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A realistic assessment requires a thorough description of relevant constraints to be considered in the selection of optimal land use. These can relate to technological conditions, physical limitations, social, institutional and economic constraints and political targets. In the following, the set of constraints that has been implemented for use in the Kenya study is briefly discussed. Note, however, that not all the constraints need to be activated in every scenario, but can be included as appropriate and relevant.
Demand Targets by Aggregate Commodity Group
Lower and/or upper bounds or equality constraints on food availability, specified by broad commodity groups, e.g., cereals, pulses, roots, meats, etc., can be used to enforce fulfillment of food demand targets from domestic production (rainfed or irrigated) and imports. Since irrigated production and imports, in the present version, are specified exogenously, these constraints imply production targets by broad commodity groups. For the year 2000 scenarios, levels of food demand have been derived from projected demographic changes and per capita income growth. The model user can either supply absolute levels of target demand or have demand targets constructed by the LP generator from per capita demand targets and demographic information.
Commodity Production Targets
Lower and/or upper bounds or equality constraints on individual commodity production, e.g., wheat, white potato, beef, etc., can be selected to achieve appropriate commodity bundles in the production plan. This, for instance, could be an appropriate device to enforce sufficient production of cash-crops in food maximizing scenarios.
Limits on Harvested Area by Aggregate Commodity Group
The harvested area by commodity group (e.g., cereals, pulses, roots, etc.) can be controlled by means of lower and/or upper bounds and equality constraints implemented at district level. This can be useful to ensure desired allocation of land to cash-crops or fuelwood production.
Crop-wise Land Use Constraints
Lower and/or upper bounds and equality constraints to limit crop-wise use of arable land resources have been implemented. Although not much applied in the assessment of production potentials, these constraints allow for much control over land allocation in the optimization procedure.
Total Arable Land Use Constraint
Lower and/or upper bounds or equality constraints on total arable land use by broad climatic zone and/or district serve to reflect considerations regarding land use other than for agricultural production purposes, e.g., forest areas, specific non-agricultural uses, etc. In the Kenya study, when assessing crop and livestock production potentials, total arable land constraints were usually not enforced, i.e., all potentially suitable land in all zones is assumed to be available for agricultural purposes, except for non-agricultural land use requirements, forest and game park areas.
Production Input Requirements
Associated with the assessment of agricultural production in each land unit is the quantification of production inputs required according to the specified level of technology. Input requirements are derived from a technology matrix by interpolation; i.e., from a set of tabular functions that relate, for each crop and livestock system, different yield levels to input requirements in terms of seed (traditional and/or improved), fertilizer (N. P. and K), power, and plant protection/veterinary inputs. In addition, labor required for soil conservation measures is quantified. This set of constraints provides a means of ensuring that production input requirements and resource use for crop and livestock production stay within the limits of the resource endowment in terms of relevant input categories, e.g., labor, capital, fertilizer, power, etc. Negative input-output coefficients are used in case of activities which generate resources, e.g., power from animals.
Crop-Mix Constraints
A set of constraints, optionally to be specified by district, either by broad climatic zones, i.e., arid and dry semi-arid (mean dominant LGP of 0-120 days), moist semi-arid (LGP of 120180 days), sub-humid (LGP of 180-270 days) and humid (LGP of 270-365 days) zone, or by agro-ecological zone, i.e., overlay of thermal zones with individual LGP zones and zones of LGP pattern, can be used to exercise control on cropping patterns by enforcing limitations on shares (minimum and maximum levels) of arable land use to be occupied by individual crop groups. Of course, care must be taken to ensure that the imposed crop distribution is in accordance with agro-ecological suitability to avoid infeasibilities. The level of enforcement for this set of constraints is controlled by means of scenario parameters.
Human Calorie/Protein Ratio Requirements
These constraints ensure that, by broad climatic zones, the crop production plan is such that the ratio of calories to protein obtained from food products stays within nutritionally acceptable ranges.
Distribution of Livestock Population over Livestock Zones
The concept of livestock zones has been introduced to relate the climatic information contained in the resource inventory to broader climatic zones relevant to describing and delineating different livestock systems and formulating their integration with the crop production plans of the respective agro-ecological zones. For the purpose of this study, it has been assumed that the livestock zones fall into a subset of the climatic subdivision used in the land resource inventory. Sixteen livestock zones are distinguished (see Appendix A, Table A. 18).
The livestock population distribution constraints allow to impose lower and/or upper bounds or equality constraints on shares in total livestock populations (herd TLUs) to be considered in each of the livestock zones.
Distribution of Livestock Systems within Livestock Zones
This set of constraints describes the composition of the supported livestock population within each livestock zone in terms of different livestock systems. This is done by imposing lower and/or upper bounds or equality constraints on the shares of individual livestock systems in the total number of livestock units supported in the zone. In the Kenya study, up to ten livestock systems, out of a total of some thirty systems, at traditional, intermediate and improved management levels, have been considered in each livestock zone: this includes pastoral production systems of camel, cattle, and sheep and goat, and sedentary production systems of cattle, sheep and goat, pigs and poultry.
Constraints on Number of Animals by Livestock System
To cater for situations when the information in the land resources inventory does not provide sufficient data regarding the appropriate livestock systems to select, e.g., water availability in pastoral areas, lower and upper bounds on the number of TLUs by livestock system can be specified.
Livestock Feed Requirement Constraints
In setting up feed demand-supply balance constraints it is important to include relevant aspects of quality and quantity of feed supplies in time and space. In the Kenya study, livestock feed balance constraints are implemented for all livestock zones that have been delineated on the basis of climatic characteristics. The livestock zones are conveniently formulated in terms of the thermal regime and the length of growing period. The required feed supply has to be provided from feed sources within each livestock zone, i.e., crop by-products and residues, pastures and browse, fallow grazing, browse from fuelwood trees, and in some scenarios - primary products. Each set of constraints, by zone, is formulated in terms of four relevant items: minimum and maximum daily dry matter intake, digestible protein of feed ration, and metabolizable energy.
Since the seasonal variation in quality and quantity of feed supplies often plays a critical role for livestock raising in pastoral areas, two feeding periods within the year - wet season and dry season - have been stipulated. The length of each period in a particular agro-ecological cell varies according to the climatic information in the land resources inventory. It is assumed that the length of the wet season equals the site specific length of growing period.
The seasonal crude protein (CP) feed quality constraints ensure that the digestible crude protein (pop) contents of the livestock system specific seasonal feed intake lies within the prescribed tolerance band and that the annual average pop contents of the feed intake does not fall below average annual requirements.
Similarly, the seasonal metabolizable energy (ME) feed quality constraints ensure that the ME contents of the seasonal feed intake lies within the prescribed tolerance band and that the annual average ME contents of the feed intake does not fall below average annual requirements. For example, improved animals with higher productivity also require higher energy concentration in the diet.
In summary, feed balance constraints have been imposed for each of the livestock zones in terms of four relevant nutritional parameters and for each of two feeding seasons.
Zone Level Production Risk Constraint
The AEZ land resources inventory of Kenya includes some information on the variability of rainfall, and hence, the varying length and type of the growing period. This allows for assessing production options in 'good' years, 'bad' years, as well as production on average. While valuations used in the objective function usually refer to average productivity, zone level risk constraints are implemented to ensure that the resulting land allocation emphasizes the stability of the production plan also in 'bad' years, i.e., in vulnerable areas to give preference to crop combinations that will produce also in 'bad' years, even at the expense of lower average performance.
Agro-ecological Cell Use Constraint
Obvious as it may appear to be, the LP algorithm requires to explicitly ensure that the sum of shares allocated to different crop production activities in each land unit does not exceed 100 percent, i.e., that each piece of land can only be used and allocated once (this does not preclude sequential multi-cropping). While the number of constraints described under the above constraint sets is independent of the number of records in the land inventory, a singleuse constraint, as discussed here, has to be implemented whenever more than one cropping activity is feasible in a particular agro-ecological cell. The detailed land inventory of Meru District, for instance, consists of well over 3000 agro-ecological cells resulting in a large number of cell use constraints in the district LP. Similarly, the cell risk and crop rotation constraints, discussed below, operate at the level of a land unit. As a consequence the number of rows in the LP may easily become large.
Crop Rotation Constraints
Continued mono-cropping over time is not considered a sustainable agricultural practice under most circumstances as it exhausts soil fertility more easily and may cause pest and disease problems.
Although the AEZ methodology is essentially static, not explicitly considering crop rotations over time, this element has been captured by imposing upper limits on the share of each cell that can be occupied by an individual cropping activity. For example, imposing a limit of 70 percent as maximum share for maize in a particular cell can be interpreted as requiring that maize cannot be grown in more than 7 out of 10 cropping years, in addition to fallow requirements.
The mono-cropping restrictions are controlled through scenario parameters and are implemented as simple lower and upper bounds on cropping activities. They are not enforced in a cell when no alternative cropping options exist. Also, cassava and perennial crops like banana, oil-palm or sugar cane, or environmentally less demanding land uses, like cropping combinations including legumes, or pastures and fuelwood species, are not restricted by mono-cropping constraints.
It is also advisable to make a provision for biological nitrogen fixation in the cropping patterns at the low level of inputs circumstance. The crop rotation constraints provide a means to control the extent to which crop combinations from a particular crop group can occupy a land unit.
Cell Level Production Risk Constraints
As outlined above for the zone level, crop production risk constraints are also implemented at the cell level to ensure that the resulting land allocation emphasizes the stability of the production plan also in 'bad' years. The constraint is specified such that land use option selected in the optimal solution on the basis of production levels attainable on average should provide output levels also in 'bad' years that do not fall below a user specified threshold level in comparison to the best possible output obtainable in 'bad' years among all viable cropping options.
Environmental Impact Constraints
Environmental impact constraints have been provided to ensure that the optimal production plans are also environmentally compatible, stipulating that the environmental impacts in each cell must not exceed tolerable limits. At this stage, only soil degradation from water erosion is quantified. To keep LP sizes down, tolerable soil loss is dealt with by filtering out unacceptable crop combinations rather than imposing constraints in the LP.