70 European Journal of Operational Research 40 (1989) 70-77 North-Holland Theory and Methodology Combinatorial aspects of cropping pattern selection in agriculture * Harry R. CLARKE Department of Economics, La Trobe University, Bundoora 3083, Austrafia Abstract: This paper selects cropping patterns which maximise the return from agricultural land using mathematical programming. The approach provides a new rationalisation for phenomena such as crop rotation and diversification. The results are applied to a crop selection problem in Bangladesh. Keywords: Agriculture, combinatorial analysis 1. Introduction Farmers rotate crops on given land for agro- nomic reasons associated with the issue of deplet- ing soil nutrients. They diversify crops on given land both because they are risk averse with respect to future market conditions and also because they face environmental uncertainties (pest infes- tations, climatic conditions etc.) which may sub- stantially influence crop yields. Finally if input supplies (particularly labor) are required mainly at planting or harvest dates and there are costs in adjusting the level of such input supplies, there may be a factor-requirements-smoothing motiva- tion for crop diversification. In this paper we discuss a case for crop rotation and diversification that is entirely unrelated to soil depletion, environmental or market uncertainty and factor-requirements-smoothing. Instead a case for crop rotation and/or crop diversification is established purely on the basis of the fact that * I wish to thank Dirk van Oudeusden, Md. Ludfar Rahman Khan and two anonymous referees for comments on earlier versions of this paper. Responsibility for remaining errors is mine. Received August 1987; revised April 1988 crops take different periods to mature and have different yield properties when planted at differ- ent dates during a year. Thus through time we show it may be rational for farmers to diversify and rotate crops simply because such policies al- low farmers to 'pack' the optimal sequence of crops onto land so as to maximise intertemporal returns. In fact, the problem of determining opti- mal cropping patterns in a deterministic setting is analogous to a type of 'set packing' task (see e.g. Balas and Padberg, 1976). Further, because of the particular structure of this task in the present instance, we show it can be solved as a conven- tional linear programming problem. To illustrate the procedure a particular crop selection problem is solved using data for Bangladesh. 2. The model Agricultural production planning problems have several distinctive characteristics in terms of classical production theory. Crop development is intrinsically dynamic and periodic (crops take time to mature and seasonal influences determine planting and harvest dates). Crop development also has discrete aspects (cropping once initiated 0377-2217/89/$3.50 © 1989, Elsevier Science Publishers B.V. (North-Holland)