Abstract

Order fulfilment systems are forced to manage a highly volatile customer demand consisting of low-volume orders effectively and efficiently while simultaneously meeting customer-required, short order deadlines. Hopp and Spearman (2004) provide three buffer types - inventory buffer, time buffer, and capacity buffer - to handle the volatile workload in production systems. These buffer types also provide several potentials for workload balancing in order fulfilment. In this thesis, we combine the potentials of time buffer and capacity buffer to develop and analytically investigate the Strategy of Levelled Order Release to balance workload in multi-stage, stochastic order fulfilment systems with customer-required order deadlines over time on a tactical level. The contribution of this thesis is three-fold: We develop (1) a workload balancing concept, the so-called Strategy of Levelled Order Release, (2) a discrete-time analytical model for performance analysis, and (3) an algorithm for capacity planning under performance constraints in multi-stage, stochastic order fulfilment systems with levelled order release and customer-required order deadlines.

The Strategy of Levelled Order Release is characterised by (1) a fixed capacity reserved for order processing in each time period, and (2) an order processing according to ascending due dates in each time period. In this way, the time buffer of each order between its time of arrival and its deadline is used to balance the variability of the customer demand. The remaining variability is compensated by using the capacity buffer depending on the performance requirements of the customers. The developed analytical model for performance analysis of multi-stage, stochastic order fulfilment systems with levelled order release and customer-required order deadlines models system behaviour of such order fulfilment systems as a discrete-time Markov chain. It calculates multiple stochastic and deterministic, system- and customer-related performance measures of order fulfilment systems based on the limiting distribution of the Markov chain. These performance measures, such as system throughput, service level, utilisation, number of lost sales, and time buffer and backlog duration of a completed order, enable a comprehensive and exact performance analysis of multi-stage, stochastic order fulfilment systems with levelled order release and customer-required order deadlines. The relationship between the provided capacity and the performance that is achieved with this capacity cannot be specified by a mathematical equation, but it is given by the analytical model. Thus, the decision problem of capacity planning in multi-stage order fulfilment systems with performance requirements is a blackbox optimisation problem. The problem-specific configurations of the blackbox optimisation algorithms Mesh Adaptive Direct Search and Surrogate Optimisation Integer enable a target-oriented determination of the minimum required, process-specific capacity to meet any performance requirement of the customers that is specified based on one or multiple performance measures of the order fulfilment system.

Numerical studies on the performance evaluation of the Strategy of Levelled Order Release show that one can achieve significantly higher values of α- and β-service level when using the Strategy of Levelled Order Release instead of First come first serve in order fulfilment systems with a utilisation higher than 0.6. Furthermore, the total required capacity to guarantee a predefined α-service level in the order fulfilment system when using the Strategy of Levelled Order Release is at most as high as the one when using First come first serve.