Introduction to Stochastic Processes and Simulation

3Inventory Management

CONCEPTS DISCUSSED IN THIS CHAPTER.– We discuss the problem of inventory management initially in a general sense, principally so we can identify the notations and clarify the definitions.

Then, we look at a very popular analytical model, Wilson’s model, with three sets of assumptions: 3.1, 3.2 and 3.3.

Finally, we discuss additional considerations on the guarantee of safety and quality.

Recommended reading: [BOU 16, FAU 79, PHE 77].

3.1. General

Do you remember learning about the problem of a leaking bath in primary school? The water flows through a hole and we have to periodically open the tap to compensate for leakage. This is actually a problem of inventory management.

It is a more realistic problem in commercial enterprises that sell items to customers. These items are stored in a location so customer demand can be met. Of course, the stock has to be replenished to avoid shortages of items. There can, however, be problems if the replenishment does not arrive in time or if the quantity to be replenished is incorrectly calculated. Demand drives a virtually continuous flow stream of items. Replenishment is a generally discontinuous supply flow.

DEFINITION.– An inventory is a set of items (people, goods, etc.) stored in a warehouse, subject to an input or supply flow, and an output or flow stream.

This definition is illustrated in Figure 3.1.

Figure 3.1 ...