the major problem in inventory system

One issue is infrequent large orders vs. frequent small orders. Large orders will increase the amount of inventory on hand, which is costly, but may benefit from volume discounts. Frequent orders are costly to process, and the resulting small inventory levels may increase the probability of stock-outs, leading to loss of customers. In principle all these factors can be calculated mathematically and the optimum found.
A second issue is related to changes in demand (predictable or random) for the product. For example having the needed merchandise on hand in order to make sales during the appropriate buying season(s). A classic example is a toy store pre-Christmas. If one does not have the items on the shelves, one will not make the sales. And the wholesale market is not perfect. There can be considerable delays, particularly with the most popular toys. So, the entrepreneur or business manager will buy on spec. Another example is a furniture store. If there is a six week, or more, delay for customers to get merchandise, some sales will be lost. And yet another example is a restaurant, where a considerable percentage of the sales are the value-added aspects of food preparation and presentation, and so it is rational to buy and store somewhat more to reduce the chances of running out of key ingredients. With all these examples, the situation often comes down to these two key questions: How confident are you that the merchandise will sell, and how much upside is there if it does?
And a third issue comes from the view that inventory also serves the function of decoupling two separate operations. For example work in process inventory often accumulates between two departments because the consuming and the producing department do not coordinate their work. With improved coordination this buffer inventory could be eliminated. This leads to the whole philosophy of Just In Time, which argues that the costs of carrying inventory have typically been underestimated, both the