X - UWSpace - University of Waterloo

F I
( L?: wi SM,. r=1.1 ..... N
~~.o,*P,>O for t = 1.2. ... , N
where the subscripts r and s indicate the part number, N is the total number of parts, x,, y, and
v, are the vecton of nt, r,, and q, variables for part t. for t=l. 2, .... N. The dual variable vecton
for the constraints of part r of P are denoted by row vecton n,, co, and p, which are the vectors
of nt,. q,, and r, variables for pm t. L, is a qtxr, matrix, A, is an m,x n, matrix, Br is a qtx n,
mütrix. DI is an m,xrs matrix, and cr, d,, MIS. b,, f,, and ut>O are vectors of suitable
dimensions for r=l. 2. .... iV and s=l, 2, ..., N. The general structure of the multi-part mode! is
dso shown in Table 1.
The sme assumption as in the two-part case is made in order to simplify the algorithm
and to gumntee convergence:
Assum~tion: For each pan. r=l. 2. ..., N. the set of nonlinking constraints. together with
46