Optimizing stock levels for rental systems with a support warehouse and partial backordering.

•We model a rental system with a support warehouse and partial backordering.•Useful upper bounds on optimal base stock levels follow by analyzing special cases.•A greedy algorithm using approximate evaluation leads to near-optimal base stock levels.•Existing methods for no backordering typically do not work well with partial backordering.•A limited partial backorder level can prevent the majority of lost demand in the system.