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Lot-Sizing for an Imperfect Continuous Production on Two Machines

by Gribkovskaia, I., Kovalev, S., Werner, F..

Series: 2009-03, Preprints

90B30 Production models
90B06 Transportation, logistics

We study the problem of planning the
production of new and recovery of defective units of the same
product. The product is assumed to be continuously
divisible. There are a main facility dedicated to
the original production and a facility dedicated to re-manufacturing
defective units coming from the main facility. Units fabricated on
the main facility are inspected for quality in batches. The quality
inspection requires some time and can be performed on-line or
off-line. After the inspection has been completed, defective units
of the inspected batch are transported to the re-manufacturing
facility. The transportation also requires some time. We
assume that the fraction of the defective units is the same in
each batch on the manufacturing facility and that the
re-manufacturing facility is perfect. Given a demand for good
quality units of the product and an upper bound K on the number of
batches, the problem is to find a sequence of batch sizes such that
the manufacturing cycle time is minimized. We suggest a linear
programming formulation, prove several properties of an optimal
solution, and finally develop an O(log K) time solution
algorithm. A similar per time unit cost minimization problem is
studied as well.

Production, Batching; Rework; Reverse Logistics

This paper was published in:
Omega, Vol. 38, No. 6, 522 - 527 (under the title: Batching for Work and Rework Processes on Dedicated Machines to Minimize the Makespan)