Production planning with load-dependent lead times and safety stocks for a single product

Abstract

Queuing models have demonstrated the nonlinear relationship between resource utilisation, which is determined by production planning decisions, and lead times. Both production planning decisions and safety stock levels are driven by lead times, and are thus tightly interrelated. However, production planning and safety stock calculations have generally been carried out separately. We propose a production planning model for a single–stage single–product system that integrates release planning and safety stock considerations. Concave clearing functions are used to capture the nonlinear relationship between resource utilisation and lead times, while chance constraints represent the need to plan inventories to achieve desired service levels. Extensive computational experiments indicate that the proposed model provides an excellent tradeoff between customer service and inventory costs.