6. Set-up cost per production run or procurement cost is C. 7. Inventory carrying cost is C = CI, where is the unit cost and I is called inventory carrying cost expressed as a percentage of the value of the average inventory This fundamental situation can be shown on an inventory-time diagram, (Fig. 4.7) with Q on the vertical axis and the time on the horizontal axis. The total time period (one year) is divided into n parts. Quantity A Time x8 The most economic point in terms of total inventory cost exists where, Inventory carrying cost = Annual ordering cost (set-up cost) Average inventory = 1/2 (maximum level + minimum level) = (Q + 0)/2 = Q2 Total inventory carrying cost = Average inventory x Inventory carrying cost per unit i.e., Total inventory carrying cost = 0.2 x , QC2 ...(1) Total annual ordering costs = Number of orders per year x Ordering cost per order i.e., Total annual ordering costs = (DQ) x C = (D/QC; ---(2) Now, summing up the total inventory cost and the total ordering cost, we get the total inventory cost C(Q). i.e., Total cost of production run = Total inventory carrying cost + Total annual ordering costs CIQ) = QC,/2 + (D/QC (cost equation) ...(3) But, the total cost is minimum when the inventory carrying costs becomes equal to the total annual ordering costs. Therefore, QC/2 = (D/QC or QC = (2D/QC or Q = 2CDC 2C.D or Q= 2CD i.e., Optimal quantity (EOQ), Q. = VC D Optimum number of orders, (N) = ...(5) Q 365 1 Q Optimum order interval. () = in days = in years or - N. N ...(6) D Average yearly cost (TC) = 2CDC, ...(7) ILLUSTRATION 4: An oil engine manufacturer purchases lubricants at the rate of Rs. 42 per piece from a vendor. The requirements of these lubricants are 1800 per year. What should be the ordering quantity per order, if the cost per placement of an order is Rs. 16 and inventory carrying charges per rupee per year is 20 paise