GISdevelopment.net --> Application --> Urban Planning
Land use planning using GIS and linear programming
Stuti Shukla
stuti@ipdpg.gov.in
P. D. Yadav
R. K. Goel
Informatics Application Division
Space Application Center, ISRO, Ahmedabad
Stuti Shukla
stuti@ipdpg.gov.in
P. D. Yadav
R. K. Goel
Informatics Application Division
Space Application Center, ISRO, Ahmedabad
Introduction
Modeling any real problem helps in understanding it’s, underlying features, which are not exhibited as such and are less understood.
However, any single approach is found to be deficient in one feature or other and an integrated approach is the best one can think of amidst of diverse techniques available for users in general to solve various complex problems.
Geographical Information system is one such tool responsible for revolutionizing the era of spatial data management. A GIS can be considered as a tool for the integration and analysis of geographically- referenced data (Maguire 1991). Basically it is a commercial system and lacks spatial statistics and modeling language, which is required in applications in the field of hydrology, soil science, forestry and land use planning. This system is found to be adjusting, these models within itself. For example general system theory, linear programming, Monte- Carlo simulation are the few which are found to be readily adopted by GIS. More efforts should therefore be devoted facilitating the integration of spatial models and spatial methods of analysis (Dueker 1987,Tomlin 1989,Openshaw 1991). We have chosen to integrate the technique of linear programming with GIS for land use planning problem.
Table 1.1: Area in hectares of different land units
Linear programming is one such technique for calculating the optimal return from, the proposed infrastructure for land use development or any development plan in general. Linear programming (LP) has been used since 1950 in wide variety of planning situations (Dantzig 1963). Its application field ranges from business planning management to the problem of spatial organization. This is not a spatial technique and does not take in to account the spatial distribution of the decision variables. Problems like transportation planning, distribution of administrative areas, and location of central facilities are solved, by linear programming and in this way, spatial distribution is implicitly considered (Dykstra 1983). Any LP analysis starts with by defining the decision variables, which are different alternatives stated by the problem. After defining the decision variables the objective function is defined. The coefficients of the objective functions, is specified depending on the criteria of the objective function. These secondary objectives act as a set of constraints in limiting the value of the objective function. Each constraint is formulated as a linear equation whose, right hand side constant represent, the limit of the available resources. To solve any linear programming problem the objective functions and all the constraints must be strictly linear over the domain of each activity. In this technique each linear variable can assume any real value including both real and integers and fractions. All right hand side values are assumed, to be, known constant. All activities must be at least equal to zero that is negative assignment should not be included in the model.
Linear programming makes it possible to obtain the optimal solution of the problem in order to make the objective function maximum or minimum while fulfilling all other requirements at the same time. Linear programming is able to give a synthetic approach to complex situations. The linear programming has been structured to solve the problem of a case study of land transformation. The input matrix is solved using simplex method of QSB using the software module SAS/OR. SAS/OR module, consist of Linear Programming procedure which solves linear programs, integer programs, and mixed integer programs.
Table 1.2: Area matrix of land use
The problem is programmed in SAS/OR (operational Research) platform and is run to get the desired output. The results and problem structure are discussed in the next section, before that an out look of the necessity for integrating the GIS along with analytical model has been elaborated in the following section.
Table 1.3: Suitable area of four types of land for conversion or development
Why Integration, of analytical models with GIS?
A model is idealized and structured representation of the part of reality and is successful in forecasting the future situations. GIS also being considered as a one of the model however cannot do some analytical jobs, as non spatial relations in most analytical models are too complex to be modeled within a standard GIS.
Whereas analytical models being selective representative of the coherent part of the reality have proved to be successful in estimating missing data, forecasting future situations. These models can be best implemented using matrix data structures and manipulations, which are not supported by GIS. Most of the human geographical problems refer, to complex non- spatial relations, which are neither explicitly nor implicitly represented in GIS. But the basic structure underlying the analytical model is very primitive and they are not flexible also. The Geographical information systems are limited in their approach to provide a general overview of the accessibility in a given area. Another limitation of the GIS is that its ability is very poor in handling the dynamic spatial models. It also not handles properly the temporal definition of any problem. However the strength of Geographical information systems lies in their flexibility and their ability to represent the irregular shapes and pattern of the problem and their relationships. GIS system do not provide tools for modeling the spatial phenomenon whereas spatial analytical models like spatial autocorrelation models are able to identify the nature of relationship between points in space in terms of their relationship to one another. Potential or gravity models are able to predict the aggregate centrality of places in relation to population in the given area. Multi-criteria decision, making model is used to assist the user to select the best alternative from the number of feasible choice alternatives under the presence of multiple choice criteria and diverse criterion priorities. Other models dealing with various spatial problem are non linear model, demographic model, model of regional economy, cellular automata model etc. which are aimed to be coupled with GIS for better interpretation of the real world problem.
Reviewing all these aspects integration of GIS and mathematical models are very much necessary and is what we wish to do in our case study.
Table1.4: Job or profit return from different land-uses per ha
The study Area
The Panchmahal district is situated in eastern Gujarat and lies between 220 17” and 230 27”, degree north latitude and 730 22” and 740 29”-degree easts, longitude. The entire northern and eastern portion is covered by hills and forests and interspersed plain cultivable land. The western part comprises plains rising gradually to the east and is drained by rivers and interspersed by sprinklings of low hills. The soil of the northern and eastern region of the district is shallow rocky and black in texture. The remaining land has fertile alluvial soil. The area is traversed by, seven rivers out of which, Mahi, is the biggest river. It flows from north- east to south- west direction. The area, also have few lakes of considerable size.
Table 1.5: Investment required per unit hectare area for land-use
Out of this district a total sub area of 17799.928 hectares is selected. This region is dominated by single crop activity and is possessing more than seventy percent of forest reserves as shown in the figure1.
Fig. 1: Land use classes for study area
In the figure 1 the symbols shown stand for different type of land-use like black color indicates water bodies, lateral inclined bars shaded area stands for forest reserves including shifting cultivation, squarely crossed area stands for single crop and horizontal lines are meant for grass land use. The tilted crossed area indicates waste land and densely checked are is for double crop region.
The entire sub-area is divided in to polygon of different land use activity namely single crop, double crop, fallow land, deciduous forest, shifting cultivation, scrub land and water bodies consisting mainly of canals, lakes and ponds. The total land area consist of, 1679.749 hectares of land use area. The total water body area is about 1040.185 hectares.
Table1.51: Decision Variables for land use transformations
The total area of each land class is calculated with the help of ARC GIS and they are listed in table 1.1. The database for determining the characteristics of specific land area is NRIS database.
Table. 1.6: Input Matrix for solving the LP problem
Shifting cultivation land has been merged into the forest- land area for the problem under study and water bodies are not taken in to account for land use transformation or development scheme.
Characteristics for each type of land is studied with the help of GIS, based on ground water, soil type and slope of the land.
Table. 1.7: Input Matrix for solving the LP problem
With the help of these characteristic technical constraints are developed for different type of land use transformation. For example those lands with an average slope of 3-5%, ground water potential moderate to poor and soil depth around 7.5 to 45 cm, mildly alkaline soil and loamy sand to sandy clay loam soil texture are to be developed as grassland.
Land with an average slope of 5-10% or greater, ground water potential poor to nil and soil texture sandy clay to coarse loam are preferred for forest development. Lands adopted for single cropping activity are having slope of 1-5%, ground water potential of moderate level and soil texture of sandy- clay to clay- loam. Double crop- lands are extremely rich in ground water potential and slope is in the range of 0-3% with soil texture sandy loam to sandy clay. These are intensively used land and are non alkaline in nature.
Waste- land parcels are selected to be suitable for forest and grassland type of transformation. The land area suitable for transformation is calculated with the help of GIS. The table 1.2 shows the area values for all possible land transitions. The suitability area values are listed in table 1.3.
The forest area under ecological constraint is calculated as 4714.254 hectares. Except waste- land some area of each type of land is kept untouched. The remaining area of grass land is 309.790 ha., 5976.720 ha of forest is untouched and 2052.507 ha is kept as single cropland. Total area of double crop- land is 7078.201 ha which is not considered for transition.
Table 2.1: for optimal profit values
The grassland is suitable for conversion into forest, single crop- land and double cropland activity. Forests are dealt with special attention of ecological norms and under the constraint that 75% of forest has to be conserved only 25% of forest- land is allowed for conversion into double crop activity. Few hectares of single crop- land are allowed to go for double crop activity in the view of soil protection constraints.
Thus for this exercise three sets of constraints (ecological, technical and financial) are proposed
Economic data for each land-use for computing the labor requirement per hectare and level of investments required for transformation are assumed empirically and presented in table 1.4.
Table 2.2: for optimal job values
However it is recommended that detail survey should be carried out in real planning situations, creating new decision variables associated not only with different land use but also with different intensities of land use.
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:
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:
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
Modeling any real problem helps in understanding it’s, underlying features, which are not exhibited as such and are less understood.
However, any single approach is found to be deficient in one feature or other and an integrated approach is the best one can think of amidst of diverse techniques available for users in general to solve various complex problems.
Geographical Information system is one such tool responsible for revolutionizing the era of spatial data management. A GIS can be considered as a tool for the integration and analysis of geographically- referenced data (Maguire 1991). Basically it is a commercial system and lacks spatial statistics and modeling language, which is required in applications in the field of hydrology, soil science, forestry and land use planning. This system is found to be adjusting, these models within itself. For example general system theory, linear programming, Monte- Carlo simulation are the few which are found to be readily adopted by GIS. More efforts should therefore be devoted facilitating the integration of spatial models and spatial methods of analysis (Dueker 1987,Tomlin 1989,Openshaw 1991). We have chosen to integrate the technique of linear programming with GIS for land use planning problem.
Table 1.1: Area in hectares of different land units
| Land type | Land area in hectares |
| Single Crop Land | 2565.47 |
| Double Crop Land | 7078.201 |
| Fallow Or Grass Land | 545.966 |
| Deciduous Forest | 4917.965 |
| Shifting Cultivation | 1367.707 |
| Waste Land | 284.442 |
| Water Bodies | 1040.185 |
Linear programming is one such technique for calculating the optimal return from, the proposed infrastructure for land use development or any development plan in general. Linear programming (LP) has been used since 1950 in wide variety of planning situations (Dantzig 1963). Its application field ranges from business planning management to the problem of spatial organization. This is not a spatial technique and does not take in to account the spatial distribution of the decision variables. Problems like transportation planning, distribution of administrative areas, and location of central facilities are solved, by linear programming and in this way, spatial distribution is implicitly considered (Dykstra 1983). Any LP analysis starts with by defining the decision variables, which are different alternatives stated by the problem. After defining the decision variables the objective function is defined. The coefficients of the objective functions, is specified depending on the criteria of the objective function. These secondary objectives act as a set of constraints in limiting the value of the objective function. Each constraint is formulated as a linear equation whose, right hand side constant represent, the limit of the available resources. To solve any linear programming problem the objective functions and all the constraints must be strictly linear over the domain of each activity. In this technique each linear variable can assume any real value including both real and integers and fractions. All right hand side values are assumed, to be, known constant. All activities must be at least equal to zero that is negative assignment should not be included in the model.
Linear programming makes it possible to obtain the optimal solution of the problem in order to make the objective function maximum or minimum while fulfilling all other requirements at the same time. Linear programming is able to give a synthetic approach to complex situations. The linear programming has been structured to solve the problem of a case study of land transformation. The input matrix is solved using simplex method of QSB using the software module SAS/OR. SAS/OR module, consist of Linear Programming procedure which solves linear programs, integer programs, and mixed integer programs.
Table 1.2: Area matrix of land use
| From/To | Waste | Grass | Forest | Single | Double |
| Waste | - | 72.637 | 211.805 | - | - |
| Grass | - | 309.790 | 20.764 | 97.821 | 117.795 |
| Forest | - | - | 5976.720 | 145.610 | 163.342 |
| Single | - | - | - | 2052.507 | 512.963 |
| Double | - | - | - | - | 7078.201 |
The problem is programmed in SAS/OR (operational Research) platform and is run to get the desired output. The results and problem structure are discussed in the next section, before that an out look of the necessity for integrating the GIS along with analytical model has been elaborated in the following section.
Table 1.3: Suitable area of four types of land for conversion or development
| SOURCE LAND | TARGET LAND | AREA SUITABLE |
| WASTE LAND (W) | FOREST (WF) | 211.805 |
| WASTE LAND | GRASS LAND (WG) | 72.637 |
| GRASS LAND (G) | FOREST (GF) | 20.764 |
| GRASS LAND (G) | SINGLE CROP (GS) | 97.821 |
| GRASS LAND (G) | DOUBLE CROP (GD) | 117.595 |
| FOREST | DOUBLE CROP (FD) | 163.342 |
| FOREST | SINGLE CROP | 145.610 |
| SINGLE CROP | DOUBLE CROP | 512.963 |
Why Integration, of analytical models with GIS?
A model is idealized and structured representation of the part of reality and is successful in forecasting the future situations. GIS also being considered as a one of the model however cannot do some analytical jobs, as non spatial relations in most analytical models are too complex to be modeled within a standard GIS.
Whereas analytical models being selective representative of the coherent part of the reality have proved to be successful in estimating missing data, forecasting future situations. These models can be best implemented using matrix data structures and manipulations, which are not supported by GIS. Most of the human geographical problems refer, to complex non- spatial relations, which are neither explicitly nor implicitly represented in GIS. But the basic structure underlying the analytical model is very primitive and they are not flexible also. The Geographical information systems are limited in their approach to provide a general overview of the accessibility in a given area. Another limitation of the GIS is that its ability is very poor in handling the dynamic spatial models. It also not handles properly the temporal definition of any problem. However the strength of Geographical information systems lies in their flexibility and their ability to represent the irregular shapes and pattern of the problem and their relationships. GIS system do not provide tools for modeling the spatial phenomenon whereas spatial analytical models like spatial autocorrelation models are able to identify the nature of relationship between points in space in terms of their relationship to one another. Potential or gravity models are able to predict the aggregate centrality of places in relation to population in the given area. Multi-criteria decision, making model is used to assist the user to select the best alternative from the number of feasible choice alternatives under the presence of multiple choice criteria and diverse criterion priorities. Other models dealing with various spatial problem are non linear model, demographic model, model of regional economy, cellular automata model etc. which are aimed to be coupled with GIS for better interpretation of the real world problem.
Reviewing all these aspects integration of GIS and mathematical models are very much necessary and is what we wish to do in our case study.
Table1.4: Job or profit return from different land-uses per ha
| Variable | Employees/profit per ha | Notes |
| Waste land | 0/0 | No employment |
| Grass land | 2.0/500 | Grazing labor |
| Forest land | 4.0/10000 | Rangers, wood cutters |
| Single Cropland | 10.0/25000 | Rural labor force |
| Double Cropland | 15.0/50000 | Labor and technical services |
The study Area
The Panchmahal district is situated in eastern Gujarat and lies between 220 17” and 230 27”, degree north latitude and 730 22” and 740 29”-degree easts, longitude. The entire northern and eastern portion is covered by hills and forests and interspersed plain cultivable land. The western part comprises plains rising gradually to the east and is drained by rivers and interspersed by sprinklings of low hills. The soil of the northern and eastern region of the district is shallow rocky and black in texture. The remaining land has fertile alluvial soil. The area is traversed by, seven rivers out of which, Mahi, is the biggest river. It flows from north- east to south- west direction. The area, also have few lakes of considerable size.
Table 1.5: Investment required per unit hectare area for land-use
| From/To | Waste | Grass | Forest | Single | Double |
| Waste | - | 100 | 500 | 750 | 1600 |
| Grass | - | 10 | 300 | 600 | 1200 |
| Forest | - | - | 20 | 650 | 1350 |
| Single | - | - | - | 40 | 950 |
| Double | - | - | - | - | 90 |
Out of this district a total sub area of 17799.928 hectares is selected. This region is dominated by single crop activity and is possessing more than seventy percent of forest reserves as shown in the figure1.
Fig. 1: Land use classes for study area
In the figure 1 the symbols shown stand for different type of land-use like black color indicates water bodies, lateral inclined bars shaded area stands for forest reserves including shifting cultivation, squarely crossed area stands for single crop and horizontal lines are meant for grass land use. The tilted crossed area indicates waste land and densely checked are is for double crop region.
The entire sub-area is divided in to polygon of different land use activity namely single crop, double crop, fallow land, deciduous forest, shifting cultivation, scrub land and water bodies consisting mainly of canals, lakes and ponds. The total land area consist of, 1679.749 hectares of land use area. The total water body area is about 1040.185 hectares.
Table1.51: Decision Variables for land use transformations
| From/to | Waste | Grass | Forest | Single | Double |
| Waste | WW | WG | WF | WS | WD |
| Grass | NA | GG | GF | GS | GD |
| Forest | NA | NA | FF | FS | FD |
| Single | NA | NA | NA | SS | SD |
| Double | NA | NA | NA | NA | DD |
The total area of each land class is calculated with the help of ARC GIS and they are listed in table 1.1. The database for determining the characteristics of specific land area is NRIS database.
Table. 1.6: Input Matrix for solving the LP problem
|
Objective Function Max {0ww+500wg+10000wf+25000ws+50000wd+500gg+10000gf+25000gs +50000gd+10000ff+25000fs+50000fd+25000ss+50000sd+50000dd} Constraints:
0ww+100wg+500wf+750ws+1600wd+10gg+300gf+600gs+1200gd +20ff+650fs+1350fd+40ss+950sd+90dd < 22 lakhs |
Shifting cultivation land has been merged into the forest- land area for the problem under study and water bodies are not taken in to account for land use transformation or development scheme.
Characteristics for each type of land is studied with the help of GIS, based on ground water, soil type and slope of the land.
Table. 1.7: Input Matrix for solving the LP problem
|
Objective Function Max {0ww+2wg+4wf+10ws+15wd+2gg+4gf+10gs +15gd+4ff+10fs+15fd+10ss+15sd+15dd} Constraints:
0ww+100wg+500wf+750ws+1600wd+10gg+300gf+600gs+1200gd +20ff+650fs+1350fd+40ss+950sd+90dd < 22 lakhs |
With the help of these characteristic technical constraints are developed for different type of land use transformation. For example those lands with an average slope of 3-5%, ground water potential moderate to poor and soil depth around 7.5 to 45 cm, mildly alkaline soil and loamy sand to sandy clay loam soil texture are to be developed as grassland.
Land with an average slope of 5-10% or greater, ground water potential poor to nil and soil texture sandy clay to coarse loam are preferred for forest development. Lands adopted for single cropping activity are having slope of 1-5%, ground water potential of moderate level and soil texture of sandy- clay to clay- loam. Double crop- lands are extremely rich in ground water potential and slope is in the range of 0-3% with soil texture sandy loam to sandy clay. These are intensively used land and are non alkaline in nature.
Waste- land parcels are selected to be suitable for forest and grassland type of transformation. The land area suitable for transformation is calculated with the help of GIS. The table 1.2 shows the area values for all possible land transitions. The suitability area values are listed in table 1.3.
The forest area under ecological constraint is calculated as 4714.254 hectares. Except waste- land some area of each type of land is kept untouched. The remaining area of grass land is 309.790 ha., 5976.720 ha of forest is untouched and 2052.507 ha is kept as single cropland. Total area of double crop- land is 7078.201 ha which is not considered for transition.
Table 2.1: for optimal profit values
| Bud | ww | wg | wf | ws | wd | gg | gf | gs | gd | ff | fs | fd | ss | sd | dd | Obj |
| 22lakhs | 0 | 0 | 0 | 124 | 160 | 0 | 0 | 0 | 546 | 6038 | 0 | 248 | 2565 | 0 | 7078 | 5292 |
| 220 | 0 | 0 | 0 | 0 | 284 | 0 | 0 | 0 | 546 | 5794 | 243 | 247 | 0 | 2565 | 7078 | 6001 |
| 11 | 0 | 0 | 0 | 0 | 0 | 353 | 0 | 0 | 193 | 6286 | 0 | 0 | 2565 | 0 | 7078 | 4907 |
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4714 | 0 | 0 | 2565 | 0 | 6701 | 4463 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4714 | 0 | 0 | 143 | 0 | 0 | 507 |
The grassland is suitable for conversion into forest, single crop- land and double cropland activity. Forests are dealt with special attention of ecological norms and under the constraint that 75% of forest has to be conserved only 25% of forest- land is allowed for conversion into double crop activity. Few hectares of single crop- land are allowed to go for double crop activity in the view of soil protection constraints.
Thus for this exercise three sets of constraints (ecological, technical and financial) are proposed
- Ecological, which requires the conservation of at least 75% of natural vegetation and forest reserves existing before the changes.
- Technical, which restricts the location of new land uses to the most suitable areas as selected by three parameters namely ground water, soil and slope values of the land in use as enumerated below:
- Those sectors of forest will go for double cropping which are having slope of 0-3%, ground water potential very good and soil sandy loam to sandy clay.
- New areas for grassland are restricted to those region which having slope of 3-5%and ground water potential moderate to poor and soil of loamy sand to sandy clay loam texture.
- New sectors for single crop are restricted to those regions with slope of 1-5%, soil of sandy clay to clay loam texture and ground water potential of moderate value.
- New areas for forest are confined to those sectors which are having slope of 5-10%, soil texture of sandy clay to coarse loam and ground water potential very poor.
- To simplify the problem only public investment of 22 lakhs is assumed to be available for land use transformations.
Economic data for each land-use for computing the labor requirement per hectare and level of investments required for transformation are assumed empirically and presented in table 1.4.
Table 2.2: for optimal job values
| Bud | ww | wg | wf | ws | wd | gg | gf | gs | gd | ff | fs | fd | ss | sd | dd | Obj |
| 22lakhs | 0 | 0 | 0 | 284 | 0 | 0 | 0 | 0 | 546 | 5807 | 243 | 235 | 2565 | 0 | 7078 | 172051 |
| 220 | 0 | 0 | 0 | 0 | 284 | 0 | 0 | 0 | 546 | 5794 | 243 | 247 | 0 | 2565 | 7078 | 186441 |
| 11 | 0 | 73 | 0 | 104 | 0 | 303 | 0 | 243 | 0 | 6286 | 0 | 0 | 2565 | 0 | 7078 | 161198 |
| 8 | 0 | 0 | 0 | 0 | 0 | 546 | 0 | 0 | 0 | 6286 | 0 | 0 | 2565 | 0 | 6291 | 146225 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4714 | 0 | 0 | 143 | 0 | 0 | 20285 |
However it is recommended that detail survey should be carried out in real planning situations, creating new decision variables associated not only with different land use but also with different intensities of land use.
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.
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)
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
- Dantzig, G. B., 1983: linear programming and Extensions (Princeton University press).
- Dykstra, D.P., 1983: Mathematical programming for Natural Resources Management (New York: McGraw hill).
- Dueker, K.J., 1987: Geographical information systems and computer aided mapping. Journal of the American Planning Association, 53, 383-399.
- Emilio Chuvieco, 1993: Integration of linear programming and GIS for land-use modeling. IJGIS, Vol. 7, 71-83.
- Maguire,D.I., 1991: An overview and definitions of GIS. In Geographical Information systems edited by D.J. Maguire, M.F. Goodchild and D.W. Rhind (London: Longman), 9-20.
- Tomlin, D., 1989: Geographic Information Systems and Cartographic Modeling (Englewood cliffs;Prentice hall)
- Openshaw, S., 1991: Developing appropriate spatial analysis method for GIS.In Geographical Information systems. Edited by D.J. Maguire, M.F. Goodchild and D.W. Rhind (London: Longman), 389-402.