Single-machine common due date total earliness/tardiness scheduling with machine unavailability

Kerem Bülbül 1 Safia Kedad-Sidhoum 2, 3 Halil Şen 4
1 Sabanci University [Istanbul]
2 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
3 RO - Recherche Opérationnelle
LIP6
4 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine as to minimize the total deviation of the job completion times from an unre-strictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put a serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and NP−complete cases. Pseudo-polynomial dynamic programming algorithms are devised for NP−complete variants in the ordinary sense.
Keywords : Semi-resumable NP−complete Dynamic programming Non-resumable Resumable Single-machine Common due date Earliness/tardiness Machine unavailability Unrestrictive Maintenance
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Kerem Bülbül, Safia Kedad-Sidhoum, Halil Şen. Single-machine common due date total earliness/tardiness scheduling with machine unavailability. Journal of Scheduling, Springer Verlag, 2019, 22 (5), pp.543-565. ⟨10.1007/s10951-018-0585-x⟩. ⟨hal-02470377⟩

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