Application of Geographical Information System in Evaluating Productivity Growth of Sale Centers Using The Malmquist Productivity Index

Evaluating productivity and efficiency is an important measure for managerial performance. Appraising and taking advantages of valid mechanisms to evaluate managerial performance is highly important. Malmquist productivity index and Geographical Information System (GIS) are two tools which their integration can provide a pervasive approach for decision making units (DMUs) appraising depend on geographical position. This research uses these techniques to evaluate productivity improvement of an Iranian company’s sale centers. For this purpose, a mathematical model is designed and also, ordinary productivity variables and GIS data base variables are considered. The results reveal that the most productivity improvement belongs to Store 2 with 24. 7 percent of improvement which is graded as inefficient centers by primary evaluation. The mean total productivity improvement for all sales centers in a given period is recognized as 15. 2 percent by this approach. Sales centers and dealerships are among the largest industries in the world. From the point of view of sales engineering, sales centers interact with two other main components of supply chain sales, namely, manufacturers and customers, in other words, there are the main interface between these two groups. Also, due to direct relationship between sales centers with customers, their performance will greatly affect the net profit and sales volume of both groups of producers and sellers (Warley, 2006). Therefore, continuous evaluation of the performance of each sales center is a central requirement for the center to recognize its strengths and weaknesses.
Calculation of the efficiency of each sales center is one of the best practices for evaluating performance. Performance is often defined for a sales center in terms of outputs to the inputs ratio of that center. Therefore, making more output with less input, will result in  more efficient sales center (Gilbert, 2003). The data envelopment analysis model (DEA) is one of the best presented models for calculating the relative efficiency of different decision making units. In this model, by finding the best weights for inputs and outputs, the maximum amount of possible  efficiency per unit is calculated; while other models depend on the constant weight of outputs and inputs thus basically applying the judgment of the decision maker will be allocated (this will affect the accuracy of the results). However, it is necessary that the efficiency of each decision making unit must be computed for several periods to assess the improvement or decline of each decision making units to procure fundamental guideline to each decision making unit directors.
The productivity index of Malmquist specifies total factor productivity changes and their components for each of the decision-making units. Thus in this paper, productivity changes were measured for some sales centers using new considerable important variables such as number of competitors and number existence population considering GIS based model. In this paper, Malmquist productivity index was used to assess the main important productivity index in its component in detail for each DMUs.   This index strongly based on distance function developed by Shephard. Based on this, Shephard defines distance function as follows (Shephard, 2015).The distance function or coefficient θ shows the possibility of reducing inputs to produce a certain value, and the vector x is the vector that represents the production factors used for the production value for a decision unit.
Accordingly, the Malmquist index can be defined as follows (Malmquist, 1953).  The findings of papers were considerably important. The results revealed that the mean technical efficiency based of  constant return to  scale (CRS)   for all seller centers equals 0. 814   and mean technical efficiency based of  variable return to  scale (VRS)   for all seller centers equals 0. 761. The following table shows all the measures in detail.   The results revealed that the combination of GIS   and Malmquist index provides strongly dependable criteria to assess efficiency factors. Using these useful measures, we found that the biggest growth relates to the seller center number 2 which categorized as inefficient center and the lower growth of efficiency based on Malmquist index relates to efficient seller centers.