Fundamentals of Supply Chain Theory, 2nd Edition

Chapter 4 Stochastic Inventory Models: Periodic Review

4.1 Inventory Policies

In this chapter and the next, we will consider inventory models in which the demand is stochastic. A key concept in these chapters will be that of a policy. A policy is a simple rule that provides a solution to the inventory problem. For example, consider a periodic‐review model with fixed costs (such as the Wagner–Whitin model) but with stochastic demands. (We will examine such a model more closely in Section 4.4.) One could imagine several possible policies for this system. Here are a few:

1. Every R periods, place an order for Q units.
2. Whenever the inventory position falls to s, order Q units.
3. Whenever the inventory position falls to s, place an order of sufficient size to bring the inventory position to S.
4. Place an order whose size is equal to the first two digits of last night's lottery number. Then, wait a number of periods equal to the last two digits of the lottery number before placing another order.

Now, you probably suspect that some of these policies will perform better (in the sense of keeping costs small) than others. For example, policy 4 is probably a bad one. You probably also suspect that the performance of a policy depends on its parameters. ¹ For example, policy 1 sounds reasonable, but only if we choose good values for R and Q.

It is often possible (and always desirable) to prove that a certain policy is optimal for a given problem—that no other policy (even policies that ...