Influence of lot size and planned lead time on service level and inventory for a single-stage production system with advance demand information and random required lead times

In this paper a single‐stage make‐to‐stock production system with advance demand information and random required lead times is investigated which produces different items with item specific lot sizes and planned lead times. Stochastic modeling is applied to investigate the influence of the interrelated planning parameters lot size and planned lead time on the key figures service level and inventory. The interrelation between the planning parameters is implemented with an endogenous production lead time distribution which depends on the lot size. Furthermore, both planning parameters lead to a pre‐production on stock either anonymous (lot size) or of known customer orders (planned lead time). Most analytical studies in this field either focus on planned lead time optimization, assuming single item processing or predefined production order processing distribution, or on the optimization of production lot sizes, neglecting the planned lead time effect. The main contribution of this paper is that it provides a simultaneous treatment of these two planning parameters linked to an endogenous production lead time. Analytical results enable the numerical optimization of both planning parameters to reach a service level constraint with minimum overall inventory and can, e.g., be applied to discuss the effect of customer required lead time variance on optimal planning parameters. Numerical study results indicate that for moderate service level objectives, optimal lot sizes are near the production lead time minimizing lot size. Furthermore, the results show that higher lot sizes can reduce the service level for predefined planned lead time values.