Online scheduling problem of incompatible batch processing with deterioration effect and delivery time in the steel rolling process

As market competition intensifies, modern enterprises prioritize customer demands, leading to an increased emphasis on multi-variety and small-batch production. In this article, we study the online scheduling problem for incompatible batch processing with the deterioration effect to minimize the maximum delivery completion time in the billet rolling process, where the batch capacity and delivery capacity are unbounded. We assume that the processing time of job Jj is expressed as pj=aj(A+Bt), where A > 0, B > 0, t denotes the start time of job and aj > 0 represents the job’s processing deterioration rate. For such an online problem, we first prove that the lower bound of the problem is (1+Bamax)k, where k denotes the number of job families and amax represents the maximum deterioration ratio in job instance. Then we design an online algorithm Largest Delivery Time With Batch Processing and demonstrate that the competitive ratio of the algorithm is no more than 1+(1+Bamax)k. Finally, experiments on randomly generated instances prove that our algorithm is reasonable and effective.