The single machine serial batch scheduling problems with rejection

We consider several serial batch scheduling problems with rejection. Each job is either processed on a single serial batching machine or rejected by paying a penalty. We analyze two models with rejection. The first model is to minimize the sum of the scheduling cost of the accepted jobs and the total penalty of the rejected jobs, where the scheduling costs are the total completion time, the makespan, the maximum lateness and the weighted number of tardy jobs, respectively. For the former two problems, we propose two polynomial time algorithms to solve them. For the last two problems, we derive efficient dynamic programming algorithms. The second model is to minimize the makespan, given an upper bound on the total rejection cost, we present a fully polynomial time approximation scheme.