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Space division multiplexing elastic optical networks (SDM-EONs) are one of the most promising network architectures that satisfy the rapidly growing traffic of the internet. However, different from traditional wavelength division multiplexing (WDM)-based networks, the problems of resource allocation become more complicated because SDM-EONs have smaller spectrum granularity and have to consider several novel network resources, such as modulation formats and spatial dimensions. In this work, we propose an integer linear programming (ILP) model without space lane change (SLC) that provides theoretically exact solutions for the problem of routing, modulation format, space, and spectrum assignment (RMSSA). Moreover, to more efficiently solve our model which is difficult to solve directly, we propose three exact algorithms based on model decomposition and evaluate their performance via simulation experiments, and we find that two of our exact algorithms can solve the model effectively in small-scale instances.