**A Decision Support Tool Based on a**

Portfolio Selection Model for Crop Planning under Risk

Portfolio Selection Model for Crop Planning under Risk

**Constanţa Zoie RĂDULESCU ^{1}, Marius RĂDULESCU^{2}**

**I C I Bucharest**

^{1 }(National Institute for R & D in Informatics)

8-10 Averescu Blvd.

011455 Bucharest 1, Romania

radulescucz@yahoo.com

^{1 }Institute of Mathematical Statistics and Applied Mathematics

Casa Academiei Romane, 13 Calea 13 Septembrie,

050711 Bucharest 5, Romania

mradulescu.csmro@yahoo.com

**Abstract**: In this paper is presented a decision support tool for crop planning under risk. The software tool is based on a portfolio selection model for crop planning. The portfolio selection model is a minimum financial risk model. It takes into account climate risk and market risk. The decision variable describes the land allocation to crops. The model was solved with the MINLP solver from GAMS. The decision support tool has an interface that facilitates the construction of the input data collection and the user parameters. It gives a flexible way of working and is mainly user oriented. Numerical results obtained with this Decision Support tool are analyzed.

**Keywords**: Decision support, software tool, mathematical model, crop planning, risk, portfolio selection.

**>>Full text**

**CITE THIS PAPER AS**:

Constanţa Zoie RĂDULESCU, Marius RĂDULESCU, **A Decision Support Tool Based on a Portfolio Selection Model for Crop Planning under Risk**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 21 (4), pp. 377-382, 2012.

**1. Introduction**

Computer-based decision support systems (DSSs) have a well-established tradition within crop planning in agriculture. The DSS for crop planning range from simple accounting-based systems to systems based on complex deterministic or stochastic models.

Romanian agriculture, which was for a long time considered a traditional, slow moving economic activity strongly dependent on subsidies and public support, is now a sector affected by many political changes and social pressures derived from environmental concerns and trade liberalizations requirements. Furthermore, the sector dynamics has dramatically increased due to technological innovations, rising world demand for food and raw materials and the new uses of traditional crops as energy sources.

One of the most important decisions faced by farmers is the selection of crops they want to grow. Prospective growers must know how to use risk management strategies in order to select the crops that best suit their needs. One of the most popular approaches to managing risk is to reduce risk exposure through diversification. The uncertainty from the agriculture problems is modeled with the help of probability theory. Many of the practical problems that occur in agriculture are stochastic programming problems with multiple objectives. In practice, in the process of mathematical modeling, one cannot take into account all the factors that have an impact to agricultural production. The number of such factors is large and the growth of their number determines the rapid growth of the complexity of the models. An important mathematical instrument which was successfully applied to modeling the problems from agriculture was portfolio theory. The above mentioned theory was developed as a result of the research in the domain of financial management. The application of portfolio theory for finding an optimal allocation of agricultural land is popular in the literature. The first application of the portfolio theory to crop planning goes back to Freund [6]. In Hardaker [7], Hazell and Norton [8], [9] and Blank [2]-[4] were presented or applied various variants of portfolio theory to the land allocation decisions.

In Collender [5], Romero [12]-[14], were studied several models for resources allocation in agriculture that are taking into account specific risks. For other references regarding applications of portfolio theory to agriculture see Radulescu [10], [11].

Our research has focused on the formulation of an original model for crop planning, based on portfolio theory and the design of a decision support software tool based on this model. The paper is organized as it follows. First a crop planning model is proposed. The model is a minimum financial risk model. It considers several classes of land quality, historical data on land productivity and crop market prices. The farmer intends to obtain optimal production plans that minimize the financial risk.

A decision support software tool based on this model is described in our paper. The model was solved with the MINLP solver from GAMS. The software application has an interface that facilitates the construction of the input data collection and the user parameters. It gives a flexible way of working and is mainly user oriented. A practical example is given before the presentation of the paper conclusions.

**REFERENCES:**

- ANDREI, N.,
**On Quadratic Internal Model Principle in Mathematical Programming,**Studies in Informatics and Control, Volume 18, Number 4, 2009, pp.337-348. - BLANK, S. C.,
**Returns to Limited Crop Diversification**. Western Journal of Agricultural Economics, no. 15, 1990, pp. 204-212. - BLANK, S. C., C. A. CARTER, J. McDONALD,
**Is the Market Failing Agricultural Producers Who Wish to Manage Risks?**, Contemporary Economic Policy, no.15, 1997, pp.103-112. - BLANK, S. C.,
**Producers Get Squeezed Up the Farming Food Chain: A Theory of Crop Portfolio Composition and Land Use**. Review of Agricultural Economics, no. 23, 2001, pp. 404-422. - COLLENDER, R. N.,
**Estimation Risk in Farm Planning under Uncertainty**. American Journal of Agricultural Economics, no. 71, 1989, pp. 996-1002. - FREUND, R. J.,
**The Introduction of Risk into a Programming Model**. Econometrica, no. 24, 1956, pp. 253-263. - HARDAKER, J. B., R. B. M. HUIRNE, J. R. ANDERSON, G. LIEN,
**Coping with Risk in Agriculture**, 2nd ed., CABI Publishing, Oxfordshire, 2004. - HAZELL, P. B. R,
**A Linear Alternative to Quadratic and Semivariance Programming for Farm Planning under Uncertainty**. American Journal of Agricultural Economics, no. 53, 1971, pp. 53-62. - HAZELL, P. B. R., R. D. NORTON,
**Mathematical Programming for Economic Analysis in Agriculture**, Macmillan, New York, 1986. - RĂDULESCU, M., S. RĂDULESCU, C. Z. RĂDULESCU,
**Mathematical Models for Optimal Asset Allocation**, (Romanian). Editura Academiei Române, Bucureşti, 2006. - RĂDULESCU, M., C. Z. RĂDULESCU, Ghe. ZBĂGANU,
**A Portfolio Theory Approach to Fishery Management**, Studies in Informatics and Control, Vol. 19, Nr. 3, 2010, pp.285-294. - ROMERO, C.,
**Una aplicación del modelo de Markowitz a la selección de planes de variedades de manzanos en la provincia de Lérida**. Revista de Estudios Agro‑sociales, no. 97, 1976, pp. 61-79. - ROMERO, C., T. REHMAN,
**Multiple Criteria Analysis for Agricultural Decisions**, Second Edition, Volume 11 (Developments in Agricultural Economics) Elsevier, Amsterdam, 2003. - ROMERO, C.,
**Risk Programming for Agricultural Resource Allocation: A Multidimensional Risk Approach**. Annals of Operations Research, 94, 2000, pp. 57-68.