05711966

j

05711966 Toksari, M.Duran Oron, Daniel G\"uner, Ertan Some scheduling problems with past sequence dependent setup times under the effects of nonlinear deterioration and time-dependent learning. RAIRO, Oper. Res. 44, No. 2, 107-118 (2010). 2010 Cambridge University Press, Cambridge; EDP Sciences, Les Ulis EN scheduling single machine past sequence dependent (p-s-d) setup times time-dependent learning effect deterioration jobs Zbl 1137.90498

doi:10.1051/ro/2010009

Summary: This paper studies scheduling problems which include a combination of nonlinear job deterioration and a time-dependent learning effect. We use past sequence dependent (p-s-d) setup times, which is first introduced by {\it C. Koulamas} and {\it G. J. Kyparisis} [Eur. J. Oper. Res. 187, No.~3, 1045--1049 (2008; Zbl 1137.90498)]. They considered a new form of setup times which depend on all already scheduled jobs from the current batch. Job deterioration and learning co-exist in various real life scheduling settings. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and a function of the total normal processing time of jobs scheduled prior to it. The following objectives are considered: single machine makespan and sum of completion times (square) and the maximum lateness. For the single-machine case, we derive polynomial-time optimal solutions.