Parallel-Batch Scheduling with Two Models of Deterioration to Minimize the Makespan

We consider the bounded parallel-batch scheduling with two models of deterioration, in which the processing time of the first model is pj=aj+αt and of the second model is pj=a+αjt. The objective is to minimize the makespan. We present O(n log n) time algorithms for the single-machine problems, respectively. And we propose fully polynomial time approximation schemes to solve the identical-parallel-machine problem and uniform-parallel-machine problem, respectively

Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan

We consider the problem of scheduling n deteriorating jobs with release dates on a single batching machine. Each job's processing time is an increasing simple linear function of its starting time. The machine can process up to b jobs simultaneously as a batch. The objective is to minimize the maximum completion time, i.e., makespan. For the unbounded model, i.e., b = [infinity], we obtain an O(n log n) dynamic programming algorithm. For the bounded model, i.e., b Scheduling Batching Deterioration Release dates Dynamic programming