ABSTRACT
A working inventory model is developed to incorporate the partial back ordering inventory with references to the back ordering inventory model by Jonah and Chukwu. The re-order point models of maximum expected cost and service level approach were also established. Data, covering the demand, set-up cost, and the Holding cost were obtained from the Champion Breweries Plc, other related data were estimated. These enabled the application of the models to obtain, the review period, (T) the fill rate (F), the stock-out (S) and finally the order quantity (Q). It was found and could be recommended that a quantity (Q) of 285022 tons of plan sorghum be placed bi-ennialy with a lead time of four (4) weeks. At a time the stock level is expected to be at 58.746 tons.
Introduction
Various definitions have been given by different authors to inventory management. Black [1] described inventory as a buffer between supply and demand. Jonah et al [2] described it as stock of goods or material awaiting delivery or dispatch. While Monks [3] described it as stock of goods or item held for future use. From the foregoing one can see that good inventory management in a firm would lead to greater profits, minimized losses, greater customer satisfaction, stabilized employment, enhanced product quality and other latent benefits of inventory. Failure to meet demand in any company usually compromises customer satisfaction and attracts high cost that characterizes emergency production. Efficient management of inventory system is therefore very critical in the operations of any firm. Black [1] outlined the basic benefits of inventory management to the customer as off-the-shelf availability of products while to the management as reduced tied-up investment capital on inventory, reduced operating cost and carrying cost associated with warehousing and reduction in the accruing obsolescence of product. From observations it can be said that a lot of failed investments did so as a result of inefficient inventory management.In this work our emphasis is on backordering. As Fisher [4] observes, there may be some economic reasons for a company to decide not to satisfy all demand, but rather lose some sales in the interest of the company. We consider a situation where rather than accumulating a lot of buffer stocks and attracting spoilage, some stocks can be back-ordered, some lost and sufficient costumer and company satisfaction achieved.