We study a system consisting of one repair shop and one stockpoint, where spare parts of multiple critical repairables are kept on stock to serve an installed base of technical systems. Part requests are met from stock if possible, and backordered otherwise. The objective is to minimize aggregate downtime via smart repair job scheduling. We evaluate various relevant dynamic scheduling policies, including two that stem from other application fields. One of them is the myopic allocation rule from the make-to-stock environment. It selects the SKU with the highest expected backorder reduction per invested time unit and has excellent performance on repairable inventory systems. It combines the following three strengths: (i) it selects the SKU with the shortest expected repair time in case of backorders, (ii) it recognizes the benefits of short average repair times even if there are no backorders, and (iii) it takes the stochasticity of the part failure processes into account. We investigate the optimality gaps of the heuristic scheduling rules, compare their performance on a large test bed containing problem instances of real-life size, and illustrate the impact of key problem characteristics on the aggregate downtime. We show that the myopic allocation rule performs well and that it outperforms the other heuristic scheduling rules.