Openshop and flowshop scheduling to minimize sum of completion times

Abstract This paper deals with efficiently solvable special cases of openshop and permutation-flowshop scheduling where the objective function is minimum sum of completion times. Two O(mn) algorithms for openshop scheduling where all operations have equal processing times, are presented. The first constructs a no-wait schedule and the second a schedule where both criteria (sum of completion times and schedule length) take on their minimal values. For permutation-flowshop scheduling where processing times satisfy dominancy and/or ordered relations, SPT rules are proved to be optimal.