Optimal System Allocations with Penalty Costs

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

Management Science, 1976, vol. 23, issue 4, 399-403

Abstract: We have N stages to sequentially construct I successful components. At each stage, we allocate a certain amount of money for the construction of a component. If y is the amount allocated, then the component constructed will be a success with probability P(y), where P is a continuous nondecreasing function satisfying P(0) = 0. After each component is constructed, we are informed as to whether or not it is successful. If, at the end of the N stages, we are i components short, then a final penalty cost C(i) is incurred. The problem is to determine at each stage how much money to allocate so as to minimize the total expected cost (construction cost plus penalty cost) incurred. The major result is that if C(i + 1) - C(i) \le C(i + 2) - C(i + 1), and if y n (i) denotes the optimal value to allocate when i components are needed with n stages remaining, then y n (i) is nondecreasing in i and nonincreasing in n.

Date: 1976
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.23.4.399 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:23:y:1976:i:4:p:399-403

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().