Mathematical model of the formation of supply chains of raw materials from a commodity exchange under conditions of uncertainty

The formation of raw material supply chains is very closely related to production problems at a timber processing plant. Since the beginning of the second industrial revolution, one urgent question has been the formation of supply chains for raw materials and the optimal calculation of production volumes for each individual day. This article examines a forestry enterprise that does not have its own sources of wood, which daily solves the problem of ensuring the supply of raw materials and optimal production load. A commodity exchange is considered as a source of raw materials where lots randomly appear every day in different raw material regions. In the scientific literature, there are many approaches to calculating the optimal profit value over the entire planning horizon, but they do not consider many features that are important for a timber processing enterprise. This paper presents a mathematical model which is a mechanism for making daily decisions over the entire planning horizon and differs in that it allows one to take into account the share of useful volume and the delivery time of raw materials under conditions of uncertainty. The result of the model is the optimal profit trajectory, considering the volume of raw materials, the delivery time of lots, the volume of profit and the production volume of goods. The model was tested on data from the Russian Commodity and Raw Materials Exchange and one of the Primorsky Territory enterprises. Analysis of the results showed that there are difficulties in planning supply chains and production volumes. An assessment of the optimality of raw material regions was carried out. The advantages and disadvantages of the mathematical model are formulated.