Land use Model
After gathering the necessary information about the objective function, constraints and coefficients a model can be constructed for the problem. For this exercise a simple matrix is sufficient, however more complication can be reached with LP problems with up to several hundred decision variables and constraints. The table1.51 summarizes the possible transitions from one land use to others, including the possible remaining land unchanged.
Land that is double cropped is considered to be stable. On the other hand transformation from the single crop- land is possible only to double crop- land because of the intensity of land use in the area. Some conversions are always denied for example Grass- land cannot be transformed into the wasteland. The conversion of forest to grass land is circumstantially favorable, and in this study it is not considered because region is already witnessing fall in forest reserves. Agriculture being the main occupancy, croplands, are also, excluded from forest development option out of their sector of use.
Some activities like afforestation would be highly encouraged along the side of canal, lakes and also along the agricultural fields but this is not taken in this case of study of land use planning.
With the information obtained from the GIS analysis, as well as from the economic data, the input matrix can be specified as shown in table1.6.
The input matrix in table 1.7 shows the same problem but with objective function as maximizing the employment return from each type of land use transformation.
The main objective of the present exercise is to maximize the profit and labor returns from new allocation of the land use. The coefficient of the objective functions, are the no. Of employees or the amount of investment for each land use. The first five constraints are related with the land available for transformation, namely forest land, waste- land, grassland, single crop- land and double crop- land. The sixth constraint is ecological constraint, which requires that about 75 percent of the forest- land be retained. The seventh constraints refer to technical constraint and finally the financial constraint is also included.
The input matrix is solved by iterative process using the simplex method of QSB. This execution is done in SAS/OR software module, which provides procedures for running linear program. The results are summarized in table2.1 and 2.2. The budget values and objective values (for profit) are in lakhs and land allocation values and objective values are rounded off at their nearest decimal value.
Evaluation of this table, illustrate the relevance of LP technique in Land use planning problems. First of all it shows the maximum value of the objective function that can be reached after satisfying all constraints.
In this case maximum of new jobs can be obtained and maximum of profit return can be obtained while recognizing the ecological technical and financial constraints. These labor returns and profit returns will be generated from the new land use allocations. Picking the case of maximum objective value we observe from the table data:
- 5794.3 ha will remain as a forest land,
- 243.4 ha will be transferred from forest land to single cropland,
- 247.9 ha will be transferred from forest land to double cropland,
- 2565.4 ha of single crop land will be transferred to double cropland,
- 7078.2 ha of double cropland currently in use will be maintained
- 284.4 ha of wasteland will be devoted to double cropland activity
- 545.9 ha of grassland will also be
devoted to double cropland.
According to the optimal solution no waste- land should be changed to grass, forest, or single cropland and no grass- land should change to single or forest land.
Analysis of output results
One of the most interesting contributions to Linear programming to land use planning is towards its capacity to explore the relations in the optimal solution between the decision variables and the constraints. The constraint, limit the optimal solution but not all of them are influential. The amount of any resource that is not used in the optimal solution is called ‘slack.’
On the contrary when the slack of any constraint is zero, it is going to put restriction on the optimal solution. The importance of that limitation is expressed in the form of reduced cost. The increase or decrease of value of constraint will result in variation in value of the optimal solution.
For example picking the optimal value case for the budget amount of 220 lakhs we observe that technical requirement for the grassland do not affect the job or profit return because dedication of that amount of waste-land to grass is very small to bring any considerable changes in the desired return output. However technical constraints eight and nine are very much sensitive for any possible augmentation. This has been not shown in the paper.
Any amount of increment in available resources is also going to change not only the value of the optimal solution but also the coefficients of the decision variables. The more or less land is available the more or less job or profit would be expected but not on the same land use pattern. For example a decrease in budget value shows a decrease in optimal solution as listed in table. The simulations depict this effect very clearly.
Any technical or economic improvement will change the basis of the problem. Thus the relationship between the coefficients of the decision variables in both the constraints and the objective function is crucial for the final solution.
In nutshell, the Linear Programming models provide an interesting insight into the relation between decision variables and constraints in land use planning. Therefore once the problem is modeled, it is possible to study the following modifications namely:
- Changes in the coefficient of the decision variables, either in the objective function or in the constraints,(for example, technical improvements)
- An increase or reduction in available resources (the RHS of the constraints)
- The introduction of the new constraints
(Introducing new planning limitations)
In this context it is recommended that the consequences of the reducing cost with particular type of land transformation must also be considered which has been left as the part of future model simulation work.
Conclusion
This exercise is able to depict that Linear- programming is a valuable tool for modeling the land use using the GIS framework. It provides objective criteria for the different land use where different goals are being considered (Chuvieco, 1993). LP is also a flexible method for generating different planning scenarios, and with the help of LP multiple relationships between the decision variables and the constraints can be interpreted. The contribution of the GIS to Linear Programming is considered as a method for data collection and mapping of the results with GIS is put as future work to be done. It has proved the spatial domain of the linear programming problems, which has to be enhanced further by carrying out some more exercise in this subject.
Acknowledgements
The author wishes to express her sincere thanks to Mr. S.A. Shah and Mr. B. Vaishnav for providing computing facilities and system support during the execution of the work. The author also thanks her gratitude to the Dy. Director SAC Dr. A.R. Dasgupta for his continuous support and encouragement to carry out the work.
References
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