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Unformatted text preview: t not sold; when
dj > qj , dj − qj is the amount of unmet demand.) The revenue from selling the products is pT s,
where p ∈ Rn is the vector of product prices. The proﬁt is pT s − cT r. (Both d and q are real
vectors; their entries need not be integers.)
You are given A, c, and p. The product demand, however, is not known. Instead, a set of K
possible demand vectors, d(1) , . . . , d(K ) , with associated probabilities π1 , . . . , πK , is given. (These
satisfy 1T π = 1, π 0.)
You will explore two diﬀerent optimization problems that arise in choosing r and q (the variables).
I. Choose r and q ahead of time. You must choose r and q , knowing only the data listed
above. (In other words, you must order the raw materials, and commit to producing the chosen
quantities of products, before you know the product demand.) The objective is to maximize the
II. Choose r ahead of time, and q after d is known. You must choose r, knowing only the
data listed above. Some time after you have ch...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid