For the case of column non-full rank of X,let the LS estimator and the mixed estimator of estimable function c′β be c′β^ and c′β_m,respectively,then the boundary of relative efficiency e_(3)(c′β^,c′β_m)=Var(c′β_m)/Var(c′β^) was obtained.
In this paper,orthogonal arrays L'16(212),L'16(214),L36(211×312),L108(349),L108(23 x 349),L108(211 x 348) and L108(235x 336)are given. Since these arrays do notcontain interaction column of any two columns they would be useful for parameter designs.
After giving a suitable model for the cutting strips problem, we present a branch-and-price algorithm for it by combining the column generation technique and the branch-and-bound method with LP relaxations.
Some theoretical issues and implementation details about the algorithm are discussed, including the solution of the pricing subproblem, the quality of LP relaxations, the branching scheme as well as the column management.
Let U(R,S) denote the class of all (0,1)-m × n matrices having row sum vector R and column sum vector S.
Enumeration of (0,1)-matrices with constant row and column sums
Let fs,t(m,n) be the number of (0,1) - matrices of size m × n such that each row has exactly s ones and each column has exactly t ones (sm = nt).