In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.

This paper addresses scheduling a set of weighted jobs on a single machine in presence of release date for delivery in batches to customers or to other machines for further processing. The problem is a natural extension of minimizing the sum of weighted flow times by considering the possibility of delivering jobs in batches and introducing batch delivery costs. The classical problem is NP-hard and then the extended version of the problem is NP-hard. The objective function is that of minimizing the sum of weighted flow times and delivery costs. The extended problem arises in a real supply chain network by cooperation between two layers of chain. Structural properties of the problem are investigated and used to devise a branch-and-bound solution scheme. Computational experiments show the efficiency of suggested algorithm for solving instances up to 40 jobs.

This paper considers the dynamic variant of single processor scheduling problem of minimizing total tardiness. In practice, it occurs when minimizing tardiness penalty. The problem is NP-hard; thus two heuristics were proposed. The utility of the proposed models was demonstrated through computational experiments and comparative analyses against existing solution methods and the Branch and Bound (BB) method. The results show that the proposed models yield effi-cient solutions and in most cases perform effectively better than the existing heuristics in the lit-erature.