Christoph H. Glock
and
Mohamad Y. Jaber 

ABSTRACT

The paper studies a production system with two producing stages, where the first stage supplies items of a product to the second stage, which in turn processes the items and subsequently transfers it to another stage or to the final customer. A buffer stock is located between the two stages where the items received from stage 1 are stored until they are processed on stage 2. Since setup costs are connected with every restart of a production facility, the questions of how long each stage should produce and when and how long each stage should be interrupted arise. In contrast to earlier models, which often assumed that the production rate remains constant over time, the paper assumes that learning and forgetting effects occur on both stages. Consequently, complex interdependencies arise since interruptions in the production process influence inventory levels and the production rates. Since the parameters of the learning and forgetting effects may differ between the stages, the ratio of the production rates may vary over time since a production facility that is slower at the outset is likely to overtake an originally faster production facility due to a higher learning or a lower forgetting effect. The ratio of the production rates, in turn, is important for determining the run time of the production facilities, since the faster stage has to be interrupted more frequently to avoid excessive inventory build-up in the system or to give the slower stage enough time to refill the buffer stock. The paper studies these effects and develops strategies of how to exploit learning effects by simultaneously economizing on inventory and setup costs.