Mathematical Methods for Crop Losses Risk Evaluation and Account for Sown Areas Planning
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MATHEMATICAL METHODS FOR CROP LOSSES RISK EVALUATION AND ACCOUNT FOR SOWN AREAS PLANNING V. A. Pepelyaeva† and N. A. Golodnikova a‡
UDC 631.153.3:330.131.7
Abstract. The sown areas optimization problem taking into account the risk of crop losses is considered. For the solution, a mathematical model based on the approach accepted in the portfolio optimization theory is proposed. Its essence is in maximizing the average expected result while constraining the risk of losses. The results of the analysis of optimal solutions using statistical data are provided. Keywords: risk, sown areas, crop, mathematical model, efficiency. INTRODUCTION At the present stage of the development of the Ukrainian agrarian sector, agricultural producers independently define the structure of sown areas, guided predominantly by the current conjuncture of the food market. Weather risk is only considered intuitively. The insufficient attention to this aspect in practice leads to large crop losses under unfavorable weather conditions. For example, due to unfavorable overwintering conditions in 2012, 3 to 3.5 million hectare of winter crops were subject to replanting. Thus, during spring time field cultivation campaign, the government decided to subsidize agricultural producers 300 million hryvnias for partial compensation for losses caused by the replanting. Such irrational use of agricultural and financial resources does not promote solidifying of food security and aggravates difficult situation of impoverished. In this connection, development of mathematical methods of crop losses risk evaluation and its consideration for planning the structure of sown areas gains the special importance countrywide. To solve this problem, we developed a mathematical model for the optimization of the structure of sown areas of agricultural crops accounting for crop losses countrywide. It is based on the portfolio optimization theory proposed by Markowitz in [1]. According to this approach, limited monetary resources are arranged among financial tools in order to maximize the average profit while constraining the risk of losses. In the papers [2–6] this approach is modified and implemented for the solution of applied problems not only in risk management and financial engineering but also in modern statistics, stochastic programming, logistics, medicine, mechanics, and agriculture. In terms of the optimization of sown areas, the task is to find the distribution of the total harvestable area among regions of Ukraine, maximizing average annual crop yield while constraining the crop shortage risk. The first section of the paper describes the mathematical risk valuation methods developed in [2–6] and suggests the mathematical model of the optimal distribution of sown areas growing single agricultural crop among regions of Ukraine. The second section presents the results of the analysis of winter wheat crop loss risk both in separate regions and countrywide. Using the proposed mathematical model, the numerical problem of optimal distribution of sown areas of winter
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