Lot sizing in a production system with rework and product deterioration

Producing new and recovering defective products often takes place on a common facility, with these activities carried out in lots. Consequently, there is a necessity to coordinate the production and rework activities with respect to the timing of operations and also regarding appropriate lot sizes for both processes while completely satisfying a given demand. Thereby, it has to be taken into account whether the state of defective items may change in the course of time while they wait to be reworked. Such a deterioration of reworkable goods can result in increasing rework time and rework cost per unit. In this paper an EPQ model which addresses all of these aspects is presented. Considering set-up and inventory holding costs as well as set-up times, optimization algorithms are developed covering different planning situations. Closed-form results for optimal lot sizes can be obtained and exploited for new analytical insights into coordinated lot sizing in the case of returns and product deterioration.     

Lot-sizing for a single-stage single-product production system with rework of perishable production defectives

We consider a single-stage single-product production system. Produced units may be non-defective, reworkable defective, or non-reworkable defective. The system switches between production and rework. After producing a fixed number (N) of units, all reworkable defective units are reworked. Reworkable defectives are perishable or can become technologically obsolete. We assume that the rework time and the rework cost increase linearly with the time that a unit is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using this expression, the optimal value for N can be determined numerically. Moreover, it is easy to perform a sensitivity analysis, as we illustrate. RID="*" ID="*"The research of Dr. Ruud H. Teunter has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research presented in this paper is part of the research on re-use in the context of the EU sponsored TMR project REVersed LOGistics (ERB 4061 PL 97-5650) in which take part the Otto-von-Guericke Universitaet Magdeburg (D), the Erasmus University Rotterdam (NL), the Eindhoven University of Technology (NL), INSEAD (F), the Aristoteles University of Thessaloniki (GR), and the University of Piraeus (GR). We thank the anonymous referees for their many helpful comments. Correspondence to: R. H. Teunter