Fast approximation algorithms for scheduling uniform parallel batch machines with inclusive processing set restriction

We address the problem on uniform parallel batch machines to minimize makespan where each job is restricted to a specific subset of machines, known as its processing set. Batch machines have diverse speeds and capacities. Each batch machine has the ability to concurrently process multiple jobs as long as the capacity allows. The length of a batch is defined as the largest length of all the jobs contained within it. We present fast approximation algorithms for inclusive processing set.