A Branch and Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching
We study the parallel machine scheduling problem to minimize the sum of the weighted completion times of the jobs to be scheduled (problem Pm||SwjCj in the standard three field notation) We use the set covering formulation that was introduced by van den Akker et al. (1999) for this problem, and we improve the computational performance of their branch and price (B&P) algorithm by a number of techniques, including a different generic branching scheme, zero suppressed binary decision diagrams (ZDDs) to solve the pricing problem, dual price smoothing as a stabilization method, and Farkas pricing to handle infeasibilities. We report computational results that show the effectiveness of the algorithmic enhancements, which depends on the characteristics of the instances. To the best of our knowledge, we are also the first to use ZDDs to solve the pricing problem in a B&P algorithm for a scheduling problem.