Nondiscriminatory transmission services are an essential requirement of open access and constitute a basic premise for the smooth functioning of competitive electricity markets. This requirement is particularly critical when there are bilateral transactions coexisting side-by-side with the centralized day-ahead electricity markets in which the so-called pool players participate as buyers and sellers. The nondiscriminatory allocation of transmission services to the pool players and the bilateral transactions is synonymous with the determination of the market outcomes and the provision of transmission services to the bilateral transactions. We propose the formulation of a generalized transmission scheduling problem (GTSP) to simultaneously accomplish this objective. The proposed GTSP formulation not only captures more appropriately the social welfare and market efficiency loss, but also results in more efficient market outcomes than the conventional transmission scheduling problem (TSP) formulations in the presence of transmission congestion. In addition, the GTSP solutions determine more appropriate locational marginal prices (LMPs) and, consequently, LMP differences for computing the congestion charges and the payoffs for the financial transmission rights (FTR). We assess the capabilities of the proposed GTSP formulation and quantify the improvements over conventional TSP solutions. These improvements become particularly important as the load served by the bilateral transactions constitute an increasingly large portion of the total load in the system. We illustrate quantifiable benefits of the GTSP solutions on a wide range of systems including the IEEE 118-bus network. The representative numerical results in the paper provide persuasive support for the effectiveness of the proposed formulation and the superiority of its solutions over those of the conventional TSP.