Discrete-time analysis of levelled order release and staffing in order picking systems

Order picking systems are confronted with a volatile demand and short delivery time requirements. Manufacturing companies face the increasing variability requirements with Heijunka-levelling, one method of the Toyota Production System. The objectives of this publication are to develop a levelling concept for order picking systems, to analyse its performance based on a discrete-time analytical model and to develop a staffing algorithm determining the required workforce level in an order picking system with levelled order release. The levelling concept for order picking systems results from the existing models of Heijunka-levelling in the literature, which are adopted and expanded regarding the specific requirements of order picking systems. The order picking system with levelled order release is depicted as a discrete-time Markov chain. To analyse its performance, we derive several performance measures, such as service level, backlog duration and system utilisation, from the steady-state distribution of the Markov chain. The s taffing a lgorithm i s a binary search algorithm based on the Markov chain. The models developed in this publication enable a quantitative evaluation of the impact of several system parameters, such as variability of customer demand, workforce level and traffic intensity, on the performance measures of the order picking system. Furthermore, the staffing algorithm determines the workforce level which is required to guarantee a certain system performance, such as a service level of 99%, in an order picking system with levelled order release. By comparing levelled order release to FCFS-based order release strategies in a numerical example, we show the benefits of levelled order release.