PARTITIONING AND OPTIMIZATION OF EQUIPMENT DEALER SALES INPUTS TO MAXIMIZE GROSS MARGINS

WILLIAM DAVID SHOUP, Purdue University

Abstract

The complex management problems associated with managing equipment dealerships' resources so as to attain maximum gross margins were reduced to a partitioning and linear programming problem. The resulting manpower partitioning technique and optimization program can be used by agricultural equipment industry managers to answer important questions concerning business strategies. The function and structure of agricultural dealerships was explored so as to define the employees involved and their job functions. A basic organizational chart for category B-C dealerships was developed with the aid of the input of many industry managers. Since this was the first study of its kind in the agricultural equipment industry, it was necessary to correspond and interview with industry personnel to establish what the rows and the columns of the linear program would be so the gross margin could be maximized through optimizing resources. A sample of Indiana dealers was surveyed to gather data to aid in establishing coefficients and constraints for the linear programmed optimization. Based on the data obtained, a partitioning technique was used to establish where the man-hours of a dealership are spent. Employees were classed according to the various job functions they performed. All man-hours available were assigned to their proper function in the line organization chart which was developed. This partitioning technique helped establish constraints for the linear program. In the review of over 600 sales with dealer principals and salesmen, data were collected for further aid partitioning. Man-hours were divided into hours which resulted in sales and hours which did not result in sales. A new set of ratios and guides were developed for planning and measuring dealership performance. Using a series of two-way analysis of variance techniques, it was shown that the type of products being sold and the time of year have effects on the coefficients and constraints needed in the linear programming model. This resulted in seasonally adjusted coefficients for the Dealer Input Optimization Model (D.I.O.M.). With the data from the survey, a multiple regression model was also formulated for predicting annual unit sales of salesmen based on the salesmans' age, years experience, education, and exposure to sales training. The R('2) value of this model is .7357. The error of prediction of sales units by salesmen factors is reduced by 73.57%. The resultant values of some of the coefficients developed for the optimization programs were adjusted for economic conditions. A predictive model utilizing past dealer performances and market share, was developed to establish adjusted values. This was accomplished with a multiple regression technique. Hence, the D.I.O.M. coefficients can be adjusted as economic conditions might change. The three dealer examples utilizing the D.I.O.M. techniques illustrate the potential for improving dealership gross margins by testing business strategies before actually putting them into "real world" practice.

Degree

Ph.D.

Subject Area

Agricultural engineering

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