Motivated by real life, we introduce a new inventory model for spare parts where we explicitly take delivery time requirements into account. In this single-echelon, multilocation network, demand of a customer can be satisfied from multiple warehouses, but only if the customer can be reached from a warehouse within a time limit that is specified in the service contract of the customer. A delivery to a customer from a warehouse other than the closest one is referred to as a lateral transshipment. We develop a fast and accurate approximate algorithm to evaluate the performance of the network under given base stock levels and propose a fast and effective heuristic to set base stock levels. Numerical experiments show that planning with lateral transshipments can lead to cost savings up to 47% when compared to planning without lateral transshipments. Furthermore, we show the importance of taking lateral transshipments into account when designing a spare parts network