PERT scheduling with convex cost functions

Authors:
Philippe Chrétienne;Francis Sourd
Affiliations:
Lab. LIPG, LIP6, Université Pierre et Marie Curie, Case Courrier 169, 4, Place Jussieu, 75252 Paris, Cedex 05, France;Lab. LIPG, LIP6, Université Pierre et Marie Curie, Case Courrier 169, 4, Place Jussieu, 75252 Paris, Cedex 05, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

This paper deals with the problem of finding a minimum cost schedule for a set of dependent activities when a convex cost function is attached to the starting time of each activity. A first optimality necessary and sufficient condition bearing on the head and tail blocks of a schedule is first established. A second such condition that uses the spanning active equality trees of a schedule leads to design a generic algorithm for the general case. When the cost function is the usual earliness-tardiness linear function with assymetric and independent penalty coefficients, the problem is shown to be solved in O(n max{n,m}). Finally, the special cases when the precedence graph is an intree or a family of chains are then also shown to be solved by efficient polynomial algorithms.