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Among the various inventory systems, the stations in series is an interesting one. There may be a number of nodes in between the starting point or node and the end point or final node. The production process starts at the first node and the finished products are at the last node. The output of the previous node happens to be the input for the next. Using this concept a model with two machines M1 and M2 in series are considered and there is an inventory of semi finished products in order to keep uninterrupted supply to the machine at the end point. This is due to possibility of breakdown of the machine at the first node. In this paper the optimal reserve inventory between the two machines is obtained assuming that the breakdown duration of M1 is a random variable follows the first order statistic. Similarly, this problem can be extended to the case of three machines in series and in such a case the reserve S1 is the quantity of semi finished product generated by M1 and S2 stands for the quantity of semi finished product by M2. The optimal size of the reserves S1 and S2 are obtained under the assumption that the breakdown duration of the first machine M1 is a random variable distributed as first order statistic.

Some Applications of Order Statistics in Inventory Control