TY - JOUR

T1 - EFFICIENT ALGORITHMS FOR A SELECTION PROBLEM WITH NESTED CONSTRAINTS AND ITS APPLICATION TO A PRODUCTION-SALES PLANNING MODEL.

AU - Tamir, Arie

PY - 1980

Y1 - 1980

N2 - The following problem is considered. Given positive integers (n//1,. . . ,n//m) and an n//m multiplied by m matrix D with the property that the n//m elements in each column form a monotone sequence, find a set A of n//m elements of D whose sum is maximum, and such that for any j,j equals 1,. . . ,m, not more than n//j elements are chosen from columns 1,2,. . . ,j. An algorithm, solving the above problem in time O(m**2log**2n//m) is presented. The algorithm is applicable to a production-sales planning model with concave utilities. It is also demonstrated that the special case of equal columns is solvable in O(m**2) time.

AB - The following problem is considered. Given positive integers (n//1,. . . ,n//m) and an n//m multiplied by m matrix D with the property that the n//m elements in each column form a monotone sequence, find a set A of n//m elements of D whose sum is maximum, and such that for any j,j equals 1,. . . ,m, not more than n//j elements are chosen from columns 1,2,. . . ,j. An algorithm, solving the above problem in time O(m**2log**2n//m) is presented. The algorithm is applicable to a production-sales planning model with concave utilities. It is also demonstrated that the special case of equal columns is solvable in O(m**2) time.

UR - http://www.scopus.com/inward/record.url?scp=0019015598&partnerID=8YFLogxK

U2 - 10.1137/0318019

DO - 10.1137/0318019

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AN - SCOPUS:0019015598

SN - 0363-0129

VL - 18

SP - 282

EP - 287

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 3

ER -