**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

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.