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

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Abstract

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.

Original languageEnglish
Pages (from-to)282-287
Number of pages6
JournalSIAM Journal on Control and Optimization
Volume18
Issue number3
DOIs
StatePublished - 1980

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