Optimal Stocking Pattern of Chemical Fertilizers: An Application of the Waiting Time Model

Fertilizers are a crucial and vital input in crop production. 'Input dealer' is synonymously treated as 'Fertilizer dealer'. Given the high volume, high value of fertilizers, and the limitation of stocking space in relation to spurt in demand for fertilizers during growing season(s), the input dealers face the problem of deciding on optimal stocking pattern. This study addressed this crucial aspect considering the purchase pattern of different brands of fertilizers by farmers to determine the length of waiting time for fertilizer sale and optimal stocking pattern in Karnataka by using negative binomial distribution (NBD) and geometric distribution (GD). The retail purchase data (sales data) from the sale receipts of the retail outlet of Coromandel International Limited, Bada, Davangere, Karnataka, formed the database of the present study. The results indicated that NBD probability of purchase of fertilizer products varied from 0.35 to 0.62 depending upon the popularity of the fertilizer. The GD probability of purchase of any brand of fertilizer was 0.4, indicating that at least three farmers needed to visit the input dealer to get one unit of any fertilizer product sold. Both the NBD and GD were applied to find the optimal stocking pattern of fertilizers.