A Stochastic Sequential Allocation Model

C. Derman, G. J. Lieberman and S. M. Ross
Additional contact information
C. Derman: Columbia University, New York, New York
G. J. Lieberman: Stanford University, Stanford, California
S. M. Ross: University of California, Berkeley, California

Operations Research, 1975, vol. 23, issue 6, 1120-1130

Abstract: This paper considers the following model, described in terms of an investment problem. We have D units available for investment. During each of N time periods an opportunity to invest will occur with probability p . As soon as an opportunity presents itself, we must decide how much of our available resources to invest. If we invest y , then we obtain an expected profit P ( y ), where P is a nondecreasing continuous function. The amount y then becomes unavailable for future investment. The problem is to decide how much to invest at each opportunity so as to maximize total expected profit. When P ( y ) is a concave function, the structure of the optimal policy is obtained (§1). Bounds on the optimal value function and asymptotic results are presented in §2. A closed-form expression for the optimal value to invest is found in §3 for the special cases of P ( y ) = log y and P ( y ) = y α , for 0

Date: 1975
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