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Integrated batch sizing and scheduling on a single machine

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Abstract

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.

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Abbreviations

K :

Number of customer orders

N :

Total number of batches

b :

Lower bound on batch size

B :

Upper bound on batch size

B i :

ith batch of schedule Ψ

d k :

Due date for customer order k

r k :

Total number units required by customer k

R k :

Cumulative requirement of the first k orders

β k :

Unit tardiness penalty for customer order k

π :

Cost of creating a new batch (setup cost)

S i :

Starting time of batch B i

C i :

Completion time of batch B i

\(q^{k}_{i}\) :

Quantity processed for order k in batch B i

q i :

Length of batch B i

f I (Ψ):

Total cost of schedule Ψ for instance I

T(n,r):

Tardiness cost of processing r units of a single order in n batches after its due date

f(n,r):

Total cost of processing r units of a single order in n batches after its due date

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Authors and Affiliations

  1. LIP6, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris Cedex 05, France

    Philippe Chrétienne, Öncü Hazır & Safia Kedad-Sidhoum

Authors
  1. Philippe Chrétienne
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  2. Öncü Hazır
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  3. Safia Kedad-Sidhoum
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Correspondence to Safia Kedad-Sidhoum.

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Chrétienne, P., Hazır, Ö. & Kedad-Sidhoum, S. Integrated batch sizing and scheduling on a single machine. J Sched 14, 541–555 (2011). https://doi.org/10.1007/s10951-011-0229-x

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  • DOI: https://doi.org/10.1007/s10951-011-0229-x

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