Branch-and-bound algorithms for scheduling in an m-machine permutation flowshop with a single objective and with multiple objectives

This paper presents branch-and-bound algorithms developed for an m-machine permutation flowshop to minimise the maximum weighted flowtime/maximum weighted tardiness/maximum sum of weighted flowtime and weighted tardiness/maximum sum of weighted flowtime, weighted tardiness and weighted earliness of a job, where each of the objectives is considered separately. A job-based bound, integrated with a machine-based bound, on the completion time of every unscheduled job by considering each of these objectives is developed, and the overall lower bound on a given objective at a given node in the branching tree is obtained by solving a bottleneck assignment problem. The proposed algorithms are evaluated by solving problems of various sizes, and some of these branch-and-bound algorithms (with the consideration of the maximum flowtime/the maximum tardiness) are compared with the existing algorithms available in the literature. This paper also presents the development and computational performance evaluation of a multi-objective branch-and-bound algorithm which can handle various combinations of objectives involving the sum of/maximum weighted flowtime, weighted tardiness and weighted earliness of jobs. [Received: 16 November 2008; Revised: 31 July 2009; Accepted: 28 March 2010]