An algorithm for insertion of idle time in the single-machine scheduling problem with convex cost functions

Authors:
Emerson C. Colin;Roberto C. Quinino
Affiliations:
Stricto Lato Consultoria Ltda. Rua Américo Brasiliense, 2171, cj. 207, CEP 04715-005, São Paulo and Dept. of Ind. Eng., Universidade de São Paulo, São Paulo, SP, Brazil;Department of Statistics, Universidade Federal de Minas Gerais, Av. Antônio Carlos, s/n, ICEX, CEP 31270-901, Belo Horizonte, MG, Brazil
Venue:
Computers and Operations Research
Year:
2005

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Abstract

This paper addresses the problem of optimally inserting idle time into a single-machine schedule when the sequence is fixed and the cost of each job is a convex function of its completion time. We propose a pseudo-polynomial time algorithm to find a solution within some tolerance of optimality in the solution space, i.e., each completion time will belong to a small time interval z within which the optimal solution lies. Letting H be the planning horizon and |J| the number of jobs, the proposed algorithm is superior to the current best algorithm in terms of time-complexity when |J| .