The enhanced Best Performance Algorithm for the Annual Crop Planning Problem Based on Economic Factors
3.3 Formal Description of ACP
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Production costs, coupled with crop yields and producer prices determine the profit earned. This is also in accordance with the market demand of the crop. Production costs consist of the fixed and variable costs of production. Fixed costs relate to the financial outlay irrespective of production. Fixed costs include loan repayments and other types of monthly expenses incurred in order to facilitate the crop production process. Variable costs are the costs incurred in the production of a unit of the harvest.
Variable costs include that of tilling the soil, labour costs, the costs of soil nutrition, pest control, irrigated water supply costs, and harvesting costs, etc.
Production costs will differ per crop produced. This is due to crop specific cultivation practices, and the cost of it. A simple example is the cost of harvesting a crop by hand, and harvesting a crop using machinery. In harvesting using these two different ways, the costs will differ. Cultivation practices also affect the crop yields (Dukes et al., 2012). Apart from maintaining the soil moisture content level and the nutritional value of the soil, other factors need to be dealt with which will affect the crop yield. These include weeds, pests and bacteria which occur during the lifespan of a crop.
In crop planning, the exact estimates of production costs, yields and producer prices cannot be pre- determined. Rather, statistics from previous years of crop production are used in the ACP mathematical model. These statistics will be used to estimate the figures in attempting to quantify solutions. Amongst others, these statistics can be determined from published literature and/or consultancy services (Kantanantha, 2007). Realistically, the statistics should be location specific. The objective in determining solutions is to advise crop planners on how to better prepare for the production year ahead.
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Inconsistent rainfall patterns cause inconsistent soil moisture content levels. If these levels are not maintained, it can be detrimental to crop development. Also, due to the differences in climatic conditions, from one geographical location to the next, the CWR of the same crop could differentiate from one location to the next.
At irrigation schemes, several crops get produced at different time intervals within a production year.
To maximize benefits, cultivation practices such as multi-cropping and sequential cropping are thus exercised. For the ACP problem, sequential cropping is the focus at present.
Sequential cropping is the practice of cultivating different, yet complementary types of crops, in sequence of each other on the same farm area within a production year. This is achieved without having the planting and harvesting schedules of the crops being in conflict. Thus, the distinguishing factor in identifying farming areas are the number of crops that are cultivated on it within the production year.
The objective therefore in sequential cropping, given the limited resources available for crop production, is to optimize crop production in trying to maximize the total gross profits that could be earned. The profits earned are from the sale of the harvests of all the crops produced within the production year. This is the objective of the ACP problem.
The gross profits earned are the differences between the producer prices and the production costs of the crops. Production costs consist of fixed and variable costs of production. Fixed costs are the financial outlays irrespective of crop production. The variable costs are the accumulated costs of crop production, per unit of the crop produced.
Due to several types of stochastic factors that are associated with this problem, no mathematical model exists that can determine accurate resource allocation solutions in crop production. Rather, in trying to accommodate the most important factors of this problem, without making it overly complex to solve by introducing too many variables, the ACP mathematical model had been developed. This model determines resource allocation solutions in order to assist crop planners in answering some of the following questions:
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1. What is the area of land that should be allocated for producing each crop within the production year?
2. What is the volume of irrigated water that is required per crop for optimal crop development, given the land allocation?
3. What would be the cost of this irrigated water?
4. What would be the total cost of producing each crop, given the land allocation ?
5. Given the market demand and supply conditions, what would be the gross profits earned from each crop?
6. What would be the gross profit earned from producing all crops within a production year?
Hence, the ACP problem focuses on determining the resource allocation solutions related to land, irrigated water supply and the variable costs associated with crop production. It tries to maximize the total gross profits that could be earned from the production of all crops produced within a production year. The complexity to the problem is attached with determining resource allocation solutions for all crops in accommodating their different planting and harvesting schedules within the year.
Solutions for the ACP problem are determined under the following assumptions:
1. ACP solutions are determined for the land allocation stage of the crop production process.
2. ACP solutions are determined at the beginning of the production year.
3. The total area of land available for the production of each crop group is known. For the ACP problem at an existing irrigation scheme, it is considered that this area of land remains fixed due to sequential cropping practices.
4. The statistics from previous years of crop production is known. This includes information of the crop demand, the producer prices, the costs associated with production, and the yields per crop. The demand statistics will be used to estimate the lower and upper bound ranges in order to determine realistic solutions in accordance with actual demands. The pattern of the producer prices can be used to estimate what would be the producer price for the same quantity of goods demanded in the forthcoming production year. Likewise, the same can be said for the production costs; for this, it is assumed that the fixed and variable costs can be differentiated. Concerning the crop yields, it is acceptable that this statistic remains the same.
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7. The cost of irrigated water m-3 and its supply to the irrigation scheme is known. The supply of irrigated water to the farming plots are assumed to be normal throughout the production year.
8. The CWR of each crop, at the specific geographical location, is known.
9. The average volume of precipitation throughout the lifespan of each crop is known.
10. Crop production throughout the year is assumed to be under favourable conditions. Hence, no unforeseen circumstances such as drought, hail, flooding, etc., will interfere with the crop production process.
12. Crops are planted and harvested according to schedule. These dates are assumed not to overlap with other crops grown in sequence on the same farming area of land.
For the crop demand ranges, the lower bound should be set such that the minimum market demand is satisfied. Likewise, the upper bound should be set such that an excess quantity of harvest is not produced, which would result in losses. For optimized irrigated water allocations, precipitation is considered. Also, excessive applications of irrigated water to the farming plots result in environmental damages. Therefore, to tighten the grip on excessive water wastage, producers are required to pay water charges (Grove, 2008). The strain of paying water charges, and the concern over water wastage, mean that the producers are required to produce more output per m-3 of irrigated water utilized.
Several objectives as well as soft and hard constraints must be achieved in order to determine feasible solutions.
Objectives:
1. Maximize the total gross profits earned from the production of all crops within the production year.
2. Determine the resource allocation solutions of land, irrigated water supply and production costs of all crops produced within the year.
Hard constraints:
1. Crop groups must be cultivated on their allocated farm plots. For example, perennial crops must grow on single-crop farm plots, only two crop groups are allowed to grow in sequence of each other on the double crop farm plots, etc.
2. Each crop must be allocated a portion of land.
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3. The minimum and maximum market demand conditions must be satisfied.
4. The total volume of irrigated water allocated to each crop produced must not exceed the total volume of irrigated water that can be supplied to the irrigation scheme within a production year.
Soft constraints:
1. Give as much satisfaction to each crop being produced, such as land area and irrigated water allocation.
2. Resource allocations must be done as fairly as possible.
The ACP mathematical model presented in this study implements the market economic factors of the economy of scale and the demand and supply relations.