Page 303 - Sustainability in the Process Industry Integration and Optimization

280 C h apter Ele v e n

minimize the cleaning cost. This change in criterion has only a minor
effect on the solution procedure, so an effective solver for the original
problem is also useful for the reformulated problem.
Twenty-three equipment units, E1 through E23, are available to
generate six products, A through F. The changeover time is 70 minutes
for equipment units E6, E7, E8, and E9 but 100 minutes for equipment
units E1 through E5 and E10 through E20. All other changeover times
are presumed to be zero. The number of batches to be produced is
given in Table 11.10.
Cleaning the equipment units is a costly operation that involves
many pollutants. The minimal makespan schedule contains 11
cleaning operations, which are denoted by the dotted changeover
arcs on its S-graph; see Figure 11.18.
The cleaning cost of the solution with minimal makespan is
$14,000. In contrast, the solution based on minimizing the cost
involves four (rather than 11) cleaning operations and only $3,500 in
cleaning cost; its makespan is 6,910 minutes. If the cleaning cost is
limited to reach $5,500, then the corresponding makespan is reduced
to 6,700 minutes.

Product A B C D E F
Number of batches 3 5 1 3 9 3

TABLE 11.10 Number of Batches Produced of Each Product

60 120 540 40 120 60 720
E1 E6 310 E11 E22 97 E4 E6 E10 E21 109
A 0 E
0 0 0 0
0
60 310 120 540 40 120 90 720
E1 E6 E11 E22 98 A E4 E6 E12 E21 110 E
0 0 0 70 0 0 0 0
0
60 310 120 540 40 120 60 720
E1 E6 E11 E22 99 A E4 E6 E10 E21 111 E
0 70 0 0 0 0
E1 60 E7 240 E15 120 E22 540 100 B E4 40 E6 300 E12 90 E21 720 112 E
0 0 0 0 0 0 0
70
60 120 540 40 300 60 720
E1 E7 240 E19 E22 101 B E4 E6 E10 E21 113 E
0 0 100 0 0 0 0 0
60 240 120 E22 540 40 300 90 720
E1 E7 E11 102 B E4 E6 E12 E21 114 E
0 0 0 0 0
0 0
60 240 60 540 40 300 60 720
E1 E7 E13 E22 103 B E4 E6 E10 E21 115 E
0 0 100 0 0 0 0 0
E1 60 E7 240 E15 120 E22 540 104 B E4 40 E6 300 E12 90 E21 720 116 E
70 0 0 0 0
100
60 E8 120 50 540 40 300 90 720
E2 E16 E22 105 E4 E6 E16 E21 117
0 C 100 E
60 240 90 540 40 240 120 720
E3 E7 E18 E22 106 D E5 E7 E19 E23 118
0 0 0 0 0 0 F
60 240 90 540 40 240 60 720
E3 E7 E14 E22 107 E5 E7 E20 E23 119
D 0 F
0 0 100 0 0
0
60 240 60 720 40 240 120 720
E3 E7 E20 E23 108 E5 E7 E15 E23 120
D F
70 100
FIGURE 11.18 Schedule graph of the solution that minimizes makespan (after
Adonyi et al., 2008).