Inventory Control- Insensitivity of Total Cost near Optimum

You must have studied the famous EOQ (Economic Order Quantity) formula—

EOQ = Sqrt (AD/ VR) where Sqrt means square root of, A = Ordering cost/ order, D = total demand or consumption or requirement, V = unit cost of the item and R = rate of inventory carrying cost. This is a deterministic model because all these variables are assumed to be certain.

EOQ is economic order quantity because, if this quantity is ordered in every order of the item then the total cost is minimum. If you order for lesser quantity than EOQ then you will have to order more number of times to meet the same demand D, thus increasing one component of the total cost. If you order for more quantity than EOQ, then inventory level will become higher and so the inventory carrying cost will increase. The total of these two costs i.e. ordering cost and inventory carrying cost is minimum if EOQ is used as order quantity.

You know that if values of A, D, V and R are known then you substitute the values in the formula to get EOQ. But have you thought how the value of these variables is obtained? The total demand or requirement or consumption (D) may be obtained by using suitable forecasting technique. Ordering cost/ order (A) may be obtained by using previous data. Similarly you may analyse the data of various components of inventory carrying cost to get the value of R. But all these cannot be considered as deterministic. No forecasting technique can forecast with certainty what the demand would be. Then, how can this formula be used in a real life scenario? And what sense it will make to have a data on EOQ where all the variables used in computation are likely to change? Estimating the value of R, A and D involves cost and one cannot keep doing it before every order.

But there is a general characteristic of optimum solution in every field. The performance becomes insensitive to changes in effort near the optimum level. If you see the graph between Total Cost and Order Quantity, you find that the curve is flat near EOQ. It means that if you change the order quantity but keep it near the EOQ value then the minimum or optimum total cost will remain almost same. A relatively larger change in order quantity will change the total cost very little if the order quantity is close to EOQ. But if you operate away from EOQ, then a small change in order quantity can bring a big change in total cost. That is why if a good student is performing much below his optimum level then a small improvement in effort can bring big improvement in performance. But once he reaches closer to his optimum level he needs bigger effort to bring improvement in performance.

In inventory model, insensitivity plays a very important role. It permits you to make errors in estimation of A, D, V and R as long as you use EOQ and try to be near the optimum. These errors will not be affecting the total cost much so you can afford to use simpler methods in estimation. But if you operate away from the optimum level which you will if scientific management techniques are not used, then the total cost will be very sensitive to order quantity and error in estimation can adversely affect the total cost drastically.

Hence, in spite of all the possibilities of uncertainty, errors etc. this deterministic model is of immense use in keeping the total cost near the minimum possible level. Uncertainty and error in estimation factors are taken care by building system of automatic response to these in the method of inventory control itself. This will be discussed in some other article.

Sometimes we hear an Inventory Manager saying ‘whenever the current stock goes below some figure say 100, we order for the item a quantity equivalent to last 3 months consumption and this method works fine for us’. There is no harm in agreeing to him on similar statements. In fact it is not necessary to do any complex mathematical modeling and computation to reach to an optimum decision. Concept of optimization techniques can be built in applications in much simpler ways. We will discuss this too in some other article.