produced by each molding pattern, because it is not possible to
know in advance how many molds A, B and C will be used in each
molding pattern defined by Preset settings 1 or 2.
This small example also considers that the setup time needed
for stopping/starting production line is 5 h (i.e. stI ¼ 5) and the
setup time for attaching/detaching any type of mold is 0.5 h
i:e: stII
i ¼ 0:5 8i 2 fA; B; C;Dg
. Times for Setup III are defined as
shown in Table 5.
Table 6 presents the optimal values for zjs and yips in two consecutive
sub-periods s and s þ 1, and also shows the molding patterns
defined and the total setup time involved. Variables which
are not in Table 6, like z2ðsþ1Þ, are equal to zero. Note that these
two molding patterns are defined by the preset settings j ¼ 1 and
j ¼ 3 respectively, which take into account operational constraints
and also the number of molds available, so they are feasible to be
used in practice.
Total setup time depends on the machine state in two consecutive
sub-periods, considering times for Setups I, II and III. For
instance, note in Table 6 that uAðsþ1Þ ¼ 0 because there were 12
molds of type A used in setting j ¼ 1 in sub-period s, and this same
number of molds is maintained in setting j ¼ 3 in sub-period s þ 1.
Note also that the total number of molds exchanges between subperiods
s and s þ 1 yields 21 (i.e. detaching 4 molds B and 8 molds
C, and attaching 9 molds D), which results in a Setup time II equal
to ð21Þð0:5Þ ¼ 10:5 h. In this way, molding patterns are defined and
total setup times are also determined, so that production planning
decisions can be approached in an integrated way as the model
(1)–(19) suggests.