Application of stochastic processes in areas like manufacturing

Concepts of queueing theory along with the knowledge of stochasticity of order and lead times is extensively used in areas like (i) Inventory Management, (ii) Production Planning and Control (PPC), (iii) Supply Chain Management (SCM) and other such related areas of manufacturing. In the context of this module, a manufacturing system denotes the whole gamut of operations like manufacturing, inventory, supply chain management, etc. We also know it includes other important concepts like scheduling, sequencing, etc., but we would not discuss the applications of stochastic processes in these areas, as it is already a part of our discussion under the module titled Application of stochastic processes in areas like scheduling. Hence this chapter would dwell into the use of stochastic process in inventory management/systems only.

In inventory management/system our aim is to effectively deal with an optimum level of stock of products so that one is able to meet the demand of goods required by the buyer(s) which is/are being supplied by the seller(s). In the real sense, the word inventory denotes the on hand stock of goods. It is likely that there may be instances when the total requirement of goods, is not met by the seller(s)/manufacturer(s) which results in shortage. These shortages are termed as back orders if the buyer(s) is/are willing to wait, else they are termed as lost sales, whereby the buyer(s) is/are not interested to wait for late delivery of the same after the agreed upon date of delivery as decide in the contract.

The quantum of goods which is the sum of inventory at hand plus the goods in order minus the back-order is known as system stock. For the convenience of the reader the schematic diagram of the flow of goods from manufacturer/supplier end to the customer's end is depicted in Figure 9.1. With respect to the figure it should be remembered that by using the word supplier and buyer we imply any two players in the system, and there may be instances where it may denote the manufacturer and distributor or the distributor and the retailer or even the distributor and the customer as the case may be.

Figure 9.1: Schematic layout of the typical Supply Chain involving different levels (echelons)