A mathematical model for the formation of the pricing policy and the plan of the production and transport system in a timber-processing enterprise

IF 0.6 Q4 BUSINESS
R. Rogulin
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Abstract

The formation of supply chains for raw materials is closely related to production problems involving the determination of prices for sold goods. The question often arises about the need to study the sources of raw materials and the methodology for pricing the goods produced, taking into account a large number of external aspects of the market. Often, only particular approaches to solving production problems are considered in the literature, and methods for solving the complex problem of forming supply chains for raw materials and pricing are poorly developed. This paper presents a mathematical model that makes it possible to assess the feasibility of interaction between a timber industry enterprise and a commodity exchange, with the daily formation of a price vector over the entire planning horizon. A two-stage algorithm for finding a suboptimal solution is considered, which at the first stage is based on linear optimization, and at the second, on gradient descent with the use of penalty functions. The model was tested on the data of the commodity and raw materials exchange of Russia and one of the enterprises of the Primorsky Territory. The result of testing was the volume of production of each type of product over the entire planning horizon, the volume of delivery of raw materials from regions to enterprises, as well as the methods of delivery of goods to the consumer and the policy of pricing. It is shown that almost all goods should increase in price due to a reduction in the excess volume of applications (demand) over the entire planning horizon, with the exception of two types of products. It is noted that the exchange can provide the necessary volume of raw materials for high-capacity production, which demonstrates the possibility, if necessary, to increase the volume of raw materials purchases. It is shown which goods will be included in the release plan more often than others when optimizing the price vector. The ways of delivery of final types of products are analyzed. The disadvantages and advantages of the mathematical model and algorithm are presented.
建立了木材加工企业价格政策和生产运输系统计划形成的数学模型
原材料供应链的形成与涉及确定售出商品价格的生产问题密切相关。经常会出现这样一个问题,即需要研究原材料的来源和所生产商品的定价方法,同时考虑到市场的大量外部因素。文献中通常只考虑解决生产问题的特定方法,而解决形成原材料供应链和定价这一复杂问题的方法发展得很差。本文提出了一个数学模型,通过在整个规划范围内每天形成价格向量,可以评估木材行业企业和商品交易所之间互动的可行性。考虑了一种用于寻找次优解的两阶段算法,该算法在第一阶段基于线性优化,在第二阶段基于使用罚函数的梯度下降。该模型在俄罗斯和普里莫尔斯基地区一家企业的商品和原材料交易所的数据上进行了测试。测试的结果是整个规划范围内每种产品的生产量,从地区到企业的原材料交付量,以及向消费者交付商品的方法和定价政策。研究表明,除了两种类型的产品外,由于整个规划范围内的超额应用量(需求)减少,几乎所有商品的价格都应该上涨。值得注意的是,交易所可以为高容量生产提供必要数量的原材料,这表明了在必要时增加原材料采购量的可能性。它显示了在优化价格向量时,哪些商品将比其他商品更频繁地包含在发布计划中。分析了最终类型产品的交付方式。介绍了数学模型和算法的优缺点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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