AbstractIn most of the past research on scheduling, it is conventional to model machine deterioration by decreasing production speed over time. However, as is observed, there is a fair number of scenarios in practice where deterioration has a little impact on machine speed but a great impact on production accuracy and a machine is unusable unless it has been calibrated recently. In this paper, we consider a single‐machine short‐term scheduling issue in distributed production systems where the engineer calibrates the machines in a round‐robin manner. The objective is to minimize total job completion time, which is a popular criterion indicating total holding or inventory cost. We consider two cases of the problem and show that one of them can be solved optimally by providing an extended shortest processing time first rule. As for the other case, which is intractable, we propose a polynomial‐time approximation scheme based on the extended rule and an exchange procedure. Computational experiments show that the proposed polynomial‐time approximation scheme is very promising even if limited number of exchangeable jobs is allowed.