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are first sent and necessary columns for other parts' linking consaaints are sent afterwards.
5.1.2 Solution phase
in the solution phase on PCs. each machine starts with its own process and receives the
subproblem's data from the RS/6000 by the routine pvrn-receive(). Using the CPLEX Callable
Library. each LP subproblem is loaded in each cornputer. For instance in SP3. the columns having
that part's nonlinking consuainu (the columns in L33, &, L3 and B3, A3) are loaded fini. then
necessxy columns for other parts' linking consuainü (the columns in L3 Li and L3?, Li2) are
loaded and finally the unnecessary linking constraints of other parts (parts 1 and 3) are delered
since column wise vecton include dl linking constraints' data. Each subproblem is solved
sirnultaneously without any information exchange aat the fint iteration and exchanges necessary
primai or dud information with other machines and solves each new subproblem again until the
gap between the objective function values of the upper-upper bound subproblem and the lower-
lower bound subproblem reaches 3 prescribed tolerance. Note that if any of the subproblems is
unbounded. the whole pmcess stops at the fint itemtion by checking the optimal statu generated
by CPXSolution().
Since C PW provides the dud values corresponding to the primai constraints by calling
the CPXsolutionO routine in the CPLEX Callable Library, we don't have to solve for the dual
variables sepmtely, so the implementation efforts are bgreatly simplified The subproblems can
be solved by the simplex method or the barrier methd For the bher method the dud and bais
information cm be obtained by crossover at the last step using CPXhybbaropt().
The new primal and duai proposais are multiplied by corresponding matrices and vecton
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