On minimizing the weighted sum of quadratic completion times on a single machine

An efficient branch and bound method for solving single machine scheduling problems with quadratic penalty function is presented. In this kind of problem N jobs have to be sequenced on a single machine with the objective of minimizing the quadratic weighted sum of completion times. An improved bounding procedure based on criteria for ordering pairs of adjacent jobs in a sequence is developed together with an efficient node elimination procedure. Computational results show that this method performs better than existing ones