caa a22 4500 44583854X CHVBK 20180317145337.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10951-011-0229-x doi (NATIONALLICENCE)springer-10.1007/s10951-011-0229-x Integrated batch sizing and scheduling on a single machine [Elektronische Daten] [Philippe Chrétienne, Öncü Hazır, Safia Kedad-Sidhoum] In this paper, we address the integrated batch sizing and scheduling problem. We consider a single machine which can handle at most one customer order at a time and for which the nominal production rate is the same for all the customer orders. Demand is deterministic, and all the orders are ready to be processed at time zero and must be delivered at a given due date. Each order can be satisfied from different batches. Upper and lower bounds on the size of the batches are considered. We seek a feasible schedule that minimizes the sum of the tardiness costs and the setup costs incurred by creating a new batch. We present some structural properties of the optimal schedules for both single-order and multiple-order problems and then propose dynamic programming algorithms based on these properties. Computational results that show the efficiency of the method are reported. Springer Science+Business Media, LLC, 2011 Batch sizing nationallicence Scheduling nationallicence Setup cost nationallicence Tardiness nationallicence Single machine nationallicence Dynamic programming nationallicence K : Number of customer orders nationallicence N : Total number of batches nationallicence b : Lower bound on batch size nationallicence B : Upper bound on batch size nationallicence B i : ith batch of scheduleΨ nationallicence d k : Due date for customer orderk nationallicence r k : Total number units required by customerk nationallicence R k : Cumulative requirement of the first k orders nationallicence β k : Unit tardiness penalty for customer orderk nationallicence π : Cost of creating a new batch (setup cost) nationallicence S i : Starting time of batch B i nationallicence C i : Completion time of batch B i nationallicence $q^{k}_{i}$ : Quantity processed for order k in batch B i nationallicence q i : Length of batch B i nationallicence f I ( Ψ ) : Total cost of schedule Ψ for instanceI nationallicence T ( n , r ) : Tardiness cost of processing r units of a single order in n batches after its due date nationallicence f ( n , r ) : Total cost of processing r units of a single order in n batches after its due date nationallicence Chrétienne Philippe LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut Hazır Öncü LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut Kedad-Sidhoum Safia LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut Journal of Scheduling Springer US; http://www.springer-ny.com 14/6(2011-12-01), 541-555 1094-6136 14:6<541 2011 14 10951 https://doi.org/10.1007/s10951-011-0229-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10951-011-0229-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chrétienne Philippe LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut NATIONALLICENCE 700 1- Hazır Öncü LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut NATIONALLICENCE 700 1- Kedad-Sidhoum Safia LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France aut NATIONALLICENCE 773 0- Journal of Scheduling Springer US; http://www.springer-ny.com 14/6(2011-12-01), 541-555 1094-6136 14:6<541 2011 14 10951 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer