Principles of Mathematics in Operations Research

278 Solutions

li norm: Li-tJi-tKi-tGi->Ii->Hi->Fi-+Ai-*Cy-*B*->Di-*E with

length 38;

l 2 norm: fHC^/nJ^i/^F^i^C^Bi-yD^B^L with

length 29.42026;

loo norm: K^G^I^J^H^Ft-^A^C^B^D^fE^L with

length 25.

For the even numbered PCBs, we reverse the order as

li norm: E*-*Di-+Bi->Ci->Ai-tFi->Hi->Ii->Gi-tKi-tJi-tL;

l 2 norm: L^tE\-^D^B^C^tA^F^H^J^I^G^K\

loo norm: Li-^Ei-^D^Bi-^Ci-^Ai-^Fi-^Hi-^J^Ih-^G^K.

Current situation (li norm): Path duration is 38 time units.

Proposition 1 (l 2 norm): Path duration is 29.42026 time units.

Proposition 2 (loo norm): Path duration is 25 time units.

Proposition 1 is economically feasible if (38 - 29.42026)./VCo > C. Simi-
larly, proposition 2 is economically feasible if (38 — 25)NC 0 > C 2.
If 8.57974 < jfe- and 13 < jf^r, then we keep the existing robot arm con-

figuration. Otherwise, we select proposition 1 if 0.65998 > Q-\ select proposi-

tion 2 if 0.65998 < £L.