A Probabilistic Inventory Model with Setup Cost and Decomposed Period of Holding Cost for the Optimization of Grain Storage Quantity

The classical single period s –S policy probabilistic inventory model with setup cost, popularly known as the Newsvendor or Newsboy model has evolved over time. In this study, we addressed the problem of determining the optimal grain storage quantity for grain storage business enterprise with setup cost and decomposed period of holding stock. Modifications of the classical newsvendor model in the development of the probabilistic inventory model was adopted. Model parameters were determined from data based on expert opinion of small scale rice paddy storage traders in Makurdi, Nigeria and sensitivity analyses were performed for uniform and exponential sale distributions for comparative purpose. It was recommended that, traders with uniformly distributed sales between 1.0 and 1.5 tons (mean = 1.25 tons) would be required to store an optimal quantity of 1.0 ton of rice paddy during the period, while, those with exponential sale distribution with mean 1.25 tons, would require an optimal storage quantity of 4.0 tons. Furthermore, traders who wish to expand their business by ten times its present storage capacity of say 1.0 tons, should prepare to incur a shortage cost of N7000.00 and N116, 824.94 respectively for a uniform and exponentially distributed sale. For a storage capacity of 55 tons, they should expect a shortage cost of N115, 000.00 for a uniformly distributed sale and N57, 432.45 for an exponentially distributed sale. The study concludes that the probabilistic inventory model formulated is flexible and adaptable for any tractable distribution function of sales units and for the prediction of future shortage costs.