited resources and problem solution of bridging production bottlenecks for only one enterprise are of limited interest. New technical capabilities due to the volume and speed of data transmission and processing, allow you to solve new problems in which the apparatus of the duality theory can be fully used.

The authors consider the problem of planning the optimal production company (firm, industry, ministry) volume, which structurally has a certain coordinating (managing) center and a network of enterprises (branches), which can be located in different regions, and are not connected with each other. Each of the branches has its own technological matrix of resource costs for output, resource reserves, expected profit from the sale of each type of product unit.

An iterative algorithm for finding production plans for each of the enterprises is proposed, when implementing which the total profit of the company can be increased. The Center finds the optimal production plan for each of the enterprises according to this algorithm and using the classical formula of the optimal production planning problem. Further, for each of them, the Center, solving the problem of resolving production bottlenecks for each of the enterprise, determines the supply volumes of resources scarce. The Center supplies scarce resources to enterprises and forms a new adjusted output plan for each of the enterprises. If it is impossible to supply scarce resources to meet the needs of all enterprises in the company, the options for the most promising planning models are offered, under which the total profit of all enterprises in the company will be the greatest.

The implementation of the planning scenarios proposed below becomes real when switching to digital production management methods.

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