Segment routing in traffic engineering is a relatively new technique in the field of networking. Segment routing is a simpler form of source routing where the seg-ments that a packet will follow are written in the header of the packet. Segments are identified using Segment IDs known as SIDs. Node SIDs and Adjacency SIDs identify different types of segments: The first one identifies the shortest-path segments and the latter identifies the non-shortest direct links between two nodes. The ingress routers direct packets towards their destinations using Equal Cost Multiple Paths (ECMPs). Recently, several solutions have been proposed for traffic engineering using segment routing. The objective in these formulations is to minimize the Maximum Link Utilization (MLU) in the network. These Mixed Integer Linear Programming (MILP) based formulations do not consider all possible paths and the Running times increase beyond a reasonable value as the number of nodes and segments increase. Considering these short-comings, we introduce new formulations and algorithms for the problem. To incorporate all segment pairs into the formulation, a path-based model K-MMILP is introduced. Moreover, a flow-based model, K-MsMILP is proposed. These formulations in-corporate all Adjacency SIDs, Node SIDs, and ECMPs. Furthermore, the effect of restricting the maximum path length followed by the flow on MLU and Running time is analyzed. The proposed flow-based formulation produces optimum results for all topologies considered for each of the 20 instances using a maximum of 3 segments per end-to-end path. It also significantly reduces the Running time for all topologies. For instance, for the 16-node German Network, the Running time is reduced by a factor of 14.9 times on the average. Moreover, for the 27-node European network, the older formulation could not produce optimum results within 24 hours while 3-MsMILP produced results in 2268 seconds on average.