## An implicit enumeration algorithm for the set partitioning problem with side constraints |

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0perations Research airline crew scheduling assigned to block assigning row B0UND binary variables candidate list candidate problem computational constraint matrix Control Data Corporation cost(g covering and partitioning covering problem crew base constraints deadheading dual enumeration phase enumeration tree enumerative algorithm equality constraints extension of g Fathoming Criterion feasible extension feasible solution Figure final tableau follows Geoffrion go to Step implicit enumeration incumbent infeasible initial linear program integer linear program Integer Programming Problems integrality conditions interference class Jeremy F large problems lexicographic ordering LHB(t logical reduction lower bound Management Science map g Marsten minimize natural integer solution node null function number of columns objective function optimal solution PEN(h pivots PLHB(t,k problem UA1 pure set partitioning Quadratic Assignment Problem relaxation reoptimization retrieved from block RHB(t rotation Section Set Covering Problem set partitioning problem side conditions singleton solution of LP staircase form Step 11 Step 9 subset T(gr v(LP y(gr