C final 1 version 11

Figure 6 Idea map for the construction of the decision-making system for problem 2

6.3 Problem 2 Modeling and Solution

6.3.1 Construction of a decision-making system to measure the advantages and disadvantages of planting programs

Eight indicators were first selected as a measure of the strengths and weaknesses of the planting program and defined for four of them.
(1) Dispersion

D

Dispersion

D

is an indicator used to quantify the degree of dispersion of a crop across land parcels, measuring the degree of dispersion of the spatial distribution of a particular crop by evaluating and calculating its distribution across available cropland. The degree of dispersion reflects the extent to which the cultivation of a particular crop across land parcels deviates from a fully intensive cultivation scenario, and based on this, the degree of dispersion of the distribution is assessed. It is defined as follows:

D = \sum_{j = 1}^{41} D_{j}

Where

D_{j}

represents the dispersion of the first

j

crop, calculated as:

D_{j} = \frac{1}{N} \cdot \sum_{i = 1}^{N} {(\frac{f_{i j}}{t_{j}} - \frac{1}{N})}^{2} (N = 54)

where

N

represents the total number of land blocks, here

54; f_{i j}

is the 0-1 variable indicating whether the first

j

crop is planted on the first

i

block of land or not, and is computed by the formula:

f_{i j} = {\begin{cases} 0 & 在第 i 个地块上未种植第 j 种作物 \\ 1 & 在第 i 个地块上种植了第 j 种作物 \end{cases}

t_{j}

denotes the sum of the number of land parcels on which the first

j

crop is grown on different types of land, calculated by the formula:

t_{j} = \sum_{i = 1}^{54} f_{i j}