Approximation for Batching via Priorities

Abstract

We consider here the one-machine serial batching problem under weighted average completion. This problem is known to be $cal Ncal P$-hard and no good approximation algorithms are known. Batching has wide application in manufacturing, decision management, and scheduling in information technology. We give an approximation algorithm with approximation ratio of $2$; the algorithm is a priority algorithm, which batches jobs in decreasing order of priority. We also give a lower bound of $frac{2 +sqrt{6}}{4} approx 1.1124$ on the approximation ratio of any priority algorithm and conjecture that there is a priority algorithm which matches this bound. Adaptive algorithm experiments are used to support the conjecture. An easier problem is the list version of the problem where the order of the jobs is given. We give a new linear time algorithm for the list batching problem.