A newspaper is concerned with controlling the number of papers to be distributed to newstands. The cost of a paper varies (i.e., Sunday vs. daily), and the demand is a random variable, with probability function Unsold papers are returned, with no salvage value the next day, losing millions of dollars in the production cost. The demand for newspapers is a random variable, with probability function = probability that demand equals It is possible, however, for a newstand to order more papers the same day. There are holding and shortage (penalty) costs. The problem is to determine a reorder policy so as to minimize total expected cost. This problem was used to consider a reorder policy with a 2-parameter decision rule:
- = inventory level at which an order is placed;
- = inventory level to which to order.
Then, the decision rule to be employed is the following policy:
- Order nothing if the inventory of papers is
- Order if there are s papers on hand and
The significance of this problem is that it was used to introduce the notion (and optimality) of an policy in inventory theory.