scheduling in ection molding operations 9ith multiple cesource constraints and sewuence

25

Upload: others

Post on 09-Feb-2022

2 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

����������� � ��� ����������������� � �� ��� ��� � �!��"$#%��������&(')�*��� � �*��� ����+ �,&-�.�"/�0� 12�.��&3�4"$#5� ���6&7#5��� �8��9:������0�<;=���!�����������=���>����

? � @ �,&7#5��� 12�.&3�6&

A6BDC�E/B�F$GIHKJ4L�MNJPOQBRMSCTGVU�B�W�XZY�B�F�[\M]J_^�BR`3GbacTd\e�f>gShihkjmlnhihporqsgutDlTvxw*yzgS{|w,}n~���{��r���xw�v*��lTh/��{����i{rguguv*�i{r�Dor��{�����guv*����wb�8lTw�f��r��lnh�}����\�s������o

f����3lnh�}�o������ d\en���ro��I�\�

�:�6  ¡S¢N£�¤n¡¥0¦ �i�4tDlTt§guv�ln�r�rv�gS���xg¨��l%t�v�}\����©�w*��}�{ª�*© ¦ gS����hi�i{r�«t�vx}�¬�h�gSy­�i{®ln{®�i{N¯bg]©�w���}�{zyz}�hi���i{r�«~°l�© �ihi��wb��±$�pw

lTt�tDg]lNv*��wx}ª¬§g�w ¦ g�²�v���wmlTwxw�gSyzt�w,w�}®�*© ¦ gS����h�g«tDlNv³lnhih�gSh�y®l�© ¦ �i{rgS�0~´}�v�y.�rh�w*��t�h�g«��wxg¨yz���i{�t�v�gS�xgS{�©�g}�~ky5��h�w*��t�h�gm©ulTtDln©u��w*lTw�gS�zv�gS�x}��rv*© gs©�}�{��xw�v*ln�i{|w���µ���w ¦ �xgS¶\�rgS{�©�g ·��rgut§gS{��rgS{|w��xguw*�rt8© }���w���ln{��ªw*�iyzgS�S±¥,¦ g�}�¬r¯bg¨©�w*����g:�i�5wx}¸y�gSguw�© ���xw�}�y�gSv5�rgSy®ln{��r�5µ ¦ �ih�g8yª�i{r�iyª��¹S�i{r��w ¦ g8w�}nw³lnh>�i{|�ng¨{�w�}�vx� ¦ }�hi���i{r�©�}��xw*�So�¬Dl�©*º�h�}��n���i{r�»©�}��xw*�®ln{r�¼�xguw*�rt½© }���w��S±Z¾¿g�trv�gS�xg¨{�w:l»y®lNw ¦ gSy®lTw���©ulnh�~´}�v�y.��h�lTw���}�{À}�~sw ¦ gt�vx}�¬�h�gSy�± ¥,¦ gª©�}�y�t��rw³lNw*��}�{�lTh6©�}�yzt�h�guÁ���wb��ln���x}r© ��lTw�gS��µ���w ¦ w ¦ g.~´}�v*y.�rh�lTw*��}�{�y®lNº�gS�I��w%����Â:© ��h�w~´}�v>�xw³ln{���lTv*�®��}�h���guv*��w�}�lT���rv�gS���>�i{����r��wxv*��lnh÷��r�iyzgS{�����}�{rgS�ªtrv�}�¬�h�gSyª���i{®vxg¨ln�x}�{�lT¬�h�gm�x}�hi�rw���}�{ªw��iyzg�±¥ }¸}N��guv³©�}�y�g�w ¦ �i�So�l»e¨·pt ¦ ln�xg�µ�}�vxº|©�gS{|w�guv.¬Dln�xgS�Z�rg¨©�}�yzt§}�����w���}�{Ä�*© ¦ gSyzg ¦ ln��¬§gug¨{Z�rgu��gSh�}�t§gS��i{Qw ¦ �i�ItDlTt§guvS± ¥,¦ g®©�}�yzt��rw³lTw���}�{�lnh$v�gS����h�w*�I~´}nv«�����§guv�gS{|wIt�v�}n¬�h�gSy=����¹ug¨�%��g¨y�}�{��xw�v*lTw�g�w ¦ lTw%w ¦ �i��*© ¦ gSyzg>�i�-lT¬�h�g�w�}s�x}�h���g>�i{r�����xw�v���lnh÷����iyzgS{�����}�{rgS�%t�vx}�¬�h�gSyª�/µ���w ¦ �i{�vxg]lT��}�{�lT¬�h�g�w*�iy�g0ln{r�.l�©u© �rv³ln© ��±

Å�Æ�Ç3È.É ¢NÊ- nË Ì�Í�Î�Ï*ÐTÑrÒÔÓ´Õ\ÖT×�Ì3Ï*Ø ÑDÏ�ÕRÍÙÏÛÚ.ÏÝÜ�Ï�ÕRÐ|Ï�ÕDÞ�Ì3Ï Þ°Ñ]ÜD×�ß$ÎràTÕ\Ö\Ï*áTânÏ�ã�ß�áNä�Þå×0æKÑrÒçÞ°ÓèÜRÒiÏ�ß�àÙÜ�à�Í ÓåéÞ�ànÞÝÏ*Ð�ê�ÏÙäuáTÑ�ã�ÍÙÏÙä

ë�ì�í�î/ï]í�ðZñxí³òVòpóxô°õ�í�ö]÷]óxö]ñøó4ôVï]í�ù]úè÷sû�ó�÷]üýòpóøñøþpóø÷�ÿDö����Ùü��/ûTù����Ùúýí]ÿ óø÷]ù

Page 2: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

� �� �������������������

��{T¯bg¨©�w*��}�{ yz}�hi�r�i{r�Q�i��l ¦ ����g8��h�}�¬�lnh>y®lTvxº�guw¨±���}�hi�rguv*�.��©�}�{r}�yª��©:��{��rg Á ���Q���ø�«�i{��r��©SlNw�g:w ¦ lNww ¦ g�yzgS����©ulnh�yz}�hi���i{��Do-�i{À�5±è�R±6lTh�}�{rg�o ¦ ln�5� ¦ }Nµ�{ l�©u© gSh�guv³lNw�gS�»��vx}Nµ�w ¦ v³lTwxg¨�5�i{¿w ¦ g:tDln�xw5w ¦ v�gug��g¨lTv��¨± ¥0¦ �i�%�i�s���rg�w�}�w ¦ gzy®ln��������g5g Á�tDln{r�*��}�{Q�i{ ¦ g¨lnh�w ¦ ©ulTv�g��xt§gS{��r�i{r���i{Kw ¦ gª�Û±Ô�§±3©uln���xgS�K¬\�ln{QlN���i{r�:t§}�t��rh�lTw*��}�{3±s��}nv�w ¦ �syzguv*��©uln{�yz}�hi���i{r�:t�h�ln{|w*� ¦ lS��g.{rgu��guvm¬§gugS{Qln�syz}��rguv*{Qln{���µ�gShihgS¶\����t�tDg¨�:lT��w ¦ gu�ªlTvxg�{r}NµÛ±6��{ªw ¦ g5�! " ��T��ln{��ªµ>gShih��i{|w�}�w ¦ g���g¨lTv>en�����%yz}�hi�rguv*���xt§gS{|w ¦ g]lS���ih��5}�{©ulTt���w*lnh��iy�t�v�}N�ng¨y�g¨{�w*�S±/��gSµ �i{T¯bg¨© w���}�{«y®l�© ¦ �i{rgS�SoNln���nlT{�©�g¨�Ûln�rwx}�y®lTw���}�{Ûln{r�Û�i{��xt§g¨© w���}�{��rgu����©�gS�Soln�rwx}�y®lTwxgS�ªln���xgSy5¬�h��5y®l�© ¦ �i{�gSvx��o��x}�t ¦ �i��w���©ulTw�gS��y®lTwxguv*��lnhi� ¦ ln{���hi�i{r�«gS¶\����t�yzgS{|w¨o�ln{��ª��g]©�}�v*lTw*�i{��ln{��Àt�v��i{|w*�i{��¸gS¶\����t�y�g¨{�wªlnhih0lnhih�}]µ�gS� yz}�hi��gSv��.w�}¸�*����{���²D©uln{|w�h��¿h�}Nµ>guv.w ¦ g�©�}��xw�}�~�����v�g¨©�wzh�lN¬§}�v���xgS�¸�i{Kw ¦ gzy®ln{\��~°l�©�w*�rvxg.}n~�gu��gS{Qh�}Nµ0·Ý©�}��xw%©�}�yªyz}\����wb��t�lTv�w��¨±«��{!ln���r��w*��}�{koR�i{T¯bg¨©�w*��}�{Kyz}�hi���i{��t�h�ln{�w*�-��gS{rguv³lnhih��%gS{T¯b}N��w ¦ g ¦ ��� ¦ gS�xw6t§}��*����¬�h�g�t�vx}�����©�w�������wb�«v³lNw�gS��© }�y5¬��i{rgS�Ûµ���w ¦�¦ ��� ¦ h��Ûln�r�Tln{�©�gS�t�vx}�����©�w,�rgS������{�ln{���y®lNw�guv*��lnhi��wxg¨© ¦ {r}�h�}�����±-��{�w ¦ �i�0hi��� ¦ w>}�~kw ¦ gst�v�}��xt§g¨©�w*� ¦ gShi�8¬\�®w ¦ g%�i{T¯bg¨©�w*��}�{yz}�hi�r�i{r�!�i{������xw�vx��o�tDlTv�w���© ��h�lTv*h��»w ¦ g ¦ g¨lnh�w ¦ ©ulTvxg�vxg¨h�lNw�gS�Z�i{T¯bg¨©�w*��}�{Äyz}�hi���i{r�!�i{������xwxv���o�µ�g�µ�guvxgyz}�w����TlTw�gS�½w�}Àµ�}�vxº¼µ���w ¦ l ¦ g¨lnh�w ¦ ©SlNv�gQ�i{T¯bg¨© w���}�{½yz}�hi���i{r�Àt�h�ln{|w8w�}Z�iy�t�v�}N�ngKw ¦ gS��v8t�v�}�© gS���xgS�w ¦ v�}��r� ¦ ¬§guw�wxgSv,t�v�}\����©�w*��}�{��³© ¦ gS���rhi�i{r�D±��{T¯bg¨©�w*��}�{Qyz}�hi���i{r�8}�tDgSv*lTw*��}�{K�i�IwÝ�\t���©ulnhih���l8���i{r��h�g ·��xw³lT�ng5y®ln{\�r~°ln© w��rv*�i{��8t�v�}�© gS���sµ ¦ guv�gS�i{Ql

{\��yÛ¬§guv�}n~>t�vx}�����©�w��ÛlTv�gªy®lT{\�r~°l�©�w*��v�gS�Q}�{»� ¦ lNv�gS�!y®l�© ¦ �i{�g¨�Iµ���w ¦ w ¦ gS��v%vxg¨�xt§g¨©�w*���ngª����gS�S± ¥,¦ gyz}�hi�r�i{r��y®l�© ¦ �i{rg����xgS��l:�nln©u�r��y w�}�y�}N��g.w ¦ g�t�h�ln�xw*��©Û~´vx}�y w ¦ g$#ø�rv*��guv&%8wx}���w��%�i{���w*��lnh ¦ }�hi���i{r�© ¦ lny5¬DgSvS± ¥,¦ �i�®© ¦ lny5¬DgSvz�i�:ln© w���lnhih��Àl¸�*yªlnhih�# ¦ }�trt§guv&%¸}�{Zw ¦ g�¬Dl�©*º }�~sw ¦ g'#ø¬DlTvxv�gSh(%¸}�~mw ¦ gy®l�© ¦ �i{�g|± ¥,¦ gs¬DlTvxv�gShR�i�>µ ¦ guvxg«lThih§w ¦ gIv�g¨lnhDµ�}nv�º®�i���r}�{�g|±��pw0�i�>g¨���xgS{|w*��lThih��®l5h�lTvx��gI�*©�v�guµ ¦ }����xgS��i{½l ¦ g¨lTw�guvªµ ¦ ��© ¦ yz}]��gS�ªw ¦ g�t�h�ln�xw*��©�©uh�}���guvªwx}¿w ¦ g�yz}�hi�k±½�m�®w ¦ g��*© vxguµ7w��rv*{��So>w ¦ g�t�h�ln�xw*��©w�v*l¨��guv*�xgS�sw ¦ g�¬DlTvxv�gSh�ln{��Qvxg¨l�© ¦ gS�«l8yz}�h�w�gS{Q�xw³lNw�g�±*)s{�h���µ ¦ gS{Q��w«�i�Iyz}�h�wxg¨{Q©uln{¸��wI¬§gz�i{T¯bg¨©�w�gS��i{|wx}�w ¦ g®yz}�hi�¸µ���w ¦ l�v*lTt��i�¸w*�rv�{»}�~>w ¦ g®�*©�v�guµÛ± ¥0¦ g®w���t»}�~�w ¦ gª¬DlNv�v�gSh4�i�Û©ulnhih�gS�¸w ¦ g+#x{r}n¹S¹Sh�g!%ln{��K~´v�}�y w ¦ �i�It§}��i{�wIw�}�w ¦ gª©ul¨����wÝ���i{Kw ¦ gzyz}�hi�Kw ¦ gzy®lTwxguv*��lnh-�i�I{r}�w ¦ g¨lTw�gS�¸ln{��¸�i�«©�}�{r��w*ln{|w�h��©�}\}�h�gS�k± ¥0¦ g,#øv���{�{rguv-%%�i��w ¦ g�©�}\}�h�gS�/.]��guw-t�h�ln�xw*��©>w ¦ lTw�g Á�w�gS{�����~´vx}�y w ¦ g�{r}�¹u¹Sh�g,wx}%w ¦ g�©ul¨����wÝ�.lT{���i�%trv�}r©�gS�����*©�v³lNt/±��s© w���lnhih���oRw ¦ g®©�}\}�h�gS�¸y®lTwxgSv���lnh-~´v�}�y w ¦ gª{r}n¹S¹Sh�g�w�}�w ¦ gªyz}�hi�!�i�%w ¦ g$#x�xt�v*�rg!%¬��rw���w>�i��©�}�{�{rg¨©�w�gS�ªw�}5w ¦ gmv*�r{�{rguv¨± ¥0¦ gmv*��{r{rguv*�0lTv�g�gx¯bg¨© wxgS�:�i{|wx}.l�#�©�}�{|�ngS�n}�v&%«¬Dg¨h�}]µ w ¦ gsyz}�hi�ln{��:���ryzt§gS�:�i{|w�}.l0#ø��v*�i{r�rguv&%�± ¥,¦ gs��v��i{��rguv�© ¦ }�t���w ¦ gmv*�r{�{rguv*�>�i{|w�}Û¬���w���ln{��®t�vxgSt�lTv�gS��w ¦ g¨y­w�}¬§g�y�}N��gS��¬Dln©³º��i{|w�}:w ¦ g���v*��guv¨±,#��3¯bg¨©�w�}�v�t��i{��-%Q�åtDlNv�ws}n~4w ¦ g.yz}�hi�D��lTv�gÛw ¦ gS{K���xg¨��w�}8gx¯bg¨©�wmw ¦ gyz}�hi��g¨��tDlNv�w*�S±� �xguw*�rt�{�gSgS���>w�}.¬§gst§guv�~´}�v�yzgS�:~´}�v,l�t�v�}��r��©�w0wx}.¬§g%yªln{\�r~°l�©�w��rv�gS�k± ¥0¦ g%�xguw*�rt��i���xgS¶\�rgS{�©�g

�rgut§gS{��rgS{|wªln{��Ät�lTv³lny�gSwxguv*�.hi��º�g Í�ÎràTÕ\Ö\Ï*áTânÏ�ã�ͳáNä�Þ ln{�� äSÏ Þ°Ñ]Ü Þ°Ó21:Ï �TlTv�� �rgut§gS{����i{��!}�{Àµ ¦ ��© ¦

e

Page 3: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

t�vx}�����©�w%�i�%�xguw*�rt!lN~´w�guvsµ ¦ ��© ¦ ±43��rv�w ¦ guv¨o3l8{|��y5¬§guvI}�~�vxg¨�x}���v³©�gS�%hi��º�g5��v��i{��rguv*�SoR�rv���gSv��«lT{��¸©�}�{�·��gu��}�v��ªlTvxg�v�gS¶\����vxg¨�À~´}�vzw ¦ g�t�vx}�����©�w*��}�{Ät�v�}�© gS���S± ¥,¦ g¨�xg�vxgS��}��rv³©�gS�ªlTv�g�©�}�{��xw�v*ln�i{rgS�À¬\� w ¦ gS��vhi�iyª��wxg¨�Z{\��yÛ¬§guv*�S±½�shi�x} �r���Rguv�gS{|wzt�v�}��r��©�w*�®vxgS¶\����v�g������§guv�gS{|w®y®ln© ¦ �i{rgS�®ln{��¼�����§guv�gS{|w®�xguw*�ª}�~v�gS�x}��rv*©�g¨��lT{���w�}\}�hi�S±�5>}�yz�i{r�ª�rt�µ���w ¦ l.��}|}����³© ¦ gS���rh�g«�i{�trv�gS�xg¨{�© g%}�~6lnhihRw ¦ gS��g�©�}�{��xw�v*ln�i{|w*�So\�i�lª© ¦ lnhih�gS{r�ng|o|gu��gS{�~´}nv,w ¦ g����i{r��h�g«�xw³lN��gÛ©uln�xg�±¾»g�t�v�gS�xgS{|w>l«yz�ÃÁ�gS�ª�i{�w�gu��guv4~´}nv*y.��h�lNw*��}�{.~´}�v��*© ¦ gS����hi�i{���t�lTv³lnhih�gSh�µ�}nv�º|©�gS{|w�guv��4�i{ztrv�gS�xg¨{�© g�}�~

y.��h�w���t�h�g«w�}\}�hi�i{r�8lT{��K©SlNtDl�© ��w³lTwxgS��vxg¨�x}���v³©�g.©�}�{r��wxv³ln�i{�w*��µ���w ¦ �xgS¶\�rgS{�©�g5�rgut§gS{���g¨{�ws��guw��rt�w*�iyzgS�ln{���©�}��xw��¨±���{�w ¦ g�²rv*�xw���w*lT��g�orµ�g��x}�h���g%w ¦ g0#�lT����vxgu�|lTw�gS�6%.t�v�}n¬�h�gSy ~´}�vml7#øtDlNv�w�~°lTyª�ih��8%�±4��{�w ¦ g�xg¨© }�{��K�xw³lT�ng|o�µ�g5�x}�h���gÛw ¦ g9#ø���i�*lT����vxgS��lTw�gS�6%zt�v�}n¬�h�gSy }�{Qlªv�}�hihi�i{r�T· ¦ }�v*��¹u}�{�¬Dln���i�S±,¾»g���gS�ng¨h�}ntl8µ>}�v�º�© gS{|wxguvI¬Dln�xgS�¸�rg¨©�}�yztD}�����w*��}�{Q�*© ¦ gSyzg.w�}���g]©�}�y�t§}��xg�w ¦ g7#x���i�*lT���nv�gu�|lTwxg¨�:%:t�v�}n¬�h�gSy �i{|w�}��y®lnhih�guv3���r¬�t�vx}�¬�h�gSyª�$lT{����x}�h���g�w ¦ gSy w�}���gS{rguv*lTw�g�w ¦ g�²�{�lnh�~´g¨ln����¬�h�g��³© ¦ gS���rh�g|±�¾¿g�lnhi�x}��rgu��gSh�}�t§gS�l,�x}�~´wbµ0lTv�g�tDl�©*ºTlT��g4w ¦ lTw/µ>}���hi�«�i{�©�}�vxt§}�v³lNw�g�w ¦ g��x}�hi�rw���}�{«yzguw ¦ }��r}�h�}n���%ln{r�«t�v�}]���i�rg�l<;%�m�D¬Dln�xgS��x}�hi�rw���}�{�~´}�v,w ¦ gÛlT����vxgu�|lTw�g«ln{���w ¦ gÛ��gSw*ln�ih�gS���*© ¦ gS����hi�i{r��t�v�}n¬�h�gSy�±��{:w ¦ gs~´}�hih�}Nµ��i{r�5�xg¨©�w*��}�{3o\lÛv�g¨©�gS{|w>hi��w�guv³lTw��rv�g�v�gu����guµ }�~3w ¦ gIvxgSh�lTw�gS�®wx}�t���© �>�i�>trv�gS�xg¨{�w�gS�k± ¥,¦ g

t�vx}�¬�h�gSy(�rgu²�{���w*��}�{�ln{��:~´}�v*y5��h�lTw*��}�{®�i��trv�gS�xg¨{�w�gS�8�i���|g¨©�w*��}�{8c�±��|g¨©�w*��}�{:d5t�v�gS�xgS{|w*�>w ¦ g%�x}�hi�rw*��}�{lTt�trv�}|l�© ¦ �i{�©uhi�r���i{r�!w ¦ gKe]·>= ¦ ln�xg�µ>}�v�º�© gS{|wxguv�¬DlT��gS�Z�rg¨©�}�yzt§}�����w���}�{Ä�³© ¦ gSyzg�±?5�}�yzt���w³lTw���}�{�lnhv�gS����h�w���lTv�gs� ¦ }Nµ�{:�i{��|g¨©�w*��}�{A@�± ¥0¦ gmv�gS����h�w*�>�i{r����©ulTw�g�w ¦ lNw>w ¦ gst�vx}�t§}��xgS�:�*© ¦ g¨y�gmt�v�}N�\�i�rgS����}|}��~´g¨ln����¬�h�g,�*© ¦ gS����h�gS��~´}�v��i{��r���xw�v*��lTh�����¹ugS��t�vx}�¬�h�gSyª�6µ���w ¦ �i{ªln{ªl�©u©�gut�w³lN¬�h�g,w��iyzg�hi�iyª��wS±k¾»gm©�}�{�© hi����gµ���w ¦ v�gSy®lNv�º��$}�~�w ¦ �i�-µ>}�v�ºÛ�i{z�|g¨© w���}�{���± ¥0¦ g�lTtrt§gS{����ÃÁ.© }�{|w³ln�i{r��lm¬�v���gu~§l�©u© }���{|w-}�~�w ¦ g,�x}�~´wbµ0lTv�g�x���xw�gSy�±

BC D?�E�GFH��I4���0��F JKFMLN��F<O

¥,¦ g«hi��wxgSv*lTw*��v�gsv�gu����guµ t�v�gS�xgS{|w�gS� ¦ guvxg«�i�0�r�����i�rgS���i{|w�}.wbµ>}��xg¨© w���}�{��S± ¥,¦ gI²�v*�xw,�xg¨©�w*��}�{�lTwxw�gSyzt�w��w�}¿��gS²�{rg�w ¦ g������Rguvxg¨{�w:© h�ln���xgS��}�~Ih�}�wx·�����¹S�i{r�¸trv�}�¬�h�gSyª�ª© }�{����i�rguv�gS� �i{Zw ¦ g�hi��w�guv³lTw��rv�g�P,ln{r�Zw ¦ g�xg¨© }�{�����g¨©�w*��}�{�����yªy®lNv*��¹ugS��w ¦ g.�����§guv�gS{|wm�x}�hi�rw*��}�{��xw�v*lTw�gu����gS���rgu��gSh�}�tDg¨��wx}8�rg¨lnh/µ���w ¦ �����§guv�gS{|w© h�ln���xg¨�0}n~6h�}�wø·�����¹¨�i{���t�v�}�¬�h�g¨yz�¨±

QSRUT VXW�Y[Z]\M^`_a^Ub<cedfbHgh\Mi/j<klgHmonU^Ub<cqp Wrg<klnUstvu�wxu�w y £D !zå¤N{ É Ê Æ8|  ¥,¦ g����iyzt�h�gS�xw5��guv*����}�{ }�~�trv�}�����© w���}�{Àt�h�ln{�{��i{r�¸�r�i��vxgu�|lTv*�r���xguw*�rt ©�}��xwzln{��À~´}�vzlQ���i{r��h�g��xw*lT��g�o���i{r��h�g�t�vx}�����©�w«�*��w���lTw���}�{koklTwxw�gSyzt�w��%w�}�yª�i{r�iyª��¹ug��i{|��gS{|wx}�v�� ¦ }�hi���i{r��©�}��xw«�i{»ln{!��{�©SlNtDl�© ��w³lTwxgS�gS{|����vx}�{�yzgS{|wS± ¥,¦ gÛ�x}�hi�rw*��}�{�wx}ªw ¦ �i��trv�}�¬�h�gSy �i��l�wxv*������lTh3h�}�wx·p~´}nvx·�h�}�w,�*© ¦ gS����h�g«¬§g¨©uln���xgÛ��w�© h�g]lNv*h��

c

Page 4: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

yª�i{��iyz��¹SgS�sw ¦ gz}�¬r¯bg]©�w�����g�± ¥0¦ �i�«yz}��rgSh��i�Iwb�\t���©SlThih��K© }�{����i�rguv�gS�Qµ���w ¦ �x}�yzgª©�}�yÛ¬��i{�lTw���}�{K}�~�w ¦ g~´}�hih�}Nµ��i{r�.²���gÛlT��tDg]©�w���wx}zv�gS����h�w��i{�l���guv��*��}�{�}�~$t�v³ln© w���©ulnhRv�gSh�gu�nlT{�©�g|±��±}=4vxgS��gS{�©�g�}�~��|guw*�rt95�}��xw*�S±,��{�w ¦ �i�s©uln�xg�o�w ¦ g5���iyzt�h�g¨�xw�h�}�wø·��*��¹S�i{r�zt�v�}�¬�h�g¨y µ0ln��~´}�v*y.�rh�lTw�gS�¬\�®¾ÀlT��{rguv�ln{���¾ ¦ ��w��i{ ~ c" ���±

er±M5�lTtDl�© ��wb��5>}�{r��wxv³ln�i{�w*�S±c�±}=4vxgS��gS{�©�g%}�~�f�l�©*º�h�}����S±dD±}����h�w*��t�h�g�=4v�}\����©�w*�S± ¥0¦ g*5�lTtDl�© ��w*lTw�gS�C�k}nwx·�����¹S�i{r�ªlT{��K��© ¦ gS����hi�i{���=4v�}�¬�h�g¨y)��5��-�8=��Ùo�µ,lT�ln�r�rv�gS���xg¨��¬\��qsvxg Árh/ln{��0�%�iyªyª��~ç�Sc���or~´}�vmlz���i{r��h�g ·��xw³lT�ng«y.��h�w*��t�h�g«t�vx}�����©�w��x���xw�gSy�± ¥,¦ gyz}\�rgShkyª�i{r�iyª��¹ug¨�>w�}�w*lnh3�xguw*�rt�ln{�� ¦ }�hi���i{r�®©�}��xw*�S±

@r±}����h�w*��t�h�gm�|w³lN��gS�¨± ¥,¦ g�y5��h�w*�÷��xw³lN��g«��#xy.�rh�w*�÷�h�gu��gSh(%\�k©ulTtDln©u��w*lTw�gS�.h�}�wx·�����¹S�i{r�ª���!�:5��-���$t�vx}�¬r·h�gSy �i��©�}�{�© guv�{rgS�zµ���w ¦ w ¦ g��rguw�guv�yª�i{�lTw���}�{.}n~Rt�vx}�����©�w���}�{zh�}�w�����¹ugS�4�i{�v�gS�x}��rv³©�g ·Ý©�}�{��xw�v*ln�i{rgS�y.�rh�w*�÷��xw³lT�ng0���r= ���KlTwxgSv���lnhi����gS¶\�r��v�gSyzgS{|w,=�h�lT{�{��i{r���5���\��wxgSyª�®�x}Àln�ªwx}Àyz�i{��iyª��¹ug�w ¦ g����y }n~4t�v�}��r��©�w*��}�{ko§�xgSwø·��rt¸ln{r�Q�i{|�ng¨{�w�}�vx��©�}��xw*�S± ¥,¦ gX�¸�65��-��t�v�}n¬�h�gSy�o§�i�s� ¦ }Nµ�{Kwx}:¬§g�0� ·`5�}�yzt�h�guw�g�¬|�93rv³ln{��©ul Ï ÞIànÒ(� ~ç�! ���± ¥,¦ �i�«�i�«�iyzt§}nv�w³lT{|w%¬§g¨©uln���xg®��w��iy�t�hi��gS�Iw ¦ lTw���w«�i���{rhi��º�gSh��®w ¦ lTw�ln{|��lTh���}�v*��w ¦ y�©SlT{�}�t�w��iy®lnhih��:�x}�h���g«h�lTvx��g%t�vx}�¬�h�gSyª�S±

tvu�wxu�t � z�� Æ0�mÆ ¢�z É Ê y £�  Æ Ê�� | £� S !z���¤�£�¡�z É/� É/� { É Ê Æ[|  ¥ µ>}�wxgSv�yª�Û���xgS� �i{¿h�}nwx·�����¹S�i{r��trv�}�¬�h�gSyª�So-lTvxg:��y®lnhih�ln{��»¬����À�å}�v5h�lTvx��gN�s¬���©*º�guwSo-ln�5�rgu²�{�g¨�»¬\�f>gSh��Tln��Á.ln{��Û¾¿}�hi��gu��~�@���± ¥,¦ gM5��-�8=!�i��©ulnhih�gS�.lIh�lTvx��g�¬���©*º�guw��´}�v6¬����I¬���©³ºngSwÙ�kt�v�}�¬�h�g¨y ¬\�.qmv�g Árhln{����%�iyªyª��~Ã�uc��-ln{��Kf>gSh��Tln��Á�ln{���¾»}�hi�xgu� ~�@���o�¬Dg]©uln�r��g5�xgu��guv³lTh/��w�gSyª��y®l¨��¬DgÛt�v�}��r��©�g¨��t§guvt§guv*��}\�k± ¥,¦ g:©uln�xgªµ ¦ guv�gªw ¦ gK�åy®l�©�v�}���t§guv*��}\���ÛlTvxg®���r¬§�������i�rgS�»�i{!�xgu��guv³lnh6yª��©�v�}n·pt§guv���}����«h�g¨ln�r�w�}®w ¦ g.qs�i�*©�v�guw�g��3}�wx·�����¹S�i{r�:ln{��¸��© ¦ gS����hi�i{r�A=�v�}�¬�h�gSy �°qo�-�8=��ÙoD©SlThih�g¨��l®��y®lThihk¬���©*º�guw�t�v�}n¬�h�gSy�o¬\� qmv�g Árhmln{r���%�iyªyz� ~Ã�uc��sln{��½f>gSh��Tln��Á ln{�� ¾»}�hi�xgu� ~�@��po�¬§g¨©uln���xgQlTw®yz}��xwª}�{rg���w�gSy ©uln{¬§g®t�v�}��r��©�g¨�»t§guvÛt§guv*��}��k± ¥0¦ g�qH�-�8= ¦ ln�Ûw ¦ g8�*lny�g®}�¬r¯bg¨©�w*����gª~å�r{�©�w*��}�{¿ln��w ¦ g�5��-�8=6±$qH�-�8=~´}�hih�}Nµ��4w ¦ gIlTt�t�vx}|l�© ¦ ± ¥0¦ g45�}�{|w*�i{|�r}����,�|guw��rt��3}�wx·ø�|��¹¨�i{��*=4vx}�¬�h�gSy ��5,�8�-�8=���©�}�{��xwxv³ln�i{|w>lnhih�}Nµ��w ¦ gÛ�x���xwxg¨y�wx}ªt�v�}\����©�g���{��rguv���w*�0~å��hihk©ulTtDl�© ��wÝ�|±

¥0¦ gC=4vx}�t§}�vxw*��}�{�lnhf�3}�wø·��*��¹S�i{r��ln{��Ä��© ¦ gS����hi�i{r��=4v�}�¬�h�g¨y ��=f�-�8=��s}r©u© �rv*��µ ¦ gS{¿w ¦ g�5,�8�-�8=yz}���g¨h��r}\gS�${�}�w$���xg�w ¦ g�~å��hih�©SlNtDl�© ��wb�m}�~�l,t§guv*��}\�koTlT�$��g¨�*©�v*��¬Dg¨�%¬\�«qmv�g Árh|ln{��4�«�iyzyª� ~ç�Sc��p±-qmv�g Árhln{��®jslnln�xg¡~Ã�!@���trv�gS�xg¨{�w�w ¦ gM=f�-�8=»µ���w ¦ ��guw��rt®w*�iyzgS����=f�-�8=�� ¥ �-µ ¦ guv�g�w ¦ gs©ulTtDln©u��wÝ��©�}�{��xwxv³ln�i{|w

d

Page 5: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

{r}Nµ �i{�© hi���rgS�>w ¦ g%�xguw*�rtk± ¥0¦ g¢;sgS{rguv³lThv�3}�wø·ø�\��¹S�i{r��ln{r����© ¦ gS���rhi�i{r�X=4v�}�¬�h�g¨y ��;o�-�8=>��o|t�vx}�t§}��xgS�¬\�ZqsvxguÁ�hmlT{��'�%�iyªyª� ~Ã�uc��mln{��'3-h�gS�i�*© ¦ y®ln{�{ ln{��'��gu�\v ~ç��£���o�~´g]lNw*�rvxg¨�ªy.��h�w���t�h�g�t�v�}\����©�w*�So���i{r��h�g ·�y®l�© ¦ �i{�gª�xgS¶\�rgS{�©�g ·��rgut§gS{��rgS{|wÛ��guw��rtÀ© }���w��So$��y®lnhih�¬���©*º�guw�w*�iyzg�ok¬��rw�µ���w ¦ {rgS��w ¦ gSv���guw��rtw*�iy�g¨�ª{r}�v®¬�l�©*º�h�}������i{��D±'��}��rgShi�:ln{��½lTt�t�hi��©SlNw*��}�{���}�~Iw ¦ g 5>}�{|w��i{\�r}��r� ¥ �iyzg0�3}�wx·ø�\��¹S�i{r� lT{����© ¦ gS����hi�i{���=4vx}�¬�h�gSy ��5 ¥ �-�8=>��or�i{�© hi���r�i{r��w ¦ gÛf0lNw³© ¦ �i{r�ªln{r�K��© ¦ gS����hi�i{r���Vf��[=���o�lTv�g«�r�i�³© �����xgS�¬\�Kf>gSh��nlT��ÁQln{���¾¿}�hi�xgu� ~�@���o3qsvxg Árh�ln{r�7�%�iyªyz�¤~Ã�Sc��pokqsvxg Árh�ln{r�!jslnln�xg¥~ç� d¦�4ln{�� =-}�w�w��«lT{��§ ln{z¾Àln���xgS{ ¦ }N�ng¨~ c��©�p±$¾»gI�r}5{r}�w�gSh�lT¬§}�v*lTw�g�}�{®w ¦ g¨�xgsyz}\�rgShi��ln{��z~å�rvxw ¦ guv�ln��w ¦ gS�xgsyz}���g¨hi�>lTvxg{r}�w,µ���w ¦ �i{�w ¦ g��*©�}�t§g«}�~$w ¦ �i�0tDlTt§guv¨±

tvu�wxu(ª {¬« | ¡�z�­ |´Æ {_£�¤�®lz �$Æ { É Ê Æ[|  ¥,¦ �i���xg¨©�w*��}�{z©�}N��guv*��w ¦ g�y.��h�w*��t�h�gu·�yªl�© ¦ �i{rg�t�v�}n¬�h�gSy µ ¦ ��© ¦ ���iy.��h�w*ln{rgu}�����h���t�v�gS�xguv���gS�4w ¦ g����i{r��h�g ·�xw³lT�ngm~´g¨lTw��rv�g�o|�p± g�±io|y®l�© ¦ �i{rgS���i{®tDlNv³lnhih�gShp±-�m{��rguv*�x}�{ Ï Þ�ànÒ(� ~ e��Rln{��8f0lTvx¬DlTv�}���}n��hi�:lT{��°¯)m¹S��lny®lTv~ c��R���i�xw*�i{������i� ¦ w ¦ v�gugI�xt§g¨© ��lnh§©uln�xgS��~´}�v����i{r��h�gu·��xw*lT��gm�i{®tDlTv*lnhih�gShDy®ln© ¦ �i{rgS��±$�i�rgS{|w*��©ulnh�tDlTv*lnhih�gShDy®lN·© ¦ �i{rgS�So���{���~´}nv*y tDlTv³lThih�g¨h-yªl�© ¦ �i{rgS�%ln{��Q��{rvxg¨h�lNw�gS�KtDlTv*lnhih�gSh-y®l�© ¦ �i{rgS�So�l:~´g]lNw*�rvxg�}�~´wxgS{K}�yª��w�wxgS�¬\��w ¦ g�v�gS�xg¨lTv³© ¦ guv*�S±o��gu�\v²~ e"£����rgu��gSh�}�t��sw ¦ g.~´}�hih�}Nµ��i{r�:~´g¨lTw*�rvxgS��±�y.��h�w���t�h�g ·pt�v�}\����©�w*�SoRy5��h�w*��t�h�g¦ guw�guvx}���gS{rgu}�����y®l�© ¦ �i{�g¨�So�©ulTtDln©u��w*lTw�gS�ko|�xgS¶\�rgS{�©�g ·��rgut§gS{��rgS{|w,��guw��rt�w*�iyzgS�So|µ���w ¦ }��rw�¬Dln©³º\h�}������i{r�ln{�� w ¦ g�}�¬r¯bg]©�w�����g�~å��{�©�w*��}�{ ¦ ln�8l¸tDlNv�w*��© ��h�lNv*��wb� �i{�© hi�����i{r�!w ¦ g ¦ }�hi���i{��Do>�xgS¶\�rgS{�©�g ·��rgut§gS{��rgS{|w©�}��xw*��lT{�� t�vx}�����©�w���}�{ ©�}��xw*�So,�i{ l �*�i{���h�g ·���w*lT��g��³© ¦ gSyzg�±³��gu�\v ~ e�£��I�rgu��gSh�}�t��®w ¦ g¸y�}��rgShm}�~3-h�gS�i�³© ¦ yªln{�{¸ln{��9��gu�\v´~ç��£���wx}�w ¦ gªy5��h�w*��t�h�g.y®l�© ¦ �i{rgz©uln�xgz�rgS{r}�w�gS�$;sgS{rguv³lTh��3}�wx·ø�\��¹S�i{r��lT{����© ¦ gS����hi�i{��C=4vx}�¬�h�gSyµ=6lTv³lnhih�gSha=4vx}�����©�w���}�{��k�i{rg���;o�-�8=f=f�-��±�� �����§guv�gS{|wmy�}��rgShi�i{r�8lTt�trv�}|l�© ¦ �i�ln�r}nt�w�gS�¸�i{$5�h�lTvxºQln{��$5>h�lTv�º ~¶ ��po3µ ¦ ��© ¦ t�v�gS�xgS{|w*�Iwbµ>}�~´}�v�y.��h�lTw���}�{��mw�}�h�}�wø·��*��¹S�i{r�8µ ¦ g¨{¸��guw��rtw*�iy�g¨�slTv�g5�xg¨¶|�rgS{�©�gu·���gStDg¨{r�rgS{|wI�i{�w ¦ g�©�}�{|wxg Á�wm}�~�v�}�hihi�i{r�T· ¦ }�v*��¹u}�{�t�h�ln{r{��i{r��ln{r�K�*© ¦ g¨�r��hi�i{r�:~´}�vtDlTv*lnhih�gShry®l�© ¦ �i{rgS�S± ¥,¦ g�²�v��xw�~´}�v�y.��h�lTw���}�{��i��ln{�guÁrl�©�w�yz}\�rgSh�µ ¦ �ih�g�w ¦ g���g¨©�}�{��z�i��ln{®lTt�trv�}]Ár�iyªlN·w*��}�{�~´}�v0v�}�hihi�i{��n· ¦ }�v���¹S}�{8�r��g�±4��{��xw�g¨ln��}�~-�����i{r�ªy®ln© vx}ªln{���yª��©�v�}�tDgSv���}����So�w ¦ g�yz}\�rgShi�0¬\��5�h�lTvxºln{��75>h�lTv�º ~� ��6t§guv*yz��w%y5��h�w*��t�h�g5�xgSw��rt��sµ���w ¦ �i{Kg¨l�© ¦ t�h�ln{�{r�i{r��tDgSv���}��k±«��{Qw ¦ g�yz}��rgSh-¬|� 5�h�lTvxºln{��·5�h�lTvxº ~� ��po�w ¦ gC¸ w ¦ �xgSw��rt ©uln{ }�©S© �rv�lTw������§guv�gS{|w.w��iyzgS�5}�{ g¨l�© ¦ y®l�© ¦ �i{rg�o-~´}�v.µ ¦ ��© ¦ o4l¬��i{�lNv��:�TlTv���lT¬�h�g%�i�0�i{|wxv�}�����© gS�k± ¥0¦ g%v�gS����h�w*ln{|w}�K�>= �i� ¦ �r��g�o�¬��rw��x}�h���gS���r�*�i{��®l.vx}�hihi�i{r� ¦ }�v*��¹u}�{¬Dln���i�So|�����i{r��©�}�{|w��i{\�r}��r���nlNv*��lT¬�h�gslTt�trv�}]Ár�iyªlTw*��}�{r��~´}nv>~å�rw��rv�gs�xgSw��rt��S±��,g¨�xg¨lTv*© ¦ �i��©�}�{�w*�i{\���i{��Û}�{����© ¦ yz}���g¨hi�S±

QSR�Q \}W¹nUmrYº^`W»b¼p k½YºjHW}gos

� v�g¨©�g¨{�wI}N��guv��\��gSµ_}�~�w ¦ gzh�}�w%����¹S�i{r�8t�v�}r©�gS���rvxgS�I~´}�vIw ¦ gzy.��h�w*�÷��xw*lT��g�oRy.�rh�w*�÷���w�gSy ©uln�xgz�i�I������gS{¬\�0�«lTw�}�º Ï Þ�ànÒ(� ~ e]d"�p±«f�l ¦ h Ï ÞmànÒ(� ~ d¦�4ln{�� �KlTgS� Ï ÞmànÒ(� ~ en��������yªy®lNv*��¹ug5gu�§}�v�w��s~´}nvI�����§guv�gS{|w

@

Page 6: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

© h�ln���xg¨�0}n~6h�}�wø·�����¹¨�i{���t�v�}�¬�h�g¨yz�¨±¥0¦ guv�g5lTvxg�wbµ>}:�r�i��w��i{�©�wmlTtrt�v�}|ln© ¦ g¨�,w�}®��}�h����i{r�,���l5��-�8=6± ¥,¦ g�²�v���w�}�{rgÛ���xg¨��w ¦ gÛ}�trw*�iyª��¹¨lN·

w*��}�{ZlTt�trv�}|l�© ¦ ln{��Àw ¦ g��xg¨©�}�{��ZlTt�t�vx}|l�© ¦ �i�.w ¦ g ¦ gS�rv*�i�xw���©�lTt�t�vx}|l�© ¦ ± j�g¨h�¬DgSv ~ e�e��,�xgSt�lTv³lTwxgS�w ¦ g ¦ gS�rv*�i�xw*��©Ût�vx}r©�g¨�r�rv�gS�%�i{|wx}�w ¦ vxgSgª©ulTwxgu��}�v*��gS�S± ¥,¦ gu�QlTvxg]±Û�]�mqsg¨©�}�yzt§}��*��w���}�{QlTtrt�v�}|ln© ¦ g¨�Soke���3}r©ulnh§��g¨lTv*© ¦ trv�}r©�gS���rvxg¨�So�ln{r��c|���/lT��v³lT{r��g¨ln{®¬Dln�xgS�:t�vx}r©�g¨�r�rv�gS�S±��«lTwx}�º Ï Þ�ànÒ(� ~ e]d"���i{�w�v�}\����©�gS�l�~´}���v�w ¦ ©ulTw�gu��}nv���w�}�w ¦ �i�«hi�i�xw�±Id\�o�a= ¬�ln�xg¨�¸t�vx}r©�g¨�r�rv�gS�S±,)m~´w�gS{¸w ¦ gS�xg®lTt�t�vx}|l�© ¦ gS� ¦ l¨��g�¬§gug¨{©�}�y5¬��i{�g¨�»w�}K��guw5¬§guw�wxguv.vxgS�*�rh�w*�S±Qj�gSh�¬§guv ~ ene����rgS�*© v���¬§gS��©�}�y5¬��i{�lTw*��}�{r��}�~��rg¨©�}�yzt§}�����w���}�{ lTtr·t�vx}|l�© ¦ gS��µ���w ¦ h�}�©SlTh§�xg¨lTv*© ¦ t�v�}�© gS����v�gS�So|µ ¦ �ih�g«��lTh�}�yz}�{¼~ c�c��3lT{�����lnh�}�yz}�{ Ï Þ�ànÒ(� ~ c�e�����g¨�*©�v*��¬Dg©�}�y5¬��i{�lTw*��}�{r�0}�~��a= ¬Dln�xgS��t�vx}r©�gS���rv�gS�,µ���w ¦ h�}r©ulnh3�xg¨lTv³© ¦ w�g¨© ¦ {��i¶\��g¨�S±

tvu�t¾u�w ¿ ­$¡�z��+z2À�£�¡�z É/� �,­l­-¢ É £D¤�® Æ  Á�Â�Ã/Ä[ÅÇÆ]È"Å�É,Ã/Ê�ÅÇÆ

¥,¦ g¨�xg5�i{|��}�h���g�yzguw ¦ }�����~´}�vm²�{����i{r���xwxv�}�{r�:h�}Nµ�guv�¬§}��r{����S±m��t�t§gS{¸lT{����QlTvxw*�i{ ~Ã�u���-�rgu��gSh�}�t§gS�w ¦ g�� ¦ }�v�wxg¨�xw.v�}���w�g8~´}�v*y.�rh�lTw*��}�{»}�~�w ¦ g����i{r��h�g��xw³lT�ng�©ulTtDl�© ��w³lNw�gS�Àh�}nw�����¹¨�i{��Qt�vx}�¬�h�gSy ��5¹�-�8=���oµ ¦ gSvxg�w ¦ g��a= v�gSh�lNÁrlTw*��}�{�t�v�}N�\�i�rgS�Q��wxv�}�{���guv«h�}Nµ>guvI¬D}���{����Iw ¦ lT{¸w ¦ gª�xw*ln{���lTv��Q~´}�v�y.��h�lTw���}�{�}�~f��ihihi�i{r�nw�}�{ Ï ÞsànÒ(� ~ ���p± ¥ gSyzt§gShiyzgS��guv«ln{��»j�gSh�¬§guvh~ c����4g Á�w�gS{���g¨�¸w ¦ �i�«� ¦ }�vxw�gS�xw«v�}��rw�gz~´}�v�y.��h�lN·w*��}�{¸w�}0���l5¹�6�[=�±¾=-}r© ¦ guw�ln{��Q¾¿}�hi�xgu� ~ c��������xgS�!w ¦ g®� ¦ }�v�wxgS��w%v�}���w�gª~´}�v�y.��h�lTw���}�{¸ln{��¿lT���rgS��Tlnhi�i�z�i{rgS¶\��lnhi��w���gS�6²�{��®{rg¨lTvø·p}�t�w��iy®lnhr�x}�hi�rw*��}�{��4~´}�v4¬D}�w ¦ ��{�©ulTtDln©u��w*lTw�gS�ko�lT{��®©ulTtDl�© ��w*lTw�gS���å���i{r��h�gv�gS�x}��rv*©�gT�/y.��h�w*�÷���wxgSy_trv�}�¬�h�gSyª� ¦ l¨�\�i{r�%gS��w ¦ guv�lI�*�i{���h�g ·���w*lT��g�}�v�lIy.��h�w��÷���w*lT��g���gS{rguv³lThr�xw�v���©�w*�rvxg|±

ËfÌºÍ Ä Ì/Î�Í Æ Ì/Î ÉAÆ]Ï ÌxÐ¾Ì ÅUÑUà Î

�|}�y�g.}�t�w��iyª��¹¨lTw*��}�{�lTt�t�vx}|l�© ¦ gS�I���xgÒ�/lT��v³lT{r����ln{�vxgSh�lNÁ�lTw���}�{�w�}8��gS{rguv³lTwxg��xw�v�}�{r��h�}]µ�guvm¬§}���{r���S±qs��lT¬\� Ï Þ�ànÒ(� ~ç���E�,���xgS�·�/lT��v³lT{r��g¨ln{ v�gSh�lNÁrlTw*��}�{¿µ���w ¦ ���r¬��nv³ln����gS{|w.}�t�w��iyª��¹¨lTw*��}�{¿w�}¸��gS{rguv³lNw�gh�}Nµ>gSv5¬§}���{����So4~´}�hih�}Nµ�gS�¿¬|�Äl�¬�v³lT{�© ¦ lT{��À¬§}���{��Zlnh���}�v���w ¦ y wx}!h�}r©ulTw�g8w ¦ g�}nt�w*�iy®lTh��x}�hi�rw���}�{��~´}�v«l����i{r��h�g.h�gS�ng¨h$t�v�}n¬�h�gSy µ���w ¦ l����i{r��h�gz©ulTtDl�© ��w*lTw�gS��v�gS�x}��rv³©�g�o��xguw*�rt»©�}��xw*�So3ln{��¸�xguw*�rtQw*�iyzgS�S±¥,¦ gS�.� ¦ }Nµ>gS�zw ¦ lTw�©ulTtDln©u��wÝ�.©�}�{��xw�v*ln�i{|w�vxg¨h�l]Á�lTw*��}�{���trv�}�����© g,¬§guw�wxgSv�h�}Nµ�guv6¬§}��r{�����w ¦ ln{ª�rgSy®lT{��©�}�{��xw�v*ln�i{|w��0v�gSh�lNÁ�lTw���}�{��S±

tvu�t¾u�t Ó Æ «$¢�z°  ¡�z°¤��,­l­-¢ É £�¤�® Æ  Ô Æ�Õ�Ã/Ö�×½ÃvÈ�ÑUÅ`Ñ-Ã Î°Ø ×¾×GÄ�Ã Ì Õ�ÂlÆ[È

¥,¦ g¨�xg>����{r}�vxg�w ¦ g>y.��h�w��÷�h�gS�ng¨hn��wxv*��©�w��rv�g�}�~º���l5��-�8=Qln{r�Û��}�h���g>l���gS¶\��g¨{�© g�}�~x5��-�8=��S±-f�h�l�©*º\¬��rv*{ln{����K�ihih�gS{¡~¶Ù�����gS�ng¨h�}nt§gS�5l��rg¨©�}�yztD}�����w*��}�{«trv�}r©�gS���rvxg>~´}�v/w ¦ g�y5��h�w*��h�gu��gSh�t�vx}�¬�h�gSyP¬|�«yz}�����~´���i{���xguw*�rt ln{�� ¦ }�hi���i{��!© }���w��S± ¥0¦ gu�Ä©�}�{r�*�i��gSvxgS�À��{�©ulTtDl�© ��w*lTw�gS�Àln����gSy5¬�h��¿�x���xw�gSyª�.µ���w ¦ ©�}�{��xw*ln{|w

Page 7: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

�rgSy®ln{r�ko\�i{r²�{���wxgsw*�iyzg ¦ }�v*��¹u}�{3o�ln{r�8�xgSw��rt�© }���w��S± ¥,¦ gu�®�x}�h���gmw ¦ g¨�xgst�vx}�¬�h�gSyª���r�*�i{��zln{:g Ár�i�xw*�i{�����i{r��h�g�h�gu��gSh0h�}nwx·�����¹S�i{r�!lTh���}�v*��w ¦ y�± ¥ gSyzt§gShiyzgS��guv�ln{�� j�g¨h�¬DgSv ~ c��������xgS�Äw ¦ g�© }���wzln�T¯ø�r��w�yzgS{|wt�vx}r©�g¨�r�rv�gS�m}n~�f�h�l�©*º\¬���v*{�ln{����K�ihih�gS{ ~�Ù��6ln{��Kj�gS�i{rv���© ¦ ln{��¸��© ¦ {rguguµ�gS�i���Ú~ er�E�6lnh�}�{r�®µ���w ¦ w ¦ g¦ gS�rv��i��w���©®w�g¨© ¦ {��i¶|�rg�trv�}�t§}���gS� ¬\� qI�ÃÁ\}�{Äln{�� �\�ih���guv ~ç�¨e���w�}¸�x}�h���g�lK��gS¶\��g¨{�© g8}�~����i{r��h�g�h�gu��gSh5��-�8=4�¨± ¥,¦ g�²�{�lnh���w*lT��g8}�~�w ¦ g�lnh��n}�v*��w ¦ y v�gS�xw�}nv�gS� ~´g¨ln����¬��ihi��wb�!�����i{r�!lQ��yz}\}�w ¦ �i{r� ¦ gS�rv*�i�xw*��©n±�|w*ln�rw*h�guv¨~ c"@��ktrv�}�t§}���gS��l.w��iyzg ·p}�v*��gS{|wxg¨����g]©�}�y�t§}�����w*��}�{ ¦ g¨��v*�i�xw*��©swx}®�x}�h��ng%w ¦ g��r��{�lnyª��©Iy.��h�w��÷��w�gSy y.��h�w��÷�h�gS�ng¨h�h�}�wx·�����¹S�i{r��t�v�}n¬�h�gSy �i{ ��gS{rguv*lnh�t�v�}\����©�wz�xw�v*��© w��rv�gS�5µ���w ¦ �*�i{���h�g�ln{��Äy5��h�w*��t�h�g©�}�{��xw�v*ln�i{rgS��v�gS�x}��rv*© gS��ln�,µ>g¨hih3ln���xguw*�rt�w*�iyzgS�S±

ËfÌºÍ Ä Ì/Î�Í Æ Ì/Î ÉAÆ]Ï ÌxÐ¾Ì ÅUÑUà Î

¥ v*���ng¨��vx} Ï ÞÛànÒ(� ~ c¦Ù��,©�}�{����i�rguvxg¨� w ¦ g��*�i{���h�g�h�gu��gSh>h�}�wx·�����¹S�i{r�Ktrv�}�¬�h�gSy µ���w ¦ ��guw��rt ©�}��xw*�So���guw��rtw*�iy�g¨�So�ln{���lz���i{r��h�g�© }�{��xw�v³lT�i{rgS��v�gS�x}��rv*© g�± ¥,¦ gS�����xgS�0�/lT�nv³ln{r�ng]lT{N�,gSh�lNÁ�lTw���}�{�}n~-w ¦ gÛ©ulTtDl�© ��wÝ�©�}�{��xw�v*ln�i{|w���wx}.�rg¨©�}�yzt§}���gmw ¦ gstrv�}�¬�h�gSyª�>�i{�w�}5��{�©ulTt�l�© ��w³lTwxg¨�®���i{r��h�g ·���w�gSy t�vx}�¬�h�gSyª�So�µ ¦ ��© ¦ µ�guvxgw ¦ g¨{Û�x}�h��ng¨�%¬\�«����{�lnyª��©�t�vx}���v*lnyªyª�i{r��±k�,w/w ¦ g�h�lT��w/�xw³lT��g�o]l ¦ gS�rv*�i�xw*��©4��yz}\}nw ¦ �i{r��t�v�}r©�gS���rvxg�µ,lT����xgS�.w�}I�ng¨{�gSv*lTw�g�~´g¨ln����¬�h�g>t�v�}��r��©�w*��}�{5t�h�ln{��S± ¥ g¨y�t§gShiyzgS��gSv6ln{���qmgSv��xw�v�}n�µ~ c]£��r���xg¨�Ò�/lT�nv³ln{r�ng]lT{v�gSh�lNÁrlTw*��}�{Q}�~>w ¦ g®y.��h�w��÷�h�gu��gSh��i{���gS{|w�}�vx��¬Dlnh�ln{�© �i{r��© }�{��xw�v³lT�i{|w*��ln{��¿©ulTt�l�© ��wb�¸©�}�{��xwxv³ln�i{|w��So$lT{���rtR��lTw�gS�$�/lT��v*ln{r��g¨ln{¸y.��h�w���t�hi��guv*�I�����i{r�����r¬��nv³ln����gS{|w%}�t�w��iyª��¹¨lTw*��}�{Kwx}�©�}�yzt���w�gªh�}Nµ�guvI¬§}���{r���S±3�g¨ln����¬�h�g��x}�hi��w*��}�{���µ�guv�g,w ¦ gS{z�ng¨{�gSv*lTw�gS�ª�r�*�i{��5l ¦ gS�rv*�i�xw*��©�²�{���wxgm�*© ¦ gS����hi�i{���trv�}r©�gS���rvxg|± ¥ v�����gS��v�}Ï Þ�ànÒ(� ~ c"Ù��/���xg¨���$lN��v³ln{���g¨ln{��,gSh�lNÁ�lTw���}�{�ln{���qm��{�lTyª��©�=4vx}���v*lnyªyª�i{r�.~´}�vr���l5��-�8=��S±

Ë Ã:Õ Ì Ï}ÁfÆ Ì Ä�Õ]Â'Û*Ä�Ã8Õ¦Æ�Ü/Ê�Ä�Æ[È

¥,¦ g¨�xg ¦ g¨��v*�i�xw*��©Ûyzguw ¦ }����I�i{�© hi���rg.���iy.��h�lTwxg¨�Kln{r{rg¨lnhi�i{r�DoDw³lT¬��Q�xg¨lTv*© ¦ o§��gS{rguw*��©5lnh��n}�v*��w ¦ yª�SoRlT{��gu��}�hi�rw���}�{ �xw�v³lNw�gu����gS�S±���lnh�}�yz}�{ ~ c�c���ln{�� j�gSh�¬§guv ~ e�e��Û©�}�yztDlNv�gS� �x}�yzg¸}�~Ûw ¦ gS��g!yzguw ¦ }��r�¨±��lnh�}�yz}�{.lT{��X�%����ºÝ~ cNd"�����i�*© �����xg¨�5���iy.��h�lNw�gS�5ln{�{rg¨lnhi�i{��s¬Dln�xgS�5yzguw ¦ }\���S±6j�gSh�¬§guvÞ~ e�e���©�}�y�tDlTv�gS��rg¨©�}�yzt§}��*��w���}�{ko�h�}r©ulnhI�xg¨lTv³© ¦ om�rg¨©�}�yzt§}��*��w���}�{ ln{�� h�}r©ulnhI��g¨lTv*© ¦ osln{�� w ¦ g$�/lT��v³lT{r��g¨ln{ ¬Dln�xgS�yzguw ¦ }�����}�~ ¥ gSyzt§gShiyzgS��guv0lT{���qmguv*�xw�vx}��¥~ c]£��p±��I©u©�}�v*�r�i{r�5w�}zj�g¨h�¬DgSv¬~ e�e���o\���iy.��h�lTwxg¨�:ln{�{rg¨lnhi�i{��h�}r©ulTwxg¨� �x}�hi�rw*��}�{��8µ���w ¦ w ¦ g¸¬§gS�xw�l¨��guv*lT��gQ¶\��lnhi��wÝ�|o0¬��rw�v�gS¶\����vxgS� y5��© ¦ ©�}�y�t��rw³lNw*��}�{�lThmgu�R}nv�wµ ¦ ��© ¦ µ�guv�g¸�x}�y�gSw��iyzgS�8trv�} ¦ ��¬���w*����gK~´}nv���y®lnhihmt�vx}�¬�h�gSyª�S± � yª�ÃÁ½}n~Ûgu��}�hi��w*��}�{½�xw�v³lNw�gu��� lT{���rg¨©�}�yzt§}��*��w���}�{8t§guv�~´}nv*yzgS��w ¦ g«¬§gS��w,~´}�v�yzgS���i��y ����¹ugS��trv�}�¬�h�gSyª�S±

Ë Û¼É,Æ[Ï Ì/ÐvÌ Å`Ñ-à Î

�KlTgS� Ï Þ>ànÒ(� ~ en����trv�gS�xg¨{�w�gS�8w ¦ vxgug��a=ĬDln�xgS� ¦ gS�rv*�i�xw*��© ��~´}nv,�x}�h��\�i{r��y.��h�w��÷���w�gSy�o|y5��h�w*�÷��xw³lN��gsh�}�wx·����¹S�i{r�5t�v�}�¬�h�g¨yz��µ���w ¦ y5��h�w*��t�h�gI©�}�{��xw�v*ln�i{rgS�®v�gS�x}��rv³©�gS�So\�xgSw��rt�© }���w��Sorln{��8{r}��xgSw��rt8w*�iyzgS�S± ¥,¦ g¨�xg

£

Page 8: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

w ¦ v�gug ¦ gS�rv��i�xw*��© �®�xw*lTv�wxg¨�Zµ���w ¦ l!�x}�hi�rw*��}�{ w�}»w ¦ g��a= vxgSh�lNÁ�lTw���}�{Z}n~Iw ¦ g�t�v�}n¬�h�gSy�o0ln{��¼��}�h���gS��xgS¶\�rgS{�©�gS�ª}�~o��= vxgS��wxv*��©�w*��}�{��ª��{|w��ih�ln{ �i{|w�gu��guvª�x}�hi�rw���}�{Zµ,ln�z~´}���{r�k± ¥,¦ guvxg�µ,ln�So ¦ }Nµ>gS�ngSvSo>lw�v*ln�rg ·p}��8¬DgSwݵ�gugS{�w ¦ g�¶\��lThi��wb�Û}�~R�x}�hi�rw*��}�{���ln{��zw ¦ gm©�}�yzt��rw*lTw*��}�{�lnh�gu�R}�vxw¨± ¥,¦ g�¬§gS�xw�t§guvx~´}�v*yª�i{��¦ gS�rv��i��w���©sv�gS¶\����vxgS��¬rv³ln{�© ¦ lT{���¬D}���{���lTw�w ¦ g�h�ln�xw��xwxgSt�}�~-w ¦ gÛlnh��n}�v*��w ¦ y�±

ß�Ã6ÆÇàµÕ]Ñ-Æ Î Å4á�Ã8Ü/Ñãâ�Õ Ì Å`Ñ-à Îåä Æ"ÊlÄ�Ñ`È"Å`ÑUÕ

jslNv�v*�i�x}�{ ln{r���3guµ��i� ~ en���«�rgS�³©�v���¬§gS� w ¦ g+5>}\guÂ:© ��gS{|w���}��r��²D©ulTw*��}�{ j�g¨��v*�i�xw*��©Ä��5��Kj%�ªµ ¦ ��© ¦�|l¨�ngm��}|}��8�x}�hi�rw���}�{���w�}.y.��h�w��÷���w�gSy�o�y5��h�w*�÷��xw³lN��gsh�}nwx·�����¹S�i{r�Ûtrv�}�¬�h�gSyª��µ���w ¦ y.��h�w���t�h�gs©�}�{��xwxv³ln�i{rgS�v�gS�x}��rv*©�g¨�kln{��«�xguv*��lnhnln���xg¨yÛ¬�h��s�x���xwxg¨yz�¨± ¥,¦ g¹5¹�Qj»µ,ln�k��g¨������{�g¨�Iwx} ¦ lT{���h�g��xguw*�rt��3w ¦ lNw$©�}�{�����y�g©ulTtDl�© ��wÝ�¼�°�xguw*��tÀw��iyzgS���«lT{��ÄlT�*����y�g¨�¿w ¦ lTw5w ¦ g��xguw*�rtÄ©�}��xw*�.lTv�g8��y®lnhih4g¨{�}��r� ¦ w�}K¬Dg�����{r}�vxgS�k±�«lTw�}nº Ï ÞÛànÒ(� ~ eNd¦�,�i{|w�vx}�����©�gS�Àw ¦ g05>}\guÂ:© ��gS{|wÒ��}�����²�©SlNw*��}�{Äj�gS�rv*�i�xw���©:µ���w ¦ 5>}��xwzf0lnh�ln{�©u�i{��ln{��¸�|guw��rt �,g¨�r��©�w*��}�{ ��5��Kjsf¹�I� ¦ gS�rv*�i�xw���©�± ¥,¦ gu��g Á�w�gS{���g¨� 5¹�Qj_wx} ¦ ln{r��h�g5�xgSw��rt¸©�}��xw*�slT{����gS{rguv³lThkln���xg¨yÛ¬�h��8�xw�v���©�w*�rvxgS�¨±

æ¢Å`ÂlÆ�Ä ä Æ�Ê�Ä�ÑUȦÅ`Ñ-Õ[È

�mº|º�guv Ï Þ/ànÒ(� ~Ã�E�\���xg}5>}�hi��yª{*;sgS{rguv³lTw���}�{�~´}nv$w ¦ gS�xg0© h�ln���/}�~rt�vx}�¬�h�gSyª�S±$qmgu��v³lTgu��g Ï Þ/ànÒ(� ~Ã�S���\���xgS�l�f>v*ln{�© ¦ ·Ýln{r��·>=4v*��©�gÛ��5>}�hi��yª{,;sgS{rguv³lTw���}�{§�6lnh��n}�v*��w ¦ y ~´}�v4w ¦ go50lTt�l�© ��w³lTwxg¨�Ò�3}�wx·ø�\��¹S�i{r�4=4v�}n¬�h�gSyµ���w ¦ª¥ �iyzg}=-guv*��}��r����5��-� ¥ =���±¦�«�r��º Ï Þ6ànÒ(� ~ e"@������i�*© �����xgS�ª���iy.�rh�lTw�gS�zln{�{�g]lThi�i{r�%¬Dln�xgS�zyzguw ¦ }��r�¨±j�gSh�¬§guvÝ~ e�e��k©�}�yztDlTvxgS���rg¨© }�yzt§}�����w*��}�{ko�h�}r©ulnhR�xg]lNv³© ¦ o���g]©�}�y�t§}�����w*��}�{�ln{���h�}r©ulnhR�xg]lNv³© ¦ orlT{���w ¦ g�/lT��v*ln{r��g¨ln{!¬DlT��gS� y�gSw ¦ }����S±��I©u©�}�v*�r�i{r��wx}»�\lnh�}�yz}�{ ~ c�c���ln{��+�%����º Ï Þ«ànÒ(� ~ e"@���o6���iy.�rh�lTw�gS�ln{�{�g]lThi�i{r�¿ln{��Zw*lT¬�� ��g¨lTv*© ¦ t§guvx~´}�v*yzgS�Ĭ§guw�wxgSvzw ¦ ln{Zt��rv�g0�a= ¬Dln�xgS� ¦ gS�rv*�i�xw*��© �S±?çn}nv*��ln{¼lT{��qmv�g Árh ~ enc��«��}�h���g!qo�-�8=2¬\� ¬�lTw³© ¦ �xgS¶\�rgS{�© �i{r�Z�����i{r�¼l ¬�v³ln{�© ¦ ·Ýln{���·p¬§}���{�� ¬Dln�xgS� ¦ gS�rv*�i�xw*��©n±���ihih�gSv Ï ÞzànÒ(� ~ e¦Ù�� ¦ l¨��g����xg¨�¼¬�v*ln{�© ¦ ·Ýln{��\·p¬§}���{��½wx}À�x}�h���g����l5��-�8=6± ¥,¦ gu� �r��gS�¼v�gS����h�w*�®}�~���ihih�gSv Ï Þ,ànÒ(� ~ e� ��-©�}�{�©�guv*{r�i{r�®w ¦ gÛtD}�h�� ¦ gS�rv*lnh/�xw�v���©�w*�rvxgÛ}�~����iyzt�hi��²�gS��yz}��rgShi��}�¬�w³lT�i{rgS��~´v�}�y7l���i{r��h�g�w*�iyzg�t§guv*��}��¸}�~�����5¹�-�8=6o�w�}�}�¬rw³ln�i{!�xwxv�}�{r���nlThi�i�!�i{rgS¶\��lnhi��w���gS�I~´}�v4���l5¹�6�[=�±kf>�rw«w ¦ gS��vlTt�trv�}|l�© ¦ v�gS¶\�r��v�gS��g Á�w�gS{�������g%¬rv³ln{�© ¦ ·ÝlT{���·p¬§}��r{���wxg]© ¦ {r�i¶\�rgS�,wx}ª����lTv*ln{|wxgSg%~´g¨ln����¬��ihi��wÝ�Q�´gu��gS{�~´}�v��y®lnhih3����¹ugS��t�v�}�¬�h�g¨yz���Ù±

QSR�è \rmoéeé�d�ê:ë

¥,¦ gÛhi��wxguv³lTw��rv�g%vxgS�\��gSµ trv�gS�xg¨{�w�gS� ¦ guv�g��i{��r��©SlNw�gS�0w ¦ lNw�w ¦ g�trv�}�����© w���}�{�t�h�lT{�{��i{r�:lT{����*© ¦ gS����hi�i{��}�~�tDlTv*lnhih�gSh$µ>}�v�º�© gS{|wxguv*�m~´}nv%y.��h�w���t�h�g.��w�gSyª� ¦ l¨��g�{r}�ws¬§gug¨{Kt�v�}nt§guv*h��Kln����v�gS����gS�Q�i{¸©�}�{T¯ø�r{�©�w*��}�{µ���w ¦ y.��h�w���t�h�gªw�}|}�hi�i{r��ln{r�À©ulTt�l�© ��w³lTwxg¨�Qv�gS�x}��rv³©�g:©�}�{��xw�v*ln�i{|w*�So$ln{��»��gS¶\��g¨{�© g ·��rgut§gS{���g¨{�w5��guw��rt©�}��xw*�6ln{r�Ûw*�iy�g¨�S± ¥,¦ g>t�v�gu����}����$gu�§}�v�w��-��}%{�}�w�©�}�{r�*�i��gSv-lnhih�}�~rw ¦ gS�xg>v�g¨lnhi�i�xw*��©�©�}�{��xwxv³ln�i{|w��/w�}n��guw ¦ guv

Ù

Page 9: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

ln�IlTvxg5~°l�©�gS��¬\��l:yz}\�rguv*{��i{T¯bg¨©�w*��}�{�yz}�hi���i{r�®~°l�© �ihi��wb��±�qI���§guv�gS{|wm�x}�hi�rw*��}�{��xw�v*lTw�gu����gS� ¦ l¨�ngÛ¬§gug¨{�rgu��gSh�}�t§gS�ª�i{ªw ¦ gmhi��wxgSv*lTw*��v�g�±-f��rw�~´}nv>h�lNv���g��*��¹ugS�zt�v�}�¬�h�g¨yz�¨onw ¦ guvxg�v�gSy®ln�i{r�>l«������{���²D©uln{�w4w�v³lT�rgu}��¬§guwbµ>gug¨{.w ¦ g��x}�hi�rw���}�{�¶\��lThi��wb�.ln{���w ¦ gm© }�yzt��rw*lTw*��}�{�lnh�w��iyzgS�¨±l3r}�v4t�v*l�©�w*��©ulnhr����¹ugS��t�vx}�¬�h�gSyª�So���w4�i��rgS����v³lT¬�h�g�wx}Û}�¬�w*ln�i{:l«�n}\}��®�x}�hi�rw���}�{zµ���w ¦ l���y®lnhihr}�t�w*�iyªlnhi��wb�Û�|lTt®µ���w ¦ �i{®l�©u© gut�w*lT¬�h�g�t�vx}r©�g¨�����i{r�w*�iy�g¨�S±ì3�ln�xw�guvª�x}�hi�rw���}�{À�ng¨{�gSv*lTw*��}�{Zy�g]© ¦ lT{��i��yª�zlTv�g�lnhi�x} ¦ gSh�t�~å��h�~´}�vzvxg]©ulnh�© ��h�lNw*��}�{ �*© ¦ g¨�r��h�gS�� ¦ }���hi�Kw ¦ guv�g�¬§gªl�© ¦ lT{r��g��i{Kw ¦ gz�rgSy®ln{��Q��lTw*l�± ¥,¦ �i�stDlTt§guv«lTw�wxgSyzt�w*�sw�}�yªlTº�g.w ¦ g�~´}�hih�}Nµ��i{r�wbµ>}n·p~´}�hi��©�}�{|wxv*��¬���w*��}�{��!±

�ø�]�8� {rguµ¿h�}�wx·�����¹S�i{r�0trv�}�¬�h�gSy ~´}�v�y.��h�lTw���}�{mµ���w ¦ �xgS¶\�rgS{�©�g��rgut§gS{��rgS{|w/�xguw*�rt«w��iyzgS�/ln{r��© ¦ ln{r�ngS}]��guv©�}��xw*�So�lT{���y.��h�w���t�h�g�©ulTtDl�© ��w*lTw�gS�8v�gS�x}��rv*©�gÛ©�}�{��xw�v*ln�i{|w��¨orln{r�

�Ve��8� �rg¨©�}�yzt§}�����w���}�{I¬�ln�xg¨� ¦ gS�rv��i�xw*��©-w ¦ lTwk�i�/©ulTtDlT¬�h�g4}�~ ¦ lT{���hi�i{r�,w ¦ g4t�vx}�¬�h�gSy ���iyzgS{�����}�{�lnhi��wb��o�x}�hi�rw���}�{�¶|��lnhi��wb�8ln{����xt§gugS��v�gS¶\����vxg¨���i{��i{T¯bg¨©�w*��}�{�yz}�hi���i{��z}�t§guv*lTw*��}�{r�¨±

í� î����Òï ð�Foñ òóFHôG�S�¹��õN�f���Ò I* �� ö��Ò�»ñ � ð�I4������

)s�rv:t�v�}n¬�h�gSy �i�8yz}�w����TlTw�gS� ¬\�¼l¿t�vx}�����©�w���}�{½t�h�ln{�{��i{r�Àln{��½�³© ¦ gS���rhi�i{r� t�vx}�¬�h�gSy ~°l�©�gS�¼¬\�¼l¦ g¨lnh�w ¦ ©ulTv�g�t�vx}�����©�w*�>yªln{\�r~°l�©�w��rv*�i{r�«t�h�ln{|wS± ¥,¦ gmy®ln{|�r~°l�©�w*�rv��i{r��~°l�© �ihi��wÝ� ¦ ln��d�c��i{T¯bg¨©�w*��}�{ªyz}�hi��·�i{r�Iµ>}�v�º�© gS{|wxguv*�$w ¦ lTw6t�v�}��r��©�g«��£¦@m�r���Rguv�gS{|w-t�lTv�w����i{�ls�*�i{���h�g0�xw³lN��g�}�tDgSv*lTw*��}�{k±k¾ ��w ¦ �i{Ûw ¦ g,�*lny�gt�vx}�����©�w�#ø~°lnyz�ih��8%�o3trv�}�����© w��Ûvxg¨¶|����v�gªw ¦ g:�*lny�g®wx}\}�hi�i{r��¬��rwÛ�TlTv��!l�©u© }nv*���i{r��w�}K©�}�h�}nvÛ�*© ¦ gSyzgS�S±¥,¦ g,}�tDgSv*lTw*��}�{��4lTvxg�©�}�{�����©�wxg¨�.}N��guv6wݵ�}z�¨e ¦ }��rv��4� ¦ ��~´w��¨o�£m��l¨���4lsµ�guguº�±l=4vxg¨�xgS{|w�h�� ¦ ��� ¦ ��}�hi��yzg¬DlTw*© ¦ gS��lTvxgm������lnhih��.t�vx}�����©�gS�:�i{C£¨·���l¨��v*��{r�¨±�)mw ¦ guv>h�}n����©ulnhrv*�rh�g¨��hi��º�g�w ¦ �i��lTvxgm���xgS�®wx}5�³© ¦ gS���rh�gw ¦ g�~°ln©u�ihi��wÝ��± ¥0¦ guv�g�lTv�g�lz{\��y5¬DgSv,}�~6© }�{��xw�v³lT�i{|w*�0w ¦ lTwmlN�Rg¨©�w,w ¦ g«t�v�}\����©�w*��}�{3± ¥,¦ g¨�xg��i{�© hi���rg�±

��±<÷ àTã�ÞVé�ø�áTãÇùnÍÙÏ�ÕDÞÝÏ�ã.æ!ànÞ�Í�Î|Ó´Õ\Ö[ú �2tDlNv�w*��© ��h�lNv�t�lTv�w5©uln{»}�{�h��¸¬Dg:t�vx}�����©�gS�»}�{ l�tDlTvxw*��© ��h�lTv���r¬��xguw�}�~kµ�}nv�º|©�gS{|w�guv��>w ¦ lTw,lTvxg«©�}�yztDlNw*��¬�h�gmµ���w ¦ wx}\}�hi�>v�gS¶\����vxgS�:w�}.trv�}�����© gIw ¦ gItDlTvxw�lT{��lTvxg.}�~�lTt�t�vx}�t�v*��lNw�g5w�}�{r{�lT��g�± ¥0¦ g.µ>}�v�º|©�gS{|wxgSv��mw ¦ lTw%©�}�yztrv*�i�xg5w ¦ �i�%©�}�y�tDlTw*��¬�h�g #x�xguw&%:~´}�vw ¦ g«tDlTv�w�lNv�g«w�vxg]lNw�gS��ln�,~å��{�© w���}�{�lnhih��:�i��g¨{�w*��©ulnhRtDlTv*lnhih�gSh�µ>}�v�º�© gS{|wxguv*�S±

er±<÷ àTã�ÞVéVê�ÏÙäuáTÑ�ã*ÍÙÏ�æ!ànÞ�Í�Î|Ó´Õ\Ö[ú ¥0¦ guv�g%lTvxgIy.��h�w���t�h�g�v�gS�x}��rv³©�gS�>w ¦ lTw0lTv�gs{rg¨© gS���*lTv��z~´}�v0l�tDlTv�w>w�}¬§g«�xguw,�rt�~´}�v�t�vx}�����©�w���}�{k± ¥,¦ g¨�xg«�i{�© hi����gI}�t�w���}�{���~´v�}�y�qsgS����©u©uln{|w,qsv���guv¨o��m�r��guvM;sv��i{��rguv¨o5�}�{|��gu��}�v¢;sv��i{��rguv¨o/��trv*��� ¦ w�;sv*�i{r�rguv5lT{��ì5�}�h�}�v4���ÃÁ�guv¨±®�|t§g¨© ��²D©.v�gS�x}��rv*©�g¨�%w ¦ lTwÛlNv�gzv�g ·¶\�r��v�gS��¬\��l�tDlNv�w�y5���xw,¬§g5l¨�Tln�ih�lT¬�h�gI~´}�v,w ¦ g�t�lTv�w,wx}ª¬§g��xgSw��rt�~´}�v,t�v�}\����©�w*��}�{3±

¥0¦ gÛ�xguw*�rt��i�mlzh�gS{r��w ¦ ��lT{���g Á�t§gS{�������g«t�v�}�© gS���mln{����i{�© �rv���h�}����xg¨���i{�w�guv*yz��}�~6trv�}�����© w�������wb��±�pw«�i{|��}�h���gS�Ihi�i{�gª© h�g¨lTv³lT{�©�gzln{��/.¨}�v�©�}�h�}nvIt��rvx���i{r��lT{��/.]}�vIw�}|}�h�© ¦ ln{r��gS�S±Û�­wÝ�\t���©ulnh-wx}\}�h�© ¦ ln{r�ng

Page 10: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

v�gS¶\�r��v�gS�4lT¬§}��rw4d ¦ }��rv*�S±6�p~RlI�����§gSvxgS{|w6tDlTv�w�{rgug¨�r��w�}I¬§g��xgSw��rt/o�y®lNw�guv*��lnh�© ¦ ln{r�ng,y®l¨��}�v4y®lS�5{r}nw}r©u© �rv¨±%�p~�w ¦ g.t�v�g¨©�gS���i{r��lT{��Qw ¦ g.~´}�hih�}Nµ��i{r�:t�lTv�w��s¬§gSh�}�{r�8w�}�w ¦ gz�*lny�g9#b~°lnyª�ih��8%ª}�~�tDlNv�w*�SoRw ¦ gS{w ¦ gÛ�xgSw��rtK© ¦ ln{r�ngÛ�i{���}�h���gS�,yª�i{��iyªlnh�w�}|}�h/© ¦ ln{r��g�±�j�}Nµ�gu��guv,w ¦ guv�gÛyª��� ¦ w,¬§g5l$#Ç5�}�h�}�vr=���v����i{r�"%}�t§guv*lTw*��}�{3±�5>}�h�}nv>t���v����i{r�5}�tDgSv*lTw*��}�{�û���� ¦ gS��}��rw�w ¦ gI�x���xw�gSy µ ¦ g¨{:w ¦ gs~´}�hih�}Nµ��i{r��tDlTv�w��i��hi��� ¦ w�guv�i{8©�}�h�}nv�w ¦ ln{®w ¦ gmt�v�gu����}��r��tDlTv�wS±�5>}�h�}�v�t��rv����i{r�.�i��l0#xh�}Nµ,·Ý©�}��xw-%«}�t§guv³lNw*��}�{®ln{��®w ¦ gmw�}\}�h÷ݩ ¦ lT{r��g}�t§guv*lTw*��}�{%~´}�vkw ¦ g��³lTyzg�#ø~°lnyª�ih��8%0}n~�t�v�}��r��©�w*�$�i�/yª�i{��iyªlnhp±/�p~�w ¦ g�wݵ�}m©�}�{��xg¨© �rw*����g4tDlTvxw*�/¬§gSh�}�{���w�}�xgutDlTv³lNw�g�t�v�}��r��©�w>~°lnyª�ihi��gS�Sonw ¦ gS{®w ¦ g Í�ÎràTÕ\Ö\Ï*áTânÏ�ãIͳáNä�Þ ©uln{ª¬§g ¦ ��� ¦ ln�>��w��i{���}�h���gS�4g Á�t§gS{�������g�w�}\}�hln{��Û����g0© ¦ ln{r�ng0lnh�}�{r�mµ���w ¦ y®lNw�guv*��lnh|© ¦ lT{r��g�ln{��/.]}nv6©�}�h�}�v/t��rvx���i{r�D±-���rg¨lnhih���o]�xgSw��rt��$}�~�l,#ø~°lnyª�ih��8%}�~�t�lTv�w��6� ¦ }���hi�Û¬§g0�r}�{rg�wx}���guw ¦ guvS± ¥,¦ �i�-yª�i{r�iyª��¹ug¨�kw ¦ g0© ¦ ln{r��gu}N��guv$w��iyzg�ln{���©�}��xw6ln{�� ¦ gS{�©�g>w ¦ g�xguw*�rt�© ¦ ln{r�ng�© }���wS± Ì3Ï*Ø ÑDÏ�ÕRÍÙÏ o\�i{�����© ¦ l��xgS¶\�rgS{�©�g���gStDg¨{r�rgS{|w��xgSw��rt/or�i�0w ¦ guvxgS~´}nv�g«ln{��iyzt§}�vxw³ln{|w�i�����rg�±0�mhi��}�o�w ¦ g.©�}�yztDlT{|��µ,ln{�w*��w�}8©�}�yzgÛ�rt�µ���w ¦ lªt�vx}�����©�w*��}�{��*© ¦ gS����h�g�w ¦ lTw�yª�i{��iyª��¹ugS�,w ¦ gw�}nw³lnh��xgSw��rt/o��i{|�ng¨{�w�}�vx� ¦ }�hi���i{r�¸lT{�� ¬�l�©*º�h�}������i{��K© }���w��S±�¾»g�yz}���g¨h�w ¦ g8t�vx}�����©�w���}�{À����w���lTw*��}�{�rgS�*©�v*��¬§gS��lT¬D}N��g«w ¦ v�}��r� ¦ l�yª�ÃÁ�gS���i{|wxgS�ngSv0t�vx}���v³lTyªyª�i{r�zyz}\�rgShk�i{�w ¦ g«~´}�hih�}Nµ��i{r���xg¨© w���}�{k±

è}RUT üåW�Y6dGYº^`W»b

� �����§gSvxgS{|w�tDlTvxw>wb�\tDg¨��lTv�gmtrv�}r©�gS����gS�®w ¦ v�}��r� ¦�ý ~å��{�©�w*��}�{�lnhih��z���iyª�ih�lNv�µ>}�v�º�© gS{|wxguv*�S± ¥0¦ gsµ>}�v�º|·©�gS{|w�guv�yªl¨�Q�����§guv��i{¸w�}�{�{�lT��gz}�v«t�v�}�© gS���%~´g¨lTw*�rvxgS�¨±ª��l�© ¦ t�lTv�w«v�gS¶\�r��v�gS��l�©�}�y5¬��i{�lNw*��}�{K}�~0����~ ·~´guv�gS{|w%v�gS�x}��rv³©�gzwb�|t§gS�«}��rw«}�~Sþ l¨�Tln�ih�lT¬�h�g.v�gS�x}��rv*©�gªwÝ�\t§gS�S±A)s{�h��K}�{rgzv�gut�hi��©ulTw�g�~´}nv�g¨l�© ¦ }n~>w ¦ gv�gS¶\�r��v�gS��v�gS�x}��rv*©�g¨�m�i�mw�}8¬§gzln��������{rgS��w�}8w ¦ g.tDlNv�wx·pµ>}�v�º�© gS{|wxguvI©�}�y5¬��i{�lTw*��}�{k±}¸vÿ-����© ¦ v�gut�hi��©ulTwxg¨�lTvxgªl¨�Tln�ih�lN¬�h�g5~´}�vsw ¦ g�� w ¦ vxgS��}��rv³©�g.wb�\t§g�±¢=4vx}�����©�w���}�{Kt�h�ln{�{r�i{r��ln{��Q��guw��rt!��gS¶\��g¨{�©u�i{�� ¦ l¨��g.w�}¬§g%t§guv�~´}�v�yzgS��}N��guv�l.t�h�lT{�{��i{r� ¦ }�v*��¹u}�{��i{�vxg¨�xt§}�{��xg%w�}ª�rguw�guv*yz�i{��i�xw*��©�}�v*��gSv��S±-¾¿g�ln���*�ryzg�lTw�lnhihw*�iy�g¨��w ¦ lNw0w ¦ g%�xguw*�rt�w��iyzgS�0lTvxg%��y®lnhih�guv�w ¦ ln{:w ¦ gIt�v�}\����©�w*��}�{:w*�iy�gItDgSv���}��k±G3��rvxw ¦ guvSo��xguw*�rt��,lTvxg{r}�w5lnhih�}Nµ>gS�¸µ���w ¦ �i{¿l�w*�iyzgªt§guv*�i�3o-�p± g|±�o$lTw5y�}��xw�}�{rg®t�vx}�����©�wÛwÝ�\t§g:�i�Ûlnhih�}Nµ�gS�¸}�{ l�tDlTvxw*��© ��h�lTvµ�}nv�º|©�gS{|w�guv�lNwml.tDlTvxw*��© ��h�lTv0w*�iyzg%tDgSv���}��k±

3r}�hih�}Nµ��i{��z�i�0w ¦ g�{r}�w*lTw*��}�{�~´}�v,�nlNv*��}����,�i{r����©�g¨��ln{���t�lTv³lny�gSwxguv*�,���xgS���i{�w ¦ g�yz}��rgShp±��{��r��© gS�!± ��� ��{r�rg Á�}�~$tDlTvxw�wÝ�\t§gS������� ��*e��������� � � � ��{r�rg Á�}�~$µ�}nv�º|©�gS{|w�guv���� � ��*e��������� ý �� � ��{r�rg Á�}�~$w*�iy�g«t§guv*��}\����� � � ��*e������������o�ln{����� ��{r�rg Á�}�~$v�gS�x}��rv*©�g¨������� ��*e���������&þ

�S�

Page 11: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

qIlTw³l:±����� � qsgSy®ln{r��~´}nv,tDlTv�w��>lTw,w*�iyzg%tDgSv���}�� � o� ��� � 50lTtDln©u��wÝ�®}�~-µ�}nv�º|©�gS{|w�guv w�}zt�vx}�����©�g«tDlTvxw���t§guv���{r��w�w*�iy�g%t§guv*��}��ko� ��� � =4v�}��r��©�w*��}�{�v³lNw�g«~´}nv,tDlTv�w���}�{�µ�}�vxº|©�g¨{�w�guv o� � ��� � ¥ }\}�hi�i{r�z�xguw*�rt�w*�iyzg%}�~-~´vx}�y�tDlTvxw"!®wx}ªtDlTvxw��4}�{�µ�}nv�º|©�gS{|w�guv o# � � � �QlTwxguv*��lnh�© ¦ ln{r��gu}N��guv0w*�iyzg%~´vx}�y�tDlTvxw"!®wx}ªtDlTvxw��³o$ � ��� � 5>}��xw����rg«wx}®�xgSw��rt�© ¦ ln{���g«~´vx}�y�tDlTv�w"!ªwx}ªtDlTvxw���}�{�µ�}�vxº|©�gS{|w�guv o%&� � =-gS{�lnh�wb�8©�}��xw,~´}�v ¦ }�hi���i{r�ª�i{|��gS{|wx}�v��®}�~6lz��{���w,}�~-t�lTv�w��³o�ln{��' � � =-gS{�lnh�wb�8©�}��xw,~´}�v,¬�l�©*º�h�}������i{���}�~�l���{r��w�}�~$tDlTvxw��³o( ÿ��� � ) � ��~�� w ¦ v�gS�x}��rv³©�g«�i�,v�gS¶\�r��v�gS��w�}zt�v�}\����©�g�tDlTvxw���}�{�µ�}nv�º|©�gS{|w�guv � }�w ¦ guv�µ��i�xg �+*��,�-*.�/�-* �0�1 ��� � ) � ��~$tDlNv�w��>©uln{�¬§g�trv�}r©�gS����gS��}�{�µ�}�vxº|©�gS{|w�guv � }�w ¦ guv�µ��i�xg �+*.�/�-* �2�qmg¨©u�i����}�{ § lNv*��lT¬�h�gS�!±ê�Ï*ànÒ(ú43 ���5� � 6s��ln{|w���wb�®}�~-t�lTv�w���t�vx}r©�g¨���xgS��}�{�µ>}�v�º�© gS{|wxguv lTw,w��iyzg«tDgSv���}�� � o7 ��� � ��{|��gS{|wx}�v��®}�~-tDlTvxw��>lTw,w*�iyzg%t§guv*��}�� � o�ln{r�8 ��� � f0l�©*º�h�}n��}�~-t�lTv�w��>lTw,w*�iyzg%t§guv���}�� � ±9 Ó´ÕRàTã0:]ú;<�=�5� � ) � ��~$tDlTvxw����i��ln��������{rgS�8w�}ªµ>}�v�º|©�gS{|wxgSv lTw,w��iyzg«t§guv���}�� �

� }�w ¦ guv�µ��i��g �+*.�/�-* �>* � �³�? � ���5� � ) � ��~$tDlTvxw����i���xguw*�rt�~´v�}�y�tDlTvxw"!ª}�{�µ�}nv�º|©�gS{|w�guv lTw�w��iyzg%t§guv*��}\� �� }�w ¦ guv�µ��i��g �+*.�/�@!A�-* �-* � �2� B�¸ �

è}R�Q CMWfêxéÝmHn`dGYº^`W»b

� � � ý ��¸7± DE�/�@!F� ��HG�I!JE�LK.MONE �+K.M $ � ���P? � ���5�RQ DE �SK.M NE �TK.M %U� 7 ���RQ DE �SK.M NE �+K.M ' �V8 ��� �

�\�r¬r¯bg¨©�w�w�}º±

���

Page 12: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

7 ���XW>8 ��� � 70�ZY[�]\<M@^ W>8 �ZY[�V\<M_^ Q JE�LK.M3 ���5�XW-�`��� *a�0�-* � � �ø�]�3 ���5��b � ���c;<���5�XW DE!d� �fe 1&� � � ��HG�I! � �=� � � � ���gQ # � � � ? � ���5�

*.�/� e 1 ��� � ��-* � � �Ve��DE �hK.M JE�LK.M ( ÿ�=� ;<���5�ib ¸vÿ *.�/� e 1 ��� � �`�>*j�,� � � �°c|�

DE �SK.M ;<���5�ib � *.�/� e 1 ��� � ��-* � � �´d��? � ���5��k ;<���5�RQI; � �PY[�V\<M_^ W � *.�/�@!A� e 1 �=� � 1&� � � ����HG�I!A�>* � � ��@��;<���5�ml n �o�u��p *.�/� e 1 �=� � ��-* � � �°�|�? � ���5�ql n �o�u��p *.�/�@!A� e 1 ��� � 1A� � � ����rG�I!s�>* � � ��£��3 ���5� � 7 ��� � 8 ���ik � *.�/�-* �-* � � ��Ù|�

¥0¦ g�}�¬r¯bg¨©�w*����g�~å�r{�©�w*��}�{¼yª�i{��iyz��¹SgS��w ¦ gKwx}�w³lTh��xguw*��t ©�}��xw8ln{r�¼w ¦ g��i{|��gS{|wx}�v�� ¦ }�hi���i{r�ÀlT{��¬Dl�©*º�h�}n�����i{r��©�}��xw*�S±�5>}�{r��wxv³ln�i{�w®�ø�]�my®ln�i{|w*ln�i{��sw ¦ gªy®lT�*�I¬Dlnh�ln{�© g�}n~>tDlNv�w*�%t�vx}�����©�gS�/.N��g¨hi���ngSvxgS�ln{��Kw ¦ g��i{|��gS{|wx}�v���h�gS�ng¨hi�sl�©�v�}����sw ¦ g�w*�iy�g.tDgSv���}����S±�5�}�{��xw�v*ln�i{|wz�Ve����rguwxgSv�yª�i{rgS�mw ¦ gz{|��y5¬§guvI}�~tDlTvxw*�.w ¦ lTwª©uln{À¬§g�t�vx}�����©�gS�Z���r¬r¯bg¨© w.w�}¸w ¦ g�©ulTtDln©u��wÝ� ©�}�{��xw�v*ln�i{|w.}�~�w ¦ g�µ�}nv�º|©�gS{|w�guv�ln{��Àw ¦ gh�}����s}�~�t�vx}�����©�w���}�{¸�i{�© �rvxv�gS�¸ln�%l:v�gS����h�wI}�~��xguw*�rt!ln{��/.¨}�v%y®lTwxguv*��lnh-© ¦ ln{r��g�o���~>ln{��|±¢5>}�{��xwxv³ln�i{|w�Vc��0gS{����rvxg¨��w ¦ lTw�w ¦ g5{|��y5¬§guv�}�~�v�gut�hi��©ulTwxgS���r��gS��~´}�vslztDlTvxw*��© ��h�lTv�v�gS�x}��rv*©�gÛwÝ�\t§g5�i�mh�gS����w ¦ ln{�}�vgS¶\��lnh4w�}�w ¦ g8{|��y5¬§guvÛ}�~0vxgut�hi��©ulTw�gS�Ûl¨�Tln�ih�lN¬�h�gz~´}�v�w ¦ lTwÛv�gS�x}��rv*© g®wÝ�\t§g�±N5>}�{r��wxv³ln�i{�w8�åd��sgS{����rv�gS�w ¦ lTw5}�{rh��!}�{rg:tDlTvxw5wÝ�\t§g�©uln{¿¬Dg8t�v�}�© gS���xgS�¿¬\�¿l�tDlTvxw*��© ��h�lTv�µ�}�vxº|©�gS{|w�guv5lTw.l�t�lTv�w���©u�rh�lTvÛw��iyzgt§guv*��}\�k±�5>}�{��xw�v³lT�i{|wm��@��-�rguw�guv�yª�i{rgS�4µ ¦ gS{ªw ¦ g���guw��rt®�xw³lTwxgm© ¦ ln{r��gS�S±�5�}�{��xw�v*ln�i{|w*���°�|��lT{�����£n��lTvxgw ¦ g�¬��i{�lTv���© }�{��xw�v³lT�i{|w*�S±�3-�i{�lnhih���or©�}�{��xw�v*ln�i{|w���Ù|�>�i{�����©ulTw�gS�0w ¦ lTw�w ¦ g�{\��y5¬DgSv�}�~$t�vx}�����©�gS��t�lTv�w��¨otDlTvxw*���i{��i{|��gS{|wx}�v��8ln{���tDlNv�w*���i{�¬�l�©*º�h�}��ªlTvxg�{r}�{\·�{rgu�|lTw*���ng|±

5�}�{��xw�v*ln�i{|w%��£n�>©uln{:¬§gIv�gSh�lNÁ�gS�8ln��w ¦ gI�nlNv*��lT¬�h�gS� ? � ���5� v�gSy®ln�i{®¬��i{�lNv��ªgS�ng¨{:µ ¦ g¨{:w ¦ g%¬��i{�lTv��v�gS�xw�v���©�w*��}�{��i�0v�gSh�lNÁ�gS�»�°�xgug¢�3gSyªy®l��]��±t�Æ �+�¿£ wºu�u Õ¸àTÕQáÙÜRÞ°Ó21®ànÒDäuánÒÔÑrÞ°ÓVáTÕQáwv �yx ÓåÞåÎ8ÞåÎ�Ïfz�Ó´ÕRàTã0:®Í³áTÕ�ä�Þ°ã*àTÓ´ÕDÞ�{}|w~�ã*Ï Ò�à��\Ï*ÐN×�ÞåÎ�Ï%âTàTãÙÓVàAz ÒiÏÙä? � ���5� Þ�à�ù�Ï5áTÕOz�Ó´ÕRàTã0:ªâTànÒÔÑDÏÙä!�

÷ ã�á¨áwv�ú �4¶\��lTw���}�{ �Ve�����}\gS�m{r}nw�����lTv³lT{|w�gug��i{�w�gu��v³lTh3�Tlnhi�rgS�,~´}�v,w ¦ g��TlTv*��lT¬�h�g¨� ? � ���5� ±�;I����gS{w ¦ lTw«w ¦ gz�nlNv*��lT¬�h�gS� ;<���5� lTvxgz¬��i{�lNv���o3w ¦ gzt§}�����w*����g.~´v³ln© w���}�{�lnh-�Tlnhi�rgS�I}�~ ? � ���5� lTvxg®ln�rwx}�y®lTw���©ulnhih��

�¨e

Page 13: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

t���� ¦ gS���rt�w�}��I¬|�®w ¦ g%gS¶\��lNw*��}�{¸��@��4w�}zy®ln�i{�w³ln�i{:~´g¨ln����¬��ihi��wÝ��± ¥,¦ g%�Tlnhi�rgS��}�~/w ¦ g%�TlTv*��lN¬�h�gS� ? � ���5�lTvxg�w ¦ gSvxgu~´}�v�g��rguwxgSv�yª�i{rgS�%¬|�Iw ¦ g4gS¶\��lTw���}�{®��@��Ù± ¥,¦ g��TlTv���lT¬�h�gS� ? � ���5� lTv�g��i{«w ¦ g�}�¬r¯bg]©�w�����g4~å�r{�©�w*��}�{µ���w ¦ t§}�����w*���ng:©�}\guÂ:© ��gS{|w��¨±ª�s� � �i�Ûl�yz�i{��iyª��¹¨lTw*��}�{Qt�vx}�¬�h�gSy�okw ¦ gu�Qw³lNº�g®�rt»w ¦ g:yª�i{r�iy.��y=}�~w ¦ g������ }�~4gS¶\��lTw���}�{À��@���oDµ ¦ ��© ¦ trv�}N���i��g¨���Tlnhi��g¨��}�~ ? � �=�5� wx}8¬Dg W �noR�8lT{��Ä�n±m��{�w ¦ g ý 7 þ �w ¦ g��TlTv���lT¬�h�gS� ?5���5� lTv�g%t§}�����w*����g�±�j�gS{�©�g«w ¦ g«�TlTv*��lT¬�h�g¨� ? � ���5� w³lNº�g«�rt��nlThi�rgS���ªln{r�»��± �� ����ð!�N������ �hõ�õ��f�XI*�P�¥,¦ g%t�vx}�¬�h�gSy2�rgS�³©�v���¬§gS� ¦ guv�gI¬§g¨© }�yzgS� ¦ �r��gI~´}�v,h�lNv���gI{\��yÛ¬§guv0}�~/t�lTv�w��¨o\µ>}�v�º|©�gS{|wxgSv��So|vxg¨�x}���v³©�gS�ln{��Ûh�gS{r��w ¦ }�~rw ¦ g>t�h�lT{�{��i{r��w*�iyzg�t§guv*��}��k±l3-h�}�v���ln{ Ï Þ/ànÒ(� ~Ã�!Ù��\� ¦ }Nµ>g¨�«w ¦ lTw$w ¦ g�h�}�wø·�����¹¨�i{���trv�}�¬�h�gSy���-�8=>���i�c�M÷�· ¦ lTv*�k±6f���wxv³ln{ Ï Þ4ànÒ(� ~�£���t�vx}N��gS�zw ¦ lTw�w ¦ gH5��-�8=¿�i��lnhi�x} ��� · ¦ lTv*�3±���{ª}��rv�©SlT��g�onw ¦ gln���r��w*��}�{�lTh\v�gS�x}��rv³©�g�©�}�{r��wxv³ln�i{�w*�4ln{r��w ¦ g�{r}�{�·p¹ugSvx}«�xg¨¶|�rgS{�©�g��rgut§gS{���g¨{�w���guw��rt®© ¦ ln{���g�ony®lTº�g�w ¦ gt�vx}�¬�h�gSy ���r¬�����y�g�trv�gu����}�����h��®t�v�}N�ng¨{ �0� · ¦ lNv*����guv��*��}�{��S±��|}�orµ���w ¦ }���w,��}��i{r��w ¦ vx}��r� ¦ l�~´}�v�y®lnht�vx}\}�~øoNµ�g,ln������yzg>w ¦ lTw6}���v6t�vx}�¬�h�gSy_�i� �0� · ¦ lTv*�k±k¾¿g,lTwxw�gSyzt�w-w�}I}]��guv³©�}�yzg�w ¦ g,©�}�yzt�h�guÁ���wb�ÛlT{�����iyzgS{�����}�{�lnhi��wb��}�~�w ¦ g®trv�}�¬�h�gSy=¬\�!��gS�ng¨h�}nt��i{r��l��rg¨©�}�yzt§}�����w���}�{¸¬Dln�xgS�»�x}�hi�rw���}�{!yzguw ¦ }��r}�h�}��n�µ ¦ gSvxg%µ>g%¬rv�g¨lTº:�r}Nµ�{�w ¦ g%}�v*�����i{�lnhDt�v�}�¬�h�g¨y2�i{|wx}ªl.��guw0}n~-���r¬rt�v�}�¬�h�g¨yz�¨±��0w0w ¦ �i�0t§}��i{|w0µ�g ¦ l¨�ngw ¦ g�~´}�hih�}Nµ��i{r�z© ¦ lnhih�gS{r��gS�!±

��± ¥0¦ g����iyzgS{�����}�{��0}�~$w ¦ gÛ���r¬rt�v�}�¬�h�g¨yz��� ¦ }���hi��¬§g�y®ln{�lT��g¨lT¬�h�g�±er± ¥0¦ g���guw,}�~6���r¬rt�v�}�¬�h�g¨yz��y.���xw�ln�r�rv�gS���,w ¦ g«gS{|w*��vxg�h�lTvx��g ·�����¹SgS���i{��r���xw�v*��lTh�t�v�}n¬�h�gSy�±c�± ¥0¦ g«}N��guv³lnhihR�*© ¦ g¨y�g�� ¦ }���hi����gS{rguv³lTwxg%��}\}���~´g¨ln����¬�h�g%�x}�hi�rw���}�{��0µ���w ¦ �i{�ln{?#�ln©S©�gut�w*lT¬�h�g!%w��iyzg«hi�iyª��w¨±�MRUT p W»bHW»nU^>YºjH^Ui������HêºWfdfi/j

¥,¦ g5©�}�y�t�h�g Ár��wb�®}�~-w ¦ g�t�vx}�¬�h�gSy ©uln{�¬§g�vxgS����©�gS��¬\�8v�gSh�lNÁr�i{r��w ¦ g�¬��i{�lTv���©�}�{r��wxv³ln�i{�wÛ��£�������g�w�}�3gSyªy®l!�x�]�Ù± ¥0¦ gzv�gS����h�w³ln{�w%t�v�}�¬�h�g¨y=�i�«�xw*�ihih�l�yª�ÃÁ\g¨�¸�i{|w�gu��guvIt�v�}�¬�h�g¨y<���Q�>=��Ù±R¾»gª�x}�h���gS�Qw ¦ ggS{|w*��vxg.t�vx}�¬�h�gSy �©#xyz}�{�}�hi��w ¦ ��©©%:lTt�t�vx}|l�© ¦ �,~´}�v%��y®lnhih6lT{��QyzgS���i��y ����¹ugS�K��guv��*��}�{Q�����i{r�N5�=��$���£�±���}�{.l5��± £<;%j�¹S=4dmt�v�}�© gS���x}�v¨one¦@n�<�Kf$���<�ÀoS¾ �i{�� ¥ dD± ��µ>}�v�º��xw*lTw*��}�{3±$j�}Nµ>gu��guv$w ¦ g�trv�}�¬�h�gSy����¹ug¨�/µ�guvxg ¦ �r��g>~´}�v-yzgS���i��y.·��*��¹ugS�5ln{��5h�lTvx��g ·�����¹SgS�«t�v�}n¬�h�gSyª�S± ¥0¦ g,©�}�yzt��rw³lTw���}�{�lnh�w��iyzg�~´}�v6�x}�y�gyzgS���i��y.·��*��¹ugS��t�v�}�¬�h�g¨yz��g Á�©�gSgS�rgS��w ¦ g5�xt§g¨©u��²rg¨��w��iyzgÛhi�iyª��w,}�~�e ¦ }��rv*�S±�3�}�v�}nw ¦ guvm�i{��xw*ln{�©�gS��}�~yzgS���i��y lT{��¿h�lTvx��gª����¹SgS�!t�vx}�¬�h�gSyª�So�5�=f�/�L� £\±i�zv*ln{¿�i{|wx}�#b}��rwx·p}n~ ·�yzgSyz}�v��[%�©�}�{�����w���}�{��S± ¥,¦ g©�}�yzt���w³lTw���}�{�lnhRw�gS�xw,v�gS����h�w���lTvxg«t�vxg¨�xgS{|wxg¨��h�lTw�guv,�i{K�|g¨©�w*��}�{N@r±

�Sc

Page 14: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

�MR�Q Q�Z`�7j<dfs[k�� Wfê<�¹i¾klb¹Y6k�ê��ìd�s8klg�� k�i¾W¹é���W»s:^>Yº^`W»bó\SY6êºd�Y6k�c�ë

5�h�g¨lTv�h���o|w ¦ g%trv�}�¬�h�gSy�©�}���hi�8{r}�w0¬§g«�x}�h��ng¨�8�i{8��w*��}�v*�����i{�lnhD~´}�v�y2~´}�v�w ¦ g«y�g¨�r�i��y lT{���h�lTvx��gI����¹SgS���guv*����}�{r�¨± ¥,¦ �i��µ0ln��w ¦ g5yz}�w����TlTw*��}�{�~´}�vm�rgu��gSh�}�t��i{��®w ¦ g�e]·>= ¦ lT��g�µ�}nv�º|©�gS{|w�guv,¬Dln�xgS�K��g]©�}�y�t§}����÷w*��}�{��*© ¦ gSyzg0wx}%w³l�©*º�h�g>w ¦ g,yzgS���i��y ln{���h�lTv���g0����¹ugS�.t�vx}�¬�h�gSyª�S±l3���v�w ¦ gSvSonw ¦ g,tDlTvxw*��© ��h�lTv�©�}�y�tDln{|����i�K{r}�wmµ,ln{|wmw�}��i{���gS��ws�i{�guÁ\t§gS{�������g�© }�yªyzguv³© ��lnhk��}�h���guv*�mhi��º�gÒ5�=f�/�L�.±�¾»gz© ¦ }��xg5wx}��x}�h���gÛw ¦ g�xguw�}�~§v�gSh�lTwxg¨�z���r¬�trv�}�¬�h�gSyª�������i{r�Ûln{z}�t§gS{�·��x}���v³©�g���}�h���guv¨o[;o�a=f� dD±ý�%�i{z}��rv�©SlT��g�± ¥,¦ g�~´}�hih�}Nµ��i{r��xg¨© w���}�{Ä�rgS�*© v���¬§gS�zw ¦ g�µ�}�vxº|©�gS{|w�guv.¬Dln�xgS�Z��vx}��rt��i{��»�xw�v³lNw�gu���¿w ¦ lNw®�xguv��ng¨�ªln��w ¦ g�¬Dln���i��~´}�v�w ¦ g�rg¨©�}�yzt§}��*��w���}�{k±� u�t¾u�w � ¢ É «�­�z ���-� ¤�® Æ � Æ�3guw � �� �rgS{r}�wxg:w ¦ lTwÛt�lTv�w��I�i�Ût�v�}�© gS���xgS�ÀlNwÛµ�}�vxº|©�g¨{�w�guvd  � ±N�kguw5���Û��vx}��rt w ¦ g:µ�}�vxº|©�gS{|w�guv*��i{|wx}�¸!�nv�}��rt��m����© ¦ w ¦ lTw¢¡ª�x�]�"� n  ¤£M oa ¤£¥ o4�����ioR ¤£¦ p\o ¡®�Ve��"� n  ¤£¦}§ M oa ¨£¦ § ¥ o4�����ioa ¤£ÿ p\o�����io ¡®�2¸$�P� n �����ioa  £J \<M oa  £J p\±�j�guv�g�oa  £� �rgS{r}�wxgÛw ¦ gÛµ>}�v�º�© gS{|wxguv�w ¦ lTwm�i��y®lNt�t§gS��wx}®w ¦ g w ¦ gS{|wxv����i{�w ¦ g��xgSwH¡ª��©ç�Ùo�ln{���yz��� ¦ w,¬§g������§guv�gS{|w,~´v�}�y w ¦ gÛl�©�w*��lTh�µ�}�vxº|©�gS{|w�guvª  � ±�3-�����rv�gª�� ¦ }Nµ��,w ¦ g�t�lTv�wø·pµ�}�vxº|©�g¨{�w�guv0v�gSh�lTw���}�{k±

P1 P1 P1

P3P4

P

P4

P3

W1 W2 W3 WM

G(1) G(2) G(n)

Pi

P6P6

P2 P2

5

3-�����rvxg®�"±�=�lNv�wx·pµ>}�v�º�© gS{|wxguv0vxgSh�lTw*��}�{�ln© vx}����,��vx}��rt�}n~-µ>}�v�º|©�gS{|wxgSv��S±

)s�rvs© ¦ }���©�gÛ~´}nvs�xgSh�g¨© w��i{r�ªw ¦ gÛµ>}�v�º|©�gS{|wxgSv���~´}�vslª��vx}��rtK�i��¬Dln�xgS��}�{�w ¦ g5~´}�hih�}Nµ��i{r�zv*lTw*��}�{�lnh�g�±¥,¦ gSvxg8lTv�g:©�guv�w³lT�i{!tDlTv�w���w ¦ lNw.©uln{!¬§g:t�vx}r©�gS�*�xgS�»}�{»~´guµ�guv�{\��y5¬DgSvÛ}n~0µ>}�v�º�© gS{|wxguv*�«w ¦ ln{¿�x}�y�g}�w ¦ guv4tDlNv�w*�S±��\��© ¦ µ�}�vxº|©�g¨{�w�guv*�4lNv�g�#�©�v*��w*��©ulnh(%mwx}«w ¦ g,t�v�}r©�gS�����i{r�«}�~Dw ¦ }��xg�#xh�gS���x·p~´}nv�w*�r{�lTw�g!%st�lTv�w��¨±3�}nv��i{��xw³lT{�©�g|o:36�����rv�gÛe�� ¦ }]µ��,w ¦ g«tDlNv�wx·pµ>}�v�º�© gS{|wxguv0v�gSh�lTw���}�{8¬§gu~´}�v�g%w ¦ g«��vx}��rt�~´}nv*y®lTw���}�{k±¥0¦ gS��g5tDlTv�w��«lNv�g.w ¦ gS{Q��}nv�w�gS��w�}��rguw�guv*yz�i{rg.w ¦ g9#�©�v*��w���©SlTh(%®µ�}nv�º|©�gS{|w�guv��Iln{��K~´}nv%���r¬���gS¶\��g¨{�w

��vx}��rt:~´}�v*yªlTw*��}�{3±G3-������v�gIcÛ� ¦ }Nµ���w ¦ gI�x}�vxw�gS�®tDlTv�w����i{®w ¦ g«lT�³©�gS{����i{��5}�v��rguv>}�~kw ¦ gS��vX#b~´}�v�w���{rgS�-%�±

� d

Page 15: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

P

P

P

P

W W W W

W

W W W W

W W

1

3

9

10

1

1 2 3

32

2

1

4

4

5

3-�����rvxg5e:±�=�lTvxw�ln{r��µ>}�v�º|©�gS{|wxgSv�v�gSh�lTw*��}�{8¬§gu~´}�v�g«��vx}��rt��i{r��±

P

P

P

P

W

W W W W

W

1

32

2

1 4

3

10

9

1

W 1

W 2

3W

W 5

W 4

3-������v�gÛc:±�=�lTvxw�lT{���µ>}�v�º�© gS{|wxguv0v�gSh�lTw���}�{�lT~´wxguv��x}�vxw*�i{r�D±

j�gSvxg�okw ¦ gªµ�}nv�º|©�gS{|w�guv���  M o«  ¥ ln{r�¬ ®­ÛlTv�g+#x© v���w*��©ulnh(%8wx}�w ¦ gªt�v�}�© gS�����i{r��}�~>tDlTvxw*� ��¯ lT{��� MV° w ¦ lT{!w�}�w ¦ gªt�v�}�© gS�����i{r��}�~>tDlTvxw*� � M ln{�� �4± ±®��g Á�wSokµ�gª²�Á¸w ¦ gª��v�}��rt¿����¹Sg®ln�%w ¦ g®{rg¨lTv�gS�xw�i{|wxgS�ngSv®w ¦ lNw��i�¸�u�A² }n~�w ¦ gKw�}�w*lnhmµ>}�v�º|©�gS{|wxgSv:����¹Sg�± ¥,¦ �i�8�i��lT{ à�Ð Îrá¨Í ��g]© �i����}�{k± ��g Á�wSo�µ>g��vx}��rtÀw ¦ g�µ>}�v�º|©�gS{|wxgSv��5�i{¿}�v*��gSv5}�~�w ¦ gS��v9#x© v���w*��©ulnhi��wÝ�8%��r{|w*�ih�gS��w ¦ gSv5w ¦ g��nv�}��rtÀ����¹ug��i�5v�g¨l�© ¦ gS�}�vIlnhihkw ¦ g5µ>}�v�º|©�gS{|wxgSv��slNv�g.©�}N��guv�gS�k±,�mh�w�guv*{�lNw*����gSh���oDl®y®lTwxv*�ÃÁ�©�v�}��*�ø·��rg¨©�}�yztD}�����w*��}�{�©uln{Klnhi�x}®¬§gt§guv�~´}nv*yzgS�Àw�}¸��vx}��rtZw ¦ g�tDlTv�w���¬DlT��gS�Ä}�{Äw ¦ gS��v7#ø~´}nv�w*�r{rgS�&%�±ì3-�����rvxg�d!� ¦ }Nµ�����vx}��rt��ªln{��Àw ¦ gyzgSy5¬§guv,µ>}�v�º|©�gS{|wxgSv��0~´}nv,w ¦ gÛlT¬§}]��g«g Á�lny�t�h�g�± ¥0¦ g«��v�}���t��i{r�®lnh���}�v���w ¦ y��i�0t�v�gS�xgS{|w�gS��¬Dg¨h�}]µÛ±

W 2 W 5

W 4W 3

W 1G(1)

G(2)

3-�����rvxg«dx±��m���*����{�yzgS{|w,}�~$µ�}�vxº|©�gS{|w�guv0��vx}��rt��S±

� u�t¾u�t � ¢ É «�­�z ��� � |]�§É ¢�z´¡�®l��|wxgSt»�"± u Õ�ÓåÞ°ÓVànÒÔÓT³]Ï�ú�´ �¶µÒP<¡·�¶µÒPR¸¹�2��±�|wxgSt�e:± 3�}nv��c�2��������º� �

��@

Page 16: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

» � � w ¦ g���guw,}�~-µ>}�v�º�© gS{|wxguv*��  � e 1 ��� � �´ � ´ ¼ » ���{r��~´}�v

�|wxgSt�c6± �|}�vxw ´ ¬�ln�xg¨��}�{�w ¦ g5lT�³©�gS{����i{��ª}nv*�rguv�}n~-w ¦ gÛ©SlNv*���i{�lThi��wb�ª}�~6��w*�,�*��¬��xgSw��So��p± g�±He » � eç±�3guw »�½ ¦¿¾ ��g¨{�}�w�g%w ¦ gÀ¸ w ¦ �xguw��i{�w ¦ g���}nv�w�gS���xguw ´ ±

�|wxgSt�dx± ¾ ¦ �ih�g ´ G�Áµ¡·�Á¡ ¼ » ½ ¦¿¾´ � ´  » ½ ¦¿¾3r}�v�lnhih<!Ã�ĸ Q ��������Xe ´ e»¢½ � ¾ � »¢½ � ¾  »�½ ¦¿¾�4{���~´}�v¸Å�¶¸ Q �

��{r��µ ¦ �ih�g�|wxgStN@8± =6lTv�w���w*��}�{®w ¦ g«�xguw�¡ �i{|wx}X¸Q���r¬r��v�}���t��So�g¨l�© ¦ }�~/����¹Sg $ �åg Á�©�gut�w�w ¦ g%h�ln�xw���v�}��rt�µ ¦ ��© ¦

©�}�{|w*ln�i{��0w ¦ g«v�gSy®ln�i{��i{��zgSh�gSyzgS{|w*��}�~L¡ lT~´w�guv�¸ W �%tDlTvxw*��w*��}�{��Ù��o�����© ¦ w ¦ lNw�2¸ W �]��Æ $ Q eÇ¡ª��¸/��eo��eÇ¡Èeç±6¾»g ¦ l¨��g�¡®�ø�]�L� n  ¤£M o< ¤£¥ o������ioR ¤£É p\o¡ª�pe��L� n   £É § M o<  £É § ¥ o������ioR  £¥ É p\o������ioR¡ª��¸/�Ê� n �����ioR  £J \<M o<  £J p�_  £� yªlTt��,w�}zw ¦ g�µ>}�v�º�© gS{|wxguv ¦ l¨���i{�� w ¦ g¨{�w�v��8�i{�w ¦ g��xgSwH¡ª±è�

�|wxgSt��6± � ¥ )o=6±�MR�è \}W¹nUmrYº^`W»bó\Mi/j<klé�k

¾»g,�x}�h���g>w ¦ g0t�v�}n¬�h�gSy �i{Ûwbµ�}st ¦ ln�xgS�S±6��{5w ¦ g0²rv*�xw6t ¦ ln�xg�oNµ�g0���xg0w ¦ g0µ>}�v�º�© gS{|wxguv-¬DlT��gS�5��v�}��rt��i{r��xw�v*lTw�gu����w�}���gS{rguv³lTwxg�w ¦ gz���r¬�t�vx}�¬�h�gSyª�S±*)s{�©�g�w ¦ g���v�}��rt��«lTvxgz�rgu��gSh�}�tDg¨�3oRw ¦ gz���r¬rt�v�}�¬�h�g¨y ~´}�vw ¦ lTwstDlTv�w���© ��h�lTv���v�}���t¸�i�m��gS{rguv³lNw�gS�k±s��{Kw ¦ g.{rg Á�wst ¦ ln�xg|o§µ>g��x}�h��ng5w ¦ g��i{��������i�r��lnh$���r¬�trv�}�¬�h�gSy�±¥,¦ gm�x}�hi��w*��}�{.}�~3lItDlNv�w*��© ��h�lNv4���r¬�t�vx}�¬�h�gSy­�xguv���gS��ln��w ¦ g�¬Dln���i��}�~��i{�t��rw�~´}nv4w ¦ g�{rg Á�w����r¬�trv�}�¬�h�gSy�±¥,¦ gSvxg,lTvxgª¸�����© ¦ ���r¬rt�v�}�¬�h�g¨yz�6~´}nvʸ�����© ¦ ��v�}��rt��S± ¥,¦ g�¬Dln©³º\h�}��s}�~�tDlTvxw5�3�i{5w ¦ gª¸ w ¦ ���r¬�trv�}�¬�h�gSy�i�sw ¦ g7#xyz}�����²rg¨�:%��rgSy®ln{��K}�~�tDlTvxw����i{Kw ¦ gȸ Q � w ¦ �*��¬�t�v�}n¬�h�gSy�± ¥,¦ gȸ w ¦ µ>}�v�º�© gS{|wxguvx·p¬Dln�xgS����r¬�t�vx}�¬�h�gSy ©uln{�¬§gÛ��gS²�{rgS��l�©u©�}�v����i{r�zwx}zw ¦ g«v�gu���i�xgS��{r}�w*lTw*��}�{8w ¦ lNw�~´}�hih�}Nµ��S±Ë k�Ì<^Us[klgKüåW�Y6dGYº^`W»b

qIlTw³l6± �Í ¦��� � ��}�����²rg¨���rgSy®ln{���~´}nv,tDlTv�w��>lTw,w*�iyzg«�i{|w�guvx�nlTh � ~´}�v����r¬�t�vx}�¬�h�gSyθRo�ln{���S�

Page 17: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

qmg]© �i����}�{ § lTv*��lT¬�h�g¨�!±u ÕDÞÝÏpÖ\Ï�ã!ú 7 ¦��� � ��{|��gS{|w�}nv��:}�~$tDlTv�w��>lTw,w*�iyzg«�i{�w�guv��Tlnh � ~´}nv��*��¬�t�v�}n¬�h�gSyϸRo�ln{��8 ¦��� � f0l�©*º�h�}���}�~$tDlTvxw��>lTw,w��iyzg��i{|wxguv��Tlnh � ~´}�v����r¬rt�v�}�¬�h�g¨yθR±¥,¦ gd¸ w ¦ ���r¬�t�vx}�¬�h�gSy �i��±

�@  � � � ¦ � ý ��¸9± DE�0�@!F� ��rG�I!JE�LK.MONE �TK.M $ � ���"? � �=�5�RQ DE �hK.MÄNE �+K.M %&� 7 ¦��� Q DE �hK.MÄNE �TK.M ' �Ð8 ¦�=� �

�\�r¬r¯bg¨©�w�w�}º±

7 ¦�=� W>8 ¦��� � 7 ¦�ZY[�]\<M@^ WI8 ¦�ZY[�V\<M_^ Q JE�LK.M3 �=�5�jW-� Í ¦��� *a�0� e 1 �=� � �� l ¡ª�Ѹ��0�L* � � �� |�3 ���5��b � ���c;<���5�XW DE!F� �Àe 1&� � � ��HG��! � ��� � � � ���®Q # � � � ? � ���5� *.�/� e 1 �=� � ��

�rG�I!s� l ¡ª�Ѹr�2�L* � � �ø�S�|�DE �SK.M JE�LK.M ( ÿ��� ;<���5� � ¸vÿ *a�0�}�,� e ( ÿ��� � �� 1 �=� � �� l ¡®�@¸��2�L* � � �ø���]�

DE �hK.M ;<���5�ib � *.�/� e 1 ��� � �� l ¡ª�Ѹr�2�Ê* � � �ø�¨e��? � ���5��k ;<���5�aQ>; � �PY[�V\<M_^ W � *a�0�@!s� e 1 ��� � 1&� � � ���rG�I!s� l ¡ª�Ѹr�2�,* � � �ø�Sc|�

� b ? � ���5��b � *a�/�Ñ!s� e 1 �=� � 1&� � � �`� l ¡ª�Ѹ��0�Ê* � � �ø� d��;<���5� l n �o�u��p *.�/� e 1 ��� � �� l ¡®�@¸��2�L* � � �ø��@��3 �=�5� � 7 ¦�=� � 8 ¦��� k � *.�/�L* l ¡ª�Ѹ��0�Ê* � � �ø�S�|�

¾»g.��}�h���g5w ¦ g�¸ w ¦ ���r¬�t�vx}�¬�h�gSy ln{��K�rguw�guv�yª�i{rg.��~4w ¦ g��rgSy®lT{��K~´}nvsw ¦ gz©�}�v�vxg¨�xt§}�{����i{r�:tDlTvxw*�¦ l¨�ngª¬DgSgS{»�*lTw��i��²rg¨�¸}�v�{r}�wS±®�p~0yzguwSokw ¦ gztDlTv�w��i��{�}�wÛ© }�{����i�rguv�gS�¸~´}�v«~å�rw��rv�g:©�}�{r�*�i��gSv*lTw*��}�{»lT{��

��£

Page 18: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

w ¦ g:���r¬�trv�}�¬�h�gSyª��lTv�g®�x}�h��ng¨�Q~´}�v«w ¦ gªvxgSy®ln�i{��i{r��tDlTv�w��«}�v���{|w��ih�lnhih�w ¦ g®µ>}�v�º|©�gS{|wxgSv�� ¦ lS��gz¬§gug¨{©�}N��guv�gS�k±Ij�}]µ�gu��guv¨oDw ¦ gzlT������w*��}�{K}�~4w ¦ g5v�gS�x}��rv³©�gz©�}�{r��wxv³ln�i{�w*�s�i{Kw ¦ g9#x���i�*lT����vxgu�|lTw�gS�6%ªtrv�}�¬�h�gSy¬�h�}Nµ����rtªw ¦ g�trv�}�¬�h�gSy ���iyzgS{�����}�{�~´}�v�yzgS���i��y­ln{r�ªh�lTv��ng��*��¹ugS��t�v�}n¬�h�gSyª�S±G3-������v�g<@st�vxgS��gS{|w��4w ¦ gû�}Nµ © ¦ lTvxw�}�~�w ¦ gmt�v�}nt§}��xgS�:�x}�hi�rw���}�{®�xw�v³lNw�gu���.~´}�v>w ¦ g%e]·pt ¦ ln�xgmµ�}�vxº|©�g¨{�w�guv�¬DlT��gS�:�rg¨©�}�yzt§}��*��w���}�{�*© ¦ gSyzg�±

part ?

Demand for all partssatisfied ?

All groupscovered ?

Stop

Delete the part from the set of parts

Analyze output andgenerate next Sub−problem

Select Group andGenerate SubProblem

Sort Workcenters

Select Workcentersand form Groups

OR

Set index to the nextgroup

YES

NO

NO

YES

Demand

based on "criticality"

Solve Sub−problem

satisfied for any

3-������v�g�@8±�3-h�}Nµ © ¦ lTv�w,vxgStrv�gS�xg¨{�w*�i{r�zw ¦ g.e¨·pt ¦ ln�xg«µ>}�v�º�© gS{|wxguv,¬DlT��gS����g]©�}�y�t§}�����w*��}�{��*© ¦ gSyzg

ÒC Ó ��ñ FH�»�!�}IXð?JKFHôG��ðE��ô

�|gu��guv³lTh-{\�ryzguv*��©ulnh/g Á�t§guv��iyzgS{|w*�mµ�guvxgz©�}�{r����©�w�gS��w�}�© }�yztDlTvxg5w ¦ g.t§guv�~´}�v�y®ln{�©�g5}�~4w ¦ gªe]·>= ¦ ln�xgqmg]©�}�y�t§}�����w*��}�{Q��© ¦ gSyzg�lN�|ln�i{��xwmw ¦ gÒ��}�{r}�hi��w ¦ ��©�lTt�t�vx}|l�© ¦ ± ¥,¦ g.trv�}�¬�h�gSy �i{��xw³lT{�©�g¨��µ�guv�gÛ��gS{�·guv³lTwxgS�À�����i{r�Q��lTw*l�t�v�}]���i�rgS� ¬|� ln{À�i{N¯bg]©�w���}�{ yz}�hi�r�i{r�¸©�}�yztDlT{|��± ¥,¦ g8w�gS�xw�¬§gS�Ä©�}�{����i�rguvxg¨�Þ@r������§guv�gS{|wmt�vx}�����©�wswÝ�\t§gS�mw ¦ lNwsµ�guvxg5w�}:¬§g.�³© ¦ gS���rh�g¨��}N�ngSvsl:y®l]Ár�iy.��y }�~�d[@®�i{N¯bg]©�w���}�{�yz}�hi���i{��y®l�© ¦ �i{�g¨�S± ¥,¦ gSvxg8µ�guvxg��������Rguvxg¨{�w5wb�|t§gS�5}�~�©�}�{��xw�v*ln�i{rgS�¿vxg¨�x}���v³©�gS�¨±0=4vx}�¬�h�gSy �i{��xw³ln{�© gS�Ûµ�guvxg

�!Ù

Page 19: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

��gS{rguv³lNw�gS�K~´}nvI�rgSy®ln{r�K}N��guv%l®w*�iyzg5t§guv���}��k± ¥0¦ g.tDlTv�w��SoRµ�}�vxº|©�gS{|w�guv*�.�°yz}�hi���i{r�8y®l�© ¦ �i{rgS�Ù��lT{��w ¦ g�vxg¨�x}���v³©�gS�.µ>gSvxg��xgSh�g]©�wxg¨�¿w ¦ v�}��r� ¦ lK��guv���g¨�Û}�~��rgSy®lT{��Ä��lNw³l�o4f})H� o$v�}��rw��i{r�Q��lTw³lQlT{��À�i{�·��gS{|wx}�v�����lTw³l�± ¥,¦ gÛvxg¨����h�w*ln{|w,t�v�}�¬�h�g¨yz��µ>guv�g«w ¦ gS{�© h�ln������²�gS���i{|w�}ªw ¦ v�gug5©ulTwxgu��}�v*��gS��ln��� ¦ }Nµ�{��i{¥ lT¬�h�gª��± Ô

Õ Ö`×oØÚÙÜÛÞÝ&ßÚàáÙ ârÖ&ãLÖ`ä�åUæçÕ è é ârÖ&ãLÖ`ä4ê"Ö`Õ}ëì â¢Ö&ãLÖ`ä4Õ}Ù�é�ÖíUÕ}î2Ù ârÖ&ãLÖ`ä�è}ßhÛfÙî2ÙÜï�è Ù�Õ/é è¿ðAå<Ùºé åoÙºÕ/ßSÖAñUéôVðS�Ùúýú a,òpawó awó}ò]ô0ó a¿ò]õ a¿òpawóð0óø÷]üèù]ð a�a¿ò]ö0÷ ô¨a,ò+ø�ö a¿ò]õ a�a¿ò]ö0óú �*ò���ó ö2õ}ò]÷Sa ø�ö ò+ø�÷ a¿ò]õ ö¨a¿ò]ô0ó¥ lT¬�h�g®�"±f5>h�ln���*��²�©SlNw*��}�{8}�~ § lTv���}����r=�v�}�¬�h�gSy7�\��¹ug¨�

¥0¦ g8ln© w���lnh�t�vx}�¬�h�gSy)�*��¹ugzµ,lT���rguw�guv*yz�i{rgS�¿ln�%w ¦ gªt�v�}\����©�wÛ}n~�w ¦ g:{\�ry5¬§guv�}�~>tDlTv�w��So/µ>}�v�º|·©�gS{|w�guv*�So§v�gS�x}��rv*©�g¨�Iln{��Kw*�iy�g.t§guv*��}��r�¨± ¥0¦ g��a= vxg¨h�l]Á�gS�K��guv��*��}�{Qln{��Kw ¦ g�yz}�{r}�hi��w ¦ ��©«��guv��*��}�{K}�~w ¦ g�}nv*�����i{�lTh½�K�>= t�v�}�¬�h�g¨y�µ>gSvxg��x}�h���gS�������i{r�C5¹=f�/�L� £�±���±�=4v�}n¬�h�gSyª�0~´}�v�w ¦ g5e]·>= ¦ lT��g�qsg¨©�}�y�·t§}�����w���}�{»��© ¦ gSyzg�µ�guvxgz��}�h���gS�Q�����i{r��;o�a=f�(d�±ý��±Û�m�«�xw³lTwxgS�Qg¨lTv*hi��guvSo3lThih6w ¦ gztrv�}�¬�h�gSy �i{��xw*ln{�©�gS�µ�guvxg.v���{K}�{QlQ�n± £A;%j�¹X=-gS{|w*�i��y7d8t�v�}�© gS���x}�v¨o�e"@n�A�Kf³���H� o�¾ �i{�� ¥ dD± �:µ>}�v�º\��w*lTw*��}�{k± ¥,¦ g}�t�w��iy®lnhi��wÝ�®�|lNt��i���rgu²�{�g¨��ln�!±

;%lTt$�@²ª��� �V��{|wxgS�ngSv<)mt�w��iy®lnh § lThi�rgN��·s��)m¬�¯bg¨©�w*���ng § lnhi��gT��°��{|w�gu��guv<)mt�w*�iyªlnh § lnhi�rgN� Æ��u���A²3�}nv�©uln�xgS�0µ ¦ gS{�ln{�}�t�w��iy®lnhR�i{|w�gu��guv,�x}�hi�rw���}�{8�i�,{r}�w�l¨�Tln�ih�lT¬�h�g|o�w ¦ g«}�t�w��iy®lnhi��wÝ�ª�|lTt��i��©SlTh�©u�rh�lTw�gS�ln�,~´}�hih�}Nµ��!±

;IlTt$�Ѳz��� ���a=?��gSh�lNÁ\g¨�N)m¬�¯bg¨©�w*����gN�4·s��)m¬�¯bg¨©�w*����g § lThi�rgN����a='�,gSh�lNÁ�gS�0)m¬r¯bg¨© w�����gN� Æ��S�n�A²¥0¦ g�l¨��guv³lN��gs�|lTt��i�,©ulnh�© ��h�lTwxg¨�:¬\�8l¨��guv³lT���i{r�.}N��guv�w ¦ g«{\��y5¬§guv0}�~$t�vx}�¬�h�gSy��i{��xw³lT{�©�g¨����gS{rguvx·

lTwxg¨��~´}�v,g¨l�© ¦ © h�ln���0}�~$t�vx}�¬�h�gSy�±ùSRUT p W»bHW»nU^>YºjH^Ui¡\Mi/j<klé�k

¥,¦ g.yz}�{�}�hi��w ¦ ��©%�³© ¦ gSyzg.lNw�w�gSyztrw�gS��wx}��x}�h��ngÛw ¦ g5gS{|w���v�g*�K�>��=½t�vx}�¬�h�gSy7µ���w ¦ �i{�lªw*�iyzg5hi�iyª��w�}�~£nen�n�z�xg¨© �Û�pe ¦ v��Ù��± ¥0¦ g¢�Q�>�a= µ,ln�,��}�h���gS��~´}nv,#x��y®lnhih(%zlT{��'#øyzgS���i��y�%.t�v�}�¬�h�g¨yz�¨±�j�}Nµ�gu��guv0w ¦ g�K�>��= ©�}��rhi��{r}�w�¬§g5�x}�h��ng¨��~´}�v��x}�yzgÛ�i{r��w*ln{�©�gS��}�~6w ¦ g�#xy�g¨�r�i��y�%®ln{��'#xh�lTvx��g!%ª����¹ug¨��t�vx}�¬�h�gSyª�S±¥ lT¬�h�gS��e�o�c�ln{��8dª� ¦ }Nµ w ¦ lTw0w ¦ g�lS��guv³lT��gs�|lNt��0~´}�v0w ¦ gN#x��y®lnhih(%.ln{�� #xyzgS���i��yÒ%�����¹ugS�8t�v�}�¬�h�g¨yz�µ�guvxg��r±ý���s² lT{��Ä�r±ý��e²=vxgS��tDg]©�w�����gSh��|o/µ ¦ guvxg]lT�.{�}Q�i{|w�gu��v*lnh��x}�hi�rw���}�{ ©�}���hi�¿¬§g:~´}���{��¿~´}�v.�x}�y�g#xyzgS���i�ry�%ªln{r��ln{|� #øh�lTv���g!%�����¹ugS��trv�}�¬�h�gSyª�S±

�!

Page 20: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

ùSR�Q Q�Z`�7j<dfs[kú� kli¾W»éÞ�¢W¹s8^>Yº^`W¹bó\MixjHklé�k

¥,¦ g�e]·>= ¦ ln�xg�qsg¨©�}�yzt§}��*��w���}�{%�*© ¦ gSyzg4µ,ln�k�r��gS�«wx}��x}�h���g�w ¦ g�g Á�ln© wk�*lnyzg��i{��xw*ln{�©�gS�3}�~\w ¦ g�#x��y®lnhih(%�o#xyzgS���i�ry�%�oTln{���#xh�lNv���g!%m����¹ug¨��t�v�}n¬�h�gSyª�S± ¥ lT¬�h�g¨��e�oncsln{��5ds� ¦ }NµÀw ¦ lTw-w ¦ g�y®lNÁr�iy5��yP}�t�w��iy®lnhi��wb��|lTt:~´}�v�w ¦ g%h�lNv���gS�xw�t�vx}�¬�h�gSy(�i{��xw*ln{�©�gmµ,ln�s��± £¦@s²�± ¥,¦ gSvxgsµ0ln�0lÛ������{���²D©uln{�w>�iyzt�vx}N��gSyzgS{|w��i{®w ¦ gw�v*ln�rgu}��À¬§guwݵ�gugS{!w ¦ g:�x}�hi��w*��}�{!¶|��lnhi��wb�Qln{��!w ¦ g:�x}�hi�rw���}�{¸w��iyzg�± ¥,¦ g®y®lNÁr�iy5��y=w*�iy�gªvxgS¶\����v�gS�w�}ª��}�h���g«w ¦ gÛh�lTvx��gS��w,�i{��xw³lT{�©�g�}n~-w ¦ g�trv�}�¬�h�gSy �����i{r�ªw ¦ g.e]·>= ¦ ln�xg�yzguw ¦ }���µ,lT�Û�Sen����± ��@.�xg¨© �Û�per�yª�i{��Ù�Ù±û ß Û ü è ý

ÔýaÖºê"ÙºÕ þ

Ôý.ÿ�� ÝsÖØZã��"ßhÛfÙ �ªæçå ��ì

Ô� æ�é�Ù ÝsÖØZã��"ßhÛfÙ �ªæ�å� ÖíïUñ �Ðé�Ùºîáé ��� �Ðé�Ùºîáé ��� a õ a�a õ ö awó��2ö}ø�õ ÿ awö awó��0ö/ø�õ ÿ a ö�� ó ÿ awö ó ÿ ó2ó a�ó��2ö/ø�õ ÿ a ö ó ÿ awö ó ÿ ó2óö � a�ø õ aÙa öSa ÷2õ��/øáô ÿ �2ö ö¨aw÷2õ��2õ0ó ÿ õ2ô�� aw÷ ÿ ÷2ô ó ÿ ó2ó ö¨a ÷0õ������ ÿ õ�� awö ÿ ø�� ó ÿ ó]aô ö2ö øNa õ ø a����/ø������ ÿ ö2÷ a���2÷¨a�Sa ÿ �0ó�� ö�� ÿ a�� ó ÿ ó2ó a���0÷2ö2÷�� ÿ ø�� ö0õ ÿ ó�� ó ÿ ó]aø ö/ø ø�ö õ õ ø��/ó��2ö¨awö ÿ �0ó ø��}ó��2ô���� ÿ ÷2÷�� ô}ø ÿ ��� ó ÿ ó2ó ø��/ó����Sa�a ÿ ø�ô ô0ö ÿ �2÷ ó ÿ ó]a

��� óøò��Ç��ó�� ó ÿ ó2ó ��� óøò��Ç��ó�� ó ÿ ó]a¥ lT¬�h�gÛe:±��,gS�*�rh�w*�0~´}�v,w ¦ g.�\y®lnhih$�|��¹Sg4=4v�}n¬�h�gSyª�

û ß Û ü è ýÔ

ýaÖºê"ÙºÕ þÔý.ÿ�� ÝsÖØZã��"ßhÛfÙ �ªæ�å ��ì

Ô� æ�é�Ù ÝÖØ]ã��"ßhÛ�Ù �ªæ�å� ÖíUïUñ �Ðé�Ùºîáé ��� �Ðé�Ù�îáé ��� a awó a�� õ � ÷����¨a ö��/ó ÿ ô�� ÷����Sa��¨a ö ÿ �2ö � ö���� ÿ ��� ó ÿ ó2ó ÷����2ö2ô2ôSa ÿ a�� �2ô ÿ ó�� ó ÿ ó¨aö a ô ô�� õ � �������Sa�� ÿ �¨a �����2õ}ø�÷ ÿ ö���� a ÷/ó0ø ÿ ö0õ ó ÿ ó2ó �������2ô2÷ ÿ õ2ô ö��Sa ÿ ø�ö ó ÿ ó2÷ô � ô¨a õ ôSa awó����¨a�ó ÿ a ô awó����0ö�� ÿ ô0õ�� ö2õ0õ2õ ÿ ó�� ó ÿ ó2ó awó����2÷�� ÿ �/ó ô¨a�ø ÿ ø�� ó ÿ ó/øø ô2ö ø�ö õ ö/ó ö/óáô¨awó0ø]a� ÿ ÷Sa ö0óáô¨aw÷/øNa�ø ÿ ö�� óÙÿ þxÿ úiÿ ó ÿ óáö ö0óáô0ö��}ø��/ø ÿ øáó ø2ø2ø ÿ õ2ö ó ÿ ó��

��� óbò�����ó�� ó ÿ ó]a ��� óbò�����ó�� ó ÿ ó2÷ "! #$! %&! K('*),+ $ $- .-�/10324 65�03270 #

¥ lT¬�h�g�c6±���gS����h�w��0~´}�v,w ¦ g¢��gS���i��y �\��¹ug¢=4vx}�¬�h�gSyª�

û ß Û ü è ýÔ

ýaÖºê"ÙºÕ þÔý.ÿ�� ÝsÖØZã��"ßhÛfÙ �ªæ�å ��ì

Ô� æ�é�Ù ÝÖØ]ã��"ßhÛ�Ù �ªæ�å� ÖíUïUñ �Ðé�Ùºîáé ��� �Ðé�Ù�îáé ���8a ö�� ø�ö õ ôSa awõ2õ¨awó]aw÷�� ÿ ��� a õ��0ô��2õ/ø�� ÿ ó2ó óÙÿ þxÿ úiÿ ó ÿ ��� a õ�� ø��0ó2ó2ó ÿ ó2ó ø��}ø ÿ ø�� ó ÿ �2ôö ô�� ø�ö õ ô/ó ö0÷2÷��2÷2÷0÷2÷ ÿ ÷/ó ö2÷��/øáö��0ö2õ ÿ �0÷ óÙÿ þxÿ úiÿ a ÿ ô2õ ö2õ0ó/ø�ö2õ��0ö ÿ ÷¨a ô2õ/ø ÿ ��� a ÿ �0÷ô øNa ø�ô õ ô/ó ö/ó]a�øáó2ó0ó2ó ÿ ó0ó ò í]ÿ í]ÿ ðmÿ ò ö0óáô/ó��/ø��2ö ÿ ö2÷ �2õ2÷ ÿ õ�� ó ÿ �/ø:9ø ÷¨a ø�ô õ ô/ó �0ö/óá÷¨a�ø�� ÿ ��� ò í]ÿ í]ÿ ðmÿ ò �/ô¨a�øNa� ø ÿ ��� awö2õ2õ ÿ óá÷ a ÿ ÷¨a�9

��� óbò�����ó�� a ÿ óáõ ��� óbò�����ó�� a ÿ ö2ô "! #$! %&! K('*),+ $ $- .-�/10324 65�03270 #$;<�! <�! 2�! K =?> #1<A@CBD $24<AEGF�;�H6IKJ"L + JA% +.> %3J"#M $-ONJ"PM $-�<"QR5�S:5�<UTV .EXWY< > Q-�!

¥ lN¬�h�g«dx±��,gS����h�w*�0~´}�v,w ¦ g¢�/lTvx��g.�\��¹ug4=4v�}�¬�h�g¨yz�

en�

Page 21: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

Z� [��� ��Mð!��ô����Ò �ô

��{»w ¦ �i�«tDlNt§guv¨o/µ�g®©SlT��wÛln{»�i{N¯bg]©�w���}�{!yz}�hi�r�i{r���³© ¦ gS���rhi�i{r��trv�}�¬�h�gSy ln�Ûl�yª�ÃÁ\g¨�¸�i{|w�gu��guv«~´}nv*y.��·h�lTw���}�{Àw ¦ lTwz�*© ¦ gS����h�gS��tDlNv³lnhih�gSh>µ�}�vxº|©�gS{|w�guv*�.�i{Ät�vxgS��gS{�©�g�}�~s�xg¨¶|�rgS{�©�gu·���gStDg¨{r�rgS{|wª�xguw*�rtÄw*�iyzgS�So© ¦ ln{r�ngS}]��guv�©�}��xw*�So�lT{��8y.��h�w���t�h�gs©SlNtDl�© ��w³lTwxgS�®v�gS�x}��rv*©�gI© }�{��xw�v³lT�i{|w*��~´}�v0lÛy.�rh�w*�÷���w�gSy�o�y.�rh�w*�÷ݩ h�ln���}�~Dt�vx}�����©�w*�4�i{zlI���i{r��h�g ·��xw³lT��g,©uln�xg�± ¥0¦ �i��t�lTt§guv�lNt�t§g¨lTv*��wx}%¬§g�w ¦ g,²�v���w�lTwxw�gSyzt�w��i{�w ¦ �i�4©SlNw�gu��}�vx�w�}�© }�y5¬��i{rgIlnhih�w ¦ gS�xgsv�g¨lnhi�i�xw*��©�©�}�{r��wxv³ln�i{�w*��ln{���©�}�yzgs�rt8µ���w ¦ ln{:guÂ:© ��gS{|w>yzguw ¦ }\�:w�}5w³ln©³º\h�gmw ¦ gt�vx}�¬�h�gSy�µ ¦ gS{�w ¦ g«w*�iyzg%w�}z��gS{rguv³lTwxg%��}\}����³© ¦ gS���rh�g¨�,�i�,}�~-~´}nv�gSyz}��xw,�iyztD}�v�w*ln{�©�g�±¥0¦ g�e]·pt ¦ ln�xg�µ>}�v�º|©�gS{|wxgSvÛ¬�ln�xg¨� �rg¨©�}�yzt§}��*��w���}�{¿�*© ¦ g¨y�g ¦ ln�5¬DgSgS{ t�v�}�tD}��xg¨�3± ¥,¦ g��*© ¦ g¨y�g

¦ gSh�t��mw�}8�rg¨© }�yzt§}��xg.h�lNv���g5���iy�g¨{r�*��}�{rgS��trv�}�¬�h�gSyª�m�i{�w�}8��y®lnhih�guvs���r¬rt�v�}�¬�h�g¨yz�¨±m�pw%lnhi�x}®t�v�}N�\�i�rgS���}\}\��~´g]lT�*��¬�h�g��*© ¦ gS����h�gS�/~´}�v-©uln�xgS�/µ ¦ guvxg>w ¦ g�y�}�{r}�hi��w ¦ ��©�lTtrt�v�}|ln© ¦ ~°ln�ihi�3w�}m��gS{rguv³lNw�g>ln{|�«�x}�hi�rw���}�{kogS��w ¦ guv®¬§g¨©uln���xg�}�~«yzgSyz}nv��Zy®ln{�lN��gSyzgS{|w®tD}�hi��©��Z}n~%w ¦ gQ�x}�h���guvª}�v:¬§g¨©uln���xg�}�~%w ¦ g�w*�iyzg�hi�iyª��wv�gS�xw�v���©�w*��}�{��«�pe ¦ }��rv����Ù±¥0¦ g8©�}�y�t��rw³lNw*��}�{�lTh�w��iyzgªv�gS¶\�r��v�gS�!¬\�Qw ¦ g�e]·>= ¦ ln�xg®�xwxv³lTwxgS�n�¸�i��������{���²D©uln{|w�h��Kh�g¨���«w ¦ ln{!w ¦ g

�x}�hi�rw���}�{�w��iyzgÛ}n~4w ¦ g5}�v������i{�lnha�Q�>=½t�v�}�¬�h�g¨y�±0��guwmw ¦ g5}�t�w*�iyªlnhi��wb�8��lTtK�i�s������lnhih���h�gS�*��w ¦ ln{¸e²�±��{8����yªyªlTv���o�w ¦ gs}N�ngSv*lnhih��x}�hi�rw���}�{8lTtrt�v�}|ln© ¦ �i��lTt�t�hi��©ulT¬�h�g�~´}�v>�i{������xw�v���lnhD����w*��lTw���}�{���w ¦ lNw>v�gS¶\����vxg¶\����©*ºzlT{��ªguÂ:© ��gS{|w4�x}�hi�rw*��}�{��4µ���w ¦ }���w>ln{|�.�i{|��gS�xw*yzgS{|w4�i{ª�x}�t ¦ �i�xw���©SlNw�gS�z��}�h���guv*��ln{��®lTw�w ¦ gm�*lny�gw*�iy�gÛ©uln{�t�v�}]���i�rg«}nt§guv³lTw���}�{�lnh�¬Dg¨{�gS²rw*���i{�© ¦ ln{r�ngS}]��guv�©�}��xw*�Sor�i{���gS{|w�}�vx�8y®lT{�lT��gSyzgS{|w�©�}��xw��mlT{���i{�yzguguw*�i{��®© ���xw�}�y�gSv,���rg���lTw�gS�S±�h��\� 0�oOKð�FH�^]�ñ FH ��

¥,¦ g0ln�rw ¦ }�v*�$µ>}���hi�Ûhi��º�g�w�}mw ¦ lT{rº«w ¦ g>wbµ>}Iln{r}�{|�\yz}����/v�gu~´guv�gugS�/~´}�v$w ¦ gS��v6©�}�{��xw�v���©�w*����g>© }�yªyzgS{|w*�S±¥,¦ g¨�xgÛ©�}�yªyzgS{|w�� ¦ gSh�t§gS���xw�vxg¨{���w ¦ gS{�w ¦ g«tDlTt§guv��*����{���²D©uln{|w�h��|±

J¼F`_¦F<�fFH ��}FHô

~ç�©����º\º�guv¨o[ç�± § ln{�qmg¨{3o�j�}\}���gu��gugS{ko[ç�±io�ln{r� § ln{8qsg § gShi�rg�o��R±[=�lTv*lnhih�gSh�y®l�© ¦ �i{rgs�*© ¦ gS����hi�i{��¬|��©�}�hi��yª{���gS{rguv³lNw*��}�{k±º)mt§guv³lNw*��}�{��}��gS�xg¨lTv³© ¦ �! " " 6P\d8£��V�|��±�Ù���e]·>Ù]£ner±

~ e����m{��rguv*�x}�{3ok��±ioa;Ih�ln���45I±�okln{�� =-}\}�w��¨o½5I±¾�Kl�© ¦ �i{rg��*© ¦ gS����hi�i{��D±v�3}r©ulnh��|g¨lTv*© ¦ �i{75>}�yÛ¬��÷{�lTw�}�v���lnha)mt�w*�iyª��¹¨lTw���}�{k±�������w�gS��¬\���slTv�w��So���±�ln{����kgS{��xwxv³l�o6ç�±k�� " ]£8P3�n�"±4c�����·pd�� dD±

er�

Page 22: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

~ c��Ûf�lTv�¬DlNv�}��x}���hi�3o¦;�±�onln{��'¯)m¹¨��lny®lTvSo���±]�m{�lnh������i�/}n~��x}�hi��w*��}�{��xtDl�©�g ·��rgut§gS{��rgS{|w$t§guv�~´}�v�y®ln{�©�g}n~��*�iy5��h�lTw�gS�ªln{�{�g]lThi�i{r�x±kw ¦ gs©uln�xg�}�~Rw ¦ gmy.��h�w��÷�h�gu��gSh�©ulTtDl�© ��wxg¨�zh�}�w�����¹S�i{r�«t�vx}�¬�h�gSy�±]5>}�y�·t��rw�guv*��ln{r��)mt§guv³lNw*��}�{��}�,gS�xg]lNv³© ¦ ±�en�n���6P�e�£r�� |�E±GÙ" �@]·> n��c�±

~ d"�Ûf�l ¦ hpoTj5±�o¦����w�¹Sy®lT{ko���±ioTlT{��Ò;I��t�w³l�o�ç�±]qsguw�guv�yª�i{��i{r�mh�}nw-����¹ugS�6lT{��Ûvxg¨�x}���v³©�g�v�gS¶\�r��v�gSyzgS{|w*�Sol.v�gu����guµÛ±º)mt§guv³lTw���}�{��}��gS�xg¨lTv³© ¦ ±��! "Ù�£8P�c�@��°c|�E±�c�e¦ ]·ÝcTd[@r±

~�@��Ûf�g¨h��Tln�\Á3oG;�±�o6ln{��!¾»}�hi�xgu�|o���± �5±$f}5�·>=f�r)Iq*±/l���tDg]© ��lnhi��¹ugS�¸¬�v*ln{�© ¦ ·Ýln{r��·Ý© �rw5�x���xw�gSy)~´}�vh�}nwx·�����¹S�i{r��t�v�}n¬�h�gSyª�S±6�QlT{�lT��gSyzgS{|wm�\©u��gS{�©�g�±�en�n���6P�d|�:±f£neNdn·`£Tc¦Ù�±

~ ���Ûf>�ihihi�i{r��w�}�{ko�=6±�o»�K©�5�h�ln�i{ko�ç�±io>ln{r� ¥,¦ }�y®ln�Sof��±��QlNw ¦ gSy®lTw���©ulnh0lTtrt�v�}|ln© ¦ g¨�.w�}»©ulTtDl�© ��wÝ�©�}�{r��wxv³ln�i{�g¨�A���r=Ä�x���xw�gSyª�!±-vxgS�\��gSµ�o|~´}nv*y.��h�lNw*��}�{:ln{r�8t�vx}�¬�h�gSy(vxg¨�r��©�w*��}�{k±[�Kln{�lT��gSyzgS{|w�\©u��gS{�©�g�±3�! ¦Ù�c6P�e¦ ��pe���±,���Sen�N·³��� d���±

~�£��Ûf>��w�v³lT{ko¹;�±��Û±�o�ln{r�À�>ln{�ln���xg�o�j5± j5±�5>}�yzt��rw*lTw*��}�{�lnh0© }�yzt�h�g Ár��wb�!}�~�w ¦ g�©ulTtDl�© ��w³lNw�gS�Àh�}�w����¹ug«trv�}�¬�h�gSy�±:�Qln{�lT��gSyzgS{|wm��© ��gS{�©�g�±3�! "Ù�e:P�e¦Ù��ø�S�|��±,����£]dn·³���!Ùn��±

~¶Ù��Ûf>h�l�©*º\¬��rv�{ko6ç�±�o�ln{r�N�K�ihih�gS{ko8�Û±���yzt�vx}N��gS� ¦ g¨��v*�i�xw*��© �0~´}�v,y.��h�w��÷���w*lT��gIvxgS¶\����v�gSyzgS{|w��0t�h�ln{�·{r�i{r�®�x���xw�gSyª�S±6�Kln{�lT�ng¨y�g¨{�ws��© ��gS{�©�g�±3�! "Ù�e:P�e¦Ù��x�¨�E±-d�dn· @n��±

~¶ ��*5>h�lTv�ºRo|�5± ��±�o�ln{r��5�h�lNv�º�o��R±�ç�±[�,}�hihi�i{r� ¦ }nv*��¹u}�{ªh�}�wx·�����¹S�i{r��µ ¦ gS{:�xguw*�rt®w*�iyzgS�>lTvxgs�xgS¶\�rgS{�©�g��gStDg¨{r�rgS{|w¨±���{|wxguv*{�lTw���}�{�lnh¾çn}��rv*{�lnh3}n~G=4vx}�����©�w���}�{���gS�xg¨lTv³© ¦ ±�eT�����6Prc"Ù��ø�S�|�Ùo�ene¦Ù]£¨·bencn�]£�±

~ç�S���Ûqmgu��v³lNgS�ng|oXa6±�o�ln{��Cç�ln{��So8��±\� {rguµ qIln{|w�¹S���n·V¾»}�h�~´g�vxgu~´}�v*y.�rh�lTw*��}�{®ln{��®¬�v³ln{�© ¦ ·Ýln{���·pt�v���©�glTh���}�v*��w ¦ y(~´}�v,w ¦ gÛ©ulTtDln©u��w*lTw�gS��h�}�w,����¹S�i{r��t�v�}n¬�h�gSy µ���w ¦ �xguw*�rt�w��iyzgS�S±�qs�i�*© �����*��}�{�=�lTtDgSvSo��v³ln��y.���}��gS�xg¨lTv³© ¦ ��{��xw*��w*��w�g«}�~��Qln{�lT��gSyzgS{|w��°�f�m�>�¸��±�en���nc6±�e�Ù�@r±

~ç���©�Ûqs��lT¬\��o�� ±�o-f0l ¦ hpo-jÛ± 5s±iol�«lTvxµ,ln{3o��À± j5±�o$ln{��ba§��}�{|w��So6�R±k���/lT��v*ln{r��g¨ln{¸vxgSh�lNÁ�lTw���}�{!lTtr·trv�}|l�© ¦ ~´}�v��ngSvx�:h�lNv���gI�*©ulnh�g%©ulTtDln©u��w*lTw�gS�:h�}�wø·��*��¹S�i{r�"%�±]�Qln{�lT��gSyzgS{|w��\©u��gS{�©�g�±§�! " �e:P�c¦Ù��� |�Ù±�uc�e¦ N·³�Scnc" �±

~ç�¨e��Ûqs�ÃÁ�}�{3oa=6±iokln{�� �\�ih���guv¨o3��±�� ¦ gS�rv*�i�xw*��©.�x}�hi��w*��}�{Kt�v�}r©�gS���rvxgz~´}�v«y.��h�w��÷���w�gSy�o����i{r��h�g ·�h�gu��gShpohi�iyz��w�gS�½©ulTtDln©u��wÝ�Zh�}�wø·�����¹¨�i{��»t�v�}�¬�h�g¨y�±fçn}��rv�{�lnh�}�~¢)mt§guv³lTw���}�{�lnhM�Kln{�lN��gSyzgS{|w¨±��� "Ù��"Pse:±eTcN·Ýc" �±

~ç�Sc��Ûqmv�g Árhpo¨�5±ioNln{��¢�%�iyªyª�So¨�5±��k}nw/�*��¹S�i{r��ln{����*© ¦ g¨�r��hi�i{r�,·§���rv���gu�%ln{��«g Á�w�gS{�����}�{r�¨±u���rv�}nt§g¨ln{çn}��rv*{�lTh3}�~�)mt§guv*lTw*��}�{�lnh¾��gS�xg¨lTv³© ¦ ±��! " �£8P6 " ��Ve��E±4e�er�Ù·benc�@r±

e�e

Page 23: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

~ç� d"�Ûqmv�g ÁrhI�.±�osln{�� jml�ln�xg7�z±���g¨¶|�rgS{|w*��lnhIln{�lnh������i�8¬DlT��gS� v³lT{��r}�yª��¹ugS��·pvxgS�nv�guwx·�yzguw ¦ }����:~´}�vh�}nwx·�����¹S�i{r��lT{��¸�³© ¦ gS���rhi�i{r�D±vçn}��rv�{�lnh6}�~�w ¦ gA)mt§guv³lTw���}�{�lnhG�,gS��g¨lTv*© ¦ �|}r© ��guwb��±6�! ¦ ��6P3d[£r�pe���±e¦@r��·ben��@�±

~ç��@��Ûqmv�g Árhk�.±�oDln{r�Kjslnln�xg��z±º=4v�}�tD}�v�w���}�{�lnh3h�}�w*����¹S�i{r�ªln{����*© ¦ gS����hi�i{r�D±���{�w�guv*{�lNw*��}�{�lThaçn}���v*{�lnh}n~G=4vx}�����©�w���}�{���©�}�{r}�yª��© �S±��! " �@8P�d����x�]��±f£TcN·>Ù]£\±

~ç�S���Û��t�t§gS{kof;�± q�±�o�ln{��ì�QlTvxw*�i{ko��Û±��z±��|}�h����i{r�Ky.��h�w��÷���w�gSy ©ulTtDl�© ��w³lNw�gS�¿h�}�wø·�����¹¨�i{���t�v�}�¬�h�g¨yz��r�*�i{��ª�TlTv*��lT¬�h�g%vxg¨��gS²�{���w*��}�{3±x)mt§guv³lTw���}�{��r�,gS�xg]lNv³© ¦ ±��! "Ù]£[P�c�@��°�|�E±GÙ�c�e]·>ÙNd]Ù�±

~ç��£��¢3-h�gS�i�*© ¦ y®ln{�{3o-fI±�o-ln{��+��gu�\v¨o-jÛ± ¥0¦ g®��gS{rguv³lTh�h�}�wø·��*��¹S�i{r��ln{��¿�*© ¦ gS����hi�i{���t�v�}�¬�h�g¨y�±l)H���t§guº\w�v���y�±k�! " �£8P��! ��x�¨�E±,����·be���±

~ç�!Ù��¢3-h�}�v���ln{ko�� ±io��3gS{��xw�v*l�o�ç�±��ª±�oTln{��¢���i{�{r}\}N�o��lT{5jÛ± ;�±¨qsguwxgSv�yª�i{��i�xw*��©6trv�}�����© w���}�{«t�h�ln{�{��i{��x±lTh���}�v*��w ¦ yª�,ln{���©�}�y�t�h�g Ár��wb��±:�Kln{�lN��gSyzgS{|ws�\©u��gS{�©�g�±3�! ¦Ù��6P�en����£��E±����" N·Ý��£� �±

~ç�! ��¢3rv³ln{l�©Slro6=6±ior�mv�yzgS{|w³ln{�}Do § ±�o�f>guv�v�guwxw³l�o:��±iox5�h�lTvxº8�5±�� ¦ gS�rv��i�xw*��©s~´}�v�h�}�wø·�����¹¨�i{��z�i{�y.��h�w��÷�xw*lT��g��x���xwxg¨yz�¨±º5>}�yzt��rw�guv*��ln{���)mt§guv³lTw���}�{��}�,g¨�xg¨lTv*© ¦ ±3�! " ]£[P�e]dx±�Ù�����·>Ù�£]dD±

~ en���ÛjmlTv�v��i�x}�{ko ¥ ±ioDln{����3guµ��i�SoDj5±x�3}�wø·��*��¹S�i{r�ª�i{���guv���lnh$ln���xgSy5¬�h����x���xwxg¨yz��µ���w ¦ y.��h�w���t�h�gÛ©�}�{�·�xwxv³ln�i{rgS��v�gS�x}��rv*©�g¨�S±6�Kln{�lN��gSyzgS{|ws�\©u��gS{�©�g�±3�! ¦ ��6P\d\e��ø�]�E±,�! ]·Ýc���±

~ er�©�Ûj�gS�i{rv*��© ¦ o�5s±io$ln{��À��© ¦ {rguguµ�gS�i���So�5s±a�K��h�w��÷��xw³lT��gzh�}�wx·�����¹S�i{r��~´}�v«��gS{rguv³lTh�t�v�}��r��©�w*��}�{»�x���ø·wxgSyª�S±��3g¨© w��rv�g���}�wxg¨�5�i{Ä��©�}�{r}�yª��© �5ln{�� �KlTw ¦ gSy®lTw*��©ulnh��|���xw�gSyª�S±-������wx}�v*�5��Ár�*lTwxgSvª�R±�o�\© ¦ {rgugSµ>gS�i�*�r5Iorln{r�K�|�ih���guv¨or��±D��t�v*�i{r�ngSv § guv*h�lT��orj�gS�i�rgSh�¬§guvx�Doº;sguv�y®ln{|��o��� "Ù��6P�en���:±0��@n�N·��Ù���±

~ e�e��Ûj�gSh�¬§guv¨o��R±G�3}�wz����¹S�i{r�!�i{Z©ulTtDl�© ��w*lTw�gS� t�vx}�����©�w*��}�{Ät�h�ln{�{��i{r�»ln{r� ©�}�{|w�vx}�h��x���xw�gSyª�S±�)H���t§guº\w�v���y�±k�! " "@:P���£8±�@]·³�!Ùr±

~ enc��¢çn}nv*��ln{3o<5s±�ln{r� qsvxguÁ�hpo,�.±>qs�i�*©�v�guw�gKh�}�wø·��*��¹S�i{r� ln{�� �*© ¦ gS����hi�i{r�¿¬\� ¬�lTw³© ¦ ��gS¶\��g¨{�©u�i{��D±�Kln{�lN��gSyzgS{|ws�\©u��gS{�©�g�±3�! ¦ "Ù6P\d�dx±4�" ¦ÙN·`£��Sc�±

~ eNd"�¢�«lTwx}�º�o]��±�o��3guµ��i�So]jÛ±Ô�R±�oNln{��ÛjmlTv�v��i��}�{ko ¥ ±�=�±��k}nwx·�����¹S�i{r���i{«��gS{rguv³lTh�lT�*�xgSy5¬�h��s�x���xw�gSyª�kµ���w ¦�xguw*��tZ©�}��xw*�So-�xguw*�rt w*�iyzgS�So6lT{��Ày5��h�w*��t�h�g:©�}�{��xw�v*ln�i{rgS�»v�gS�x}��rv*© gS�S±��Kln{�lT�ng¨y�g¨{�wz��© ��gS{�©�g�±�� " "Ù6P�dnd§�V�|��±�Ù"@¦ N·>Ù]£"£\±

enc

Page 24: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

~ e"@��¢�%����ºRol��±io��\lnh�}�yz}�{3o��À±�o § ln{¸¾Àln���xgS{ ¦ }N�ng|o���±ý�Û±io-lT{��+�KlTgS�Solç�±a�k�i{rg¨lTv�t�vx}���v*lnyªyª�i{r��o���iy.�rh�lTw�gS�Kln{�{rg¨lnhi�i{���ln{��Kw*lT¬��Q�xg¨lTv³© ¦K¦ gS�rv*�i�xw*��© �m~´}�vIh�}�wI����¹S�i{r�8�i{K¬§}�w�w�h�gS{rg¨©³º�ln����gSy5¬�h���x���xwxg¨yz�¨±r�x�Ý� ¥ v*ln{��*l�©�w*��}�{r�¨±��! ¦ �c6P�e"@r�x�]��±4��e¨·`£ner±

~ en���¢�KlTgS�So¾ç�±�o½�K©�5�h�ln�i{kov��±�okln{r� § ln{�¾Àln���xgS{ ¦ }N�ng|ov��± �5±¾����h�w*�÷�h�gu��gSh-©ulTt�l�© ��w³lTwxg¨��h�}�wx·�����¹S�i{r�©�}�y�t�h�g Ár��wb�Iln{����a=�·p¬Dln�xgS� ¦ gS�rv*�i�xw*��© �S±S���rv�}nt§g¨ln{�çn}��rv*{�lTh�}�~x)mt§guv³lNw*��}�{�lTh]�,gS��g¨lTv*© ¦ ±��� " ��"P@Tc6±,�Sc���·³��d]Ù�±

~ e�£��¢��gu�\v¨o�j5±,�\�iy.��h�w*ln{rgu}����C�3}�wø·�����¹¨�i{��Zln{r� �*© ¦ gS����hi�i{��À}�{ tDlNv³lnhih�gShmy®l�© ¦ �i{�g¨�S±>���rv�}nt§g¨ln{çn}��rv*{�lTh3}�~�)mt§guv*lTw*��}�{�lnh¾��gS�xg¨lTv³© ¦ ±�en���r�"P3�Sc" ��pe���±�e�£¦£¨·be¦ �er±

~ e¦Ù��¢���ihih�guv¨o$�5±io���gSy ¦ lT���xgSvSo�;�±�o�ln{��Z��l¨�ng¨hi�x¬§guvx� ¦ o��À±/� y5��h�w*�÷���wxg¨y)trv�}�����© w���}�{¿t�h�lT{�{��i{r�y�}��rgSh�µ���w ¦ �xguw*��tªw��iyzgS�!±$lnh���}�v���w ¦ yz�¨o]v�gu~´}�v�y.��h�lTw���}�{��Sonln{r��t§}�h�� ¦ gS�rv³lnh�© ¦ lTv*l�©�w�guv*��¹¨lTw���}�{��~´}nv�lz�xt§g¨©u��lThk©uln�xg|±:�QlTw ¦ gSy®lTw���©SlTh¾=4vx}���v³lTyªyª�i{r�D±ren����c:Pº@r�x�]��±f£���·> ���±

~ e¦ ��¢���ihih�guv¨o��.±�o���gSy ¦ ln�r��guvSoS;�±�o�ln{r� ��l¨�ng¨hi�x¬§guvx� ¦ o»� ±f)I{Zw ¦ g�t§}�h�� ¦ gS�rv*lnh��xwxv*��©�w*��v�g�}�~Ily5��h�w*�÷���wxg¨y t�v�}��r��©�w*��}�{Ût�h�ln{r{��i{r�Iy�}��rgSh|µ���w ¦ �xguw*�rt5w*�iyzgS�S±��KlTw ¦ g¨yªlTw*��©ulnh]=4vx}���v*lnyªyª�i{r��±eT����c6P6 Ndx±4c]£¦@]·pd���@r±

~ c����¢=$}r© ¦ guw¨o��z±\ln{��®¾¿}�hi�xgu��o[��± �5±��|}�h����i{��.y.��h�w��÷���w�gSy h�}�wø·��*��¹S�i{r��t�vx}�¬�h�gSyª���r�*�i{����xw�v�}�{r��©u��wx·w��i{r�zt�h�ln{rgS�S±6�Qln{�lT��gSyzgS{|wm��© ��gS{�©�g�±3�! " r�"P�c]£r�ø�]�E±�@ncN·Ý��£�±

~ c��©�¢=$}�w�w��¨o}5I±�o,ln{�� § ln{ ¾ ln����gS{ ¦ }N��g�o���±>��{�w�gu��v³lNw*�i{r�¿�³© ¦ gS���rhi�i{r�¿µ���w ¦ ¬DlTw*© ¦ �i{r�Àln{r�½h�}�wx·����¹S�i{r�x±5l�v�gu����guµ }n~�lnh���}�v���w ¦ yz�ÛlT{�� © }�yzt�h�g Ár��wb��±�)mt§guv³lNw*��}�{�lThf�,g¨�xg¨lTv*© ¦ ��}r© ��gSwÝ��±��� " �e:Pd�c���@���±4c¦ �@]·pd|���r±

~ c�e��.�\lnh�}�yz}�{3o¾� ±�o½�«�r��º�o¾��±io3ln{�� § ln{K¾ ln���xg¨{ ¦ }N��g�o¾��±k�|w³lNw*�i�xw*��©ulnh$�xg]lNv³© ¦ yzguw ¦ }\���I~´}nv%h�}�wx·����¹S�i{r��t�v�}�¬�h�g¨yz�¨±��s{�{�lThi��}n~�)mt§guv³lNw*��}�{��}��gS�xg¨lTv³© ¦ ±��! ¦ �c6P\dD�"±6d[@TcN·pd|�"Ù�±

~ c�c��.�\lnh�}�yz}�{3oº�À±�qsguw�guv�yª�i{��i�xw*��©Ih�}�wx·�����¹S�i{r�ªy�}��rgShi��~´}�v�t�vx}�����©�w*��}�{�t�h�ln{�{��i{��D±º�3g]©�w��rv�g5��}�wxgS��i{���©�}�{�}�yª��© �/lT{��4�QlTw ¦ gSy®lTw���©SlTh|�|���xwxg¨yz�¨±¨�|t�v*�i{���guv § guv*h�lN�Do]j�g¨�i��g¨h�¬DgSvx�Do�;mgSv�y®ln{|��o��! " ��¦Pc"@"@r±

~ cTd"�.�\lnh�}�yz}�{3ox� ±ioDln{��0�%����º�ox�Û±º�K�rh�w*�÷�h�gu��gSh3h�}�w�����¹S�i{r�®trv�}�¬�h�gSyN±�gu�Tlnhi��lNw*��}�{�}n~4l®���iy.�rh�lTw�gS�lT{�{rg¨lnhi�i{r� ¦ gS�rv*�i�xw*��©n±��4�rv�}�tDg]lT{Nçn}��rv�{�lnh�}�~�)mt§guv*lTw*��}�{�lnh½�,g¨�xg¨lTv*© ¦ ±3�� " ��6P\d[@��ø�]�E±�e¦@]·Ýc]£�±

~ c�@��.��w³ln�rw�h�guv¨o\j5±8����h�w*�÷�h�gu��gShDh�}nwx·�����¹S�i{r�Ûµ���w ¦ �xguw*��t�w��iyzgS�0ln{��:y.��h�w*��t�h�gmvxg¨�x}���v³©�g%©�}�{��xwxv³ln�i{rgS�vxgS��}��rv³©�gS�!±��i{|wxguv*{�lnhih��®v�}�hihi�i{��®�*© ¦ gS����h�gS��µ���w ¦ h�}�wø·�����¹¨�i{��zµ��i{r�r}Nµ��S±/)mt§guv³lNw*��}�{��r��gS�xg¨lTv³© ¦ ±eT����c6Pº@����Vc|��±6d�Ù]£¨· @n��e�±

eNd

Page 25: Scheduling In ection Molding Operations 9ith Multiple Cesource Constraints and SeWuence

~ c���� ¥ gSyztDg¨hiy�g¨��guvSo�j5±�o�ln{r�Äj�gSh�¬§guv¨o��R±-� ¦ gS�rv*�i�xw���©®~´}nv�y.��h�w��÷���w�gSy y.�rh�w*�÷�h�gu��gSh>©ulTtDl�© ��w*lTw�gS�h�}nwx·�����¹S�i{r�8~´}�vI�ng¨{�gSv*lnh-trv�}�����© w%�xw�v���©�w*�rvxg|±�����v�}�t§g¨ln{ çn}��rv�{�lnh-}�~�)mt§guv³lTw���}�{�lnh���gS�xg¨lTv³© ¦ ±�� " TdxPx£�@��pe��Ùo�e¦ ��N·Ýc��n��±

~ c]£�� ¥ gSyztDg¨hiy�g¨��guvSo�j5±�o\ln{��:qmguv*�xw�vx}���o��À±�� �/lT��v*ln{r��g¨ln{�·p¬�ln�xg¨� ¦ gS�rv*�i�xw*��©0~´}�v��r�\{�lnyª��©,y.��h�w��÷h�gu��gSh/y.��h�w��÷���w�gSy7© }�{��xw�v³lT�i{rgS��h�}�wø·��*��¹S�i{r�ªµ���w ¦ ��guw��rtKw*�iy�g¨�S±x�Kln{�lT��gSyzgS{|wI��© ��g¨{�© g�±$�� " ��6Pd|e���@���±f£Nc"ÙN·`£¦@�£\±

~ c"Ù�� ¥ v�������guv�}Do§¾ ± ¾ ±io ¥,¦ }�y®ln�Soa��±�ç�±kln{��7�Q©�5�h�lT�i{ko½ç�± ).±�5�lTtDl�© ��w³lNw�gS�¸h�}�wø·�����¹¨�i{���µ���w ¦ ��guw��rtw��iyzgS�S±6�QlT{�lT��gSyzgS{|wm�\©u��gS{�©�g�±3�! ¦Ù" 6P�c�@r�Vc|��±4c�@TcN·Ýc�����±

~ c" ��%¾ lT��{�gSvSo�j5±�� ±io�ln{��»¾ ��w ¦ �i{3o ¥ ± j5±-qm��{�lnyz��©ª��guv*����}�{»}�~0w ¦ g8g¨© }�{r}�yª��©ªh�}�w5����¹ug8y�}��rgShp±�Kln{�lN��gSyzgS{|ws�\©u��gS{�©�g�±3�! "@¦Ù6P6@��x�¨�E±�Ù" N·> n��±

e"@