Stochastic modelling in production planning: Methods for improvement and investigations on production system behaviour

In this thesis models for production planning are developed and performance indicators are analysed to investigate production system behaviour. Existing literature is extended by considering uncertainty of customer required lead time and processing times and by increasing the complexity of multi-machine multi-items production models. Results are on the one hand a decision support system for determining capacity and the further development of the production planning method Conwip and on the other hand the JIT-intensity has been developed and the effects of dispatching rules on production lead time are analytically proven. The decision support system for determining the capacity provided is based on the capacity demanded, whereby process and/or customer uncertainty can be included. The production planning method Conwip has been extended by including safety stock and by extending the inventory constraint to sum of WIP (Work-In-Process) and FGI (Finished Goods Inventory) and not only WIP. JIT-intensity measures the degree of fulfilment of the "Seven Zeros" in a production system. A high JIT-intensity leads to an increase of excess capacity and to a reduction of utilisation and means that the production system follows the customer demand fluctuations without any "Seven Zeros" relevant losses. Consequently, management has the opportunity to increase sales by selling more customer required items or to reduce excess capacity. Finally, the effects of dispatching rules on average production lead time are investigated. An analytic relationship between "processing time weighted average production lead time" and covariance between processing time and queuing time has been identified. This relationship has been proven analytically for single-machine production systems. It has been found out that the "processing time weighted average production lead time" for a multi-machine production system is not invariant of the applied dispatching rule.