Newsboy problem

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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, LaTeX: q, with probability function LaTeX: P(q). 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 LaTeX: P(q) = probability that demand equals LaTeX: q. 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:

  1. LaTeX: s = inventory level at which an order is placed;
  2. LaTeX: S = 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 LaTeX: \ge s;
Order LaTeX: S-s if there are s papers on hand and LaTeX: s < S.

The significance of this problem is that it was used to introduce the notion (and optimality) of an LaTeX: (s, S) policy in inventory theory.

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