Note---A Node Elimination Procedure for Townsend's Algorithm for Solving the Single Machine Quadratic Penalty Function Scheduling Problem

In this note, a node elimination procedure has been suggested in case the two sequences obtained by using Townsend's (Townsend, W. 1978. The single machine problem with quadratic penalty function of completion times: A branch and bound solution. Management Sci. 24 (5) 530--534.) sufficient conditions for solving the single machine quadratic penalty function scheduling problem contain a subset J_r of r jobs in the first r positions. Numerical illustrations and computational experience has been given in the end.