The cutting stock problem in relation to the assessment of the feasibility of purchasing timber from the commodity market

Abstract

The article considers a mathematical model that can be used to determine the optimal plan for the procurement of raw materials according to the preset timing of applications, determine the production plan, and calculate the optimal plan for the delivery of products. The specific feature of the model is that it can also plan the cutting of OSBs into workpieces of various lengths. It also considers the dependency between the price and the level of demand for finished goods. The purpose of our research was to assess the economic feasibility of interaction between a timber industry enterprise (with different levels of price and demand) and an international commodity market. Our hypothesis is that the interaction between the timber industry and the commodity market may be beneficial for the enterprise. The relevance of the study is determined by the lack of studies on the interaction of timber industry enterprises with the commodity market, with the latter being a source of raw materials. Various modelling methods were used for the assessment: mixed-integer linear programming (drawing up a model that finds the optimal vectors for cutting, procurement of raw materials, production of goods and their transportation based on the graph), the Monte Carlo method (generating initial conditions and parameters), and simulation modelling (for each state the cor responding task was solved). The main drawback of the model is that it requires a significant amount of RAM. The practical significance of the study is to prove the economic feasibility of purchasing raw materials from the commodity market of Russia. The theoretical value of the study is that it develops a new model for assessing the feasibility of purchasing raw materials using the market mechanisms. Scientific novelty is determined by the fact that it suggests a mathematical model for the formation of supply chains, drawing up a cutting plan and production volumes, taking into account the demand and available volume of raw materials. The model was tested using the data of one of the enterprises of the timber industry of the Primorsky Krai. It was used to optimize the volume of manufactured products and purchased raw materials from each region, as well as the number of cuts for each OSB and the stock of raw materials at the enterprise’s warehouse. Based on the results of testing, we assessed the feasibility of cooperation between the company and the commodity market. In 95 % of situations the cooperation is highly beneficial.