The　partner　selection　problem　with　bid　cost　and　completion　time　factors　with　a　due　date　constraint　is　a　fundamental　problem　in　virtual　enterprises.　This　problem　was　proved　to　be　a　NP-complete　problem.　To　develop　a　branch　and　bound　method　for　this　problem,　a　nonlinear　integer-programming　model　was　constructed.　Monotone　properties　of　objective　function　and　constraint　function　were　proved　in　this　model.　By　the　properties,　a　necessary　and　sufficient　condition　was　found　to　determine　an　infeasible　problem,　and　a　sufficient　condition　was　established　to　deter　mine　a　problem　with　a　known　optimal　solution.　Moreover,　a　binary　search　method　was　designed　to　shrink　sub-boxes　generated　by　the　method.　Numerical　experiments　showed　that　the　branch　and　bound　method　with　these　techniques　was　effective.