Load-dependant production/inventory planning with uncertain demands

Assemble-to-order (ATO) systems enable manufacturing firms to be cost-effective and at the same time responsive to changing customer orders. In this paper, we study an Assemble-to-order (ATO) system, where raw materials are released into a capacitated manufacturing stage. Inventory of produced components is kept in stock ready for final assembly once specific orders for products are received. The lead-time of the assembly stage is very small compared to the lead-time of the manufacturing stage and no inventory of final products is kept. An important planning issue is to find an optimal trade-off between capacity utilization and components inventory holding cost with the aim to meet uncertain demand of end products. When considering customer satisfaction, demand uncertainty becomes a complicating factor requiring safety stocks. Consequently, additional releases into the manufacturing stage are required, increasing further the workload, and resulting in longer lead-times. In this paper, we formulate two integrated production/inventory planning models using clearing functions while considering demand uncertainty. In the first model, we assume that demand distributions are known and propose a chance constrained formulation. The case of normally distributed demands is considered leading to a tractable formulation. In the second model, we consider the case of unknown demand distributions and use a robust optimization approach. The proposed models are linear programs that provide safe production and inventory plans. We compare the presented models using a real case study from the literature.