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

**Series:** 2009-03, Preprints

- MSC:
- 90B30 Production models
- 90B06 Transportation, logistics

**Abstract:**

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.

**Keywords:**

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)