Single-machine batch scheduling minimizing weighted flow times and delivery costs

This paper addresses scheduling a set of jobs on a single machine for delivery in batches to one customer or to another machine for further processing. The problem is a natural extension of that of minimising the sum of weighted flow times, considering the possibility of delivering jobs in batches and introducing batch delivery costs. The scheduling objective adopted is that of minimising the sum of weighted flow times and delivery costs. The extended problem arises in the context of coordination between machine scheduling and a distribution system in a supply chain network. Structural properties of the problem are investigated and used to devise a branch-and-bound solution method. For the special case, when the maximum number of batches is fixed, the branch-and-bound scheme provided shows significant improvements over an existing dynamic-programming algorithm.