Effect of limited capacity on optimal planning parameters for a multi-item production system with setup times and advance demand information

An analytical production/inventory model to optimise the planning parameters lot-size, safety stock and planned lead time is developed for a stochastic single-stage production system with multiple items and limited capacity. Based on queuing analysis, the influence of item specific lot-sizes on the production lead time distribution is modelled. Applying stochastic advance demand information, the expected values for finished-goods-inventory, backorders and service level are explicitly stated. Numerical optimisation is applied to solve the respective cost minimisation problem and a solution heuristic is developed to support this approach. A numerical study provides managerial insights concerning capacity limitation effects on the optimal planning parameters. Higher shop loads, i.e. tighter capacity constraints, are found to significantly increase optimal lot-size and optimal safety stock. Safety stock and planned lead time are substitutes, an increase of both leads to higher FGI and lower backorders, however, the specific trade-off depends on the demand information quality. A sensitivity analysis investigating other (non-) financial system parameters is conducted as well. The main contribution of this paper is that the interaction of different planning parameters, i.e. lot-size, safety stock and planned lead time, for different items is simultaneously studied for a capacity constrained production/inventory system.