A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints
Table 8
The results of numerical examples for both methods.
(a)
DHIP
MILP_T
()
165180
10
818 (788)
1367
570715
35
987 (948)
1376
897015
71
1264 (1220)
1381
1564990
145
1536 (1492)
1381
2619310
201
1696 (1652)
1381
2963030
254
2080 (2036)
1381
3860300
290
2240 (2196)
1381
4786960
320
2512 (2468)
1381
5964200
321
2779 (2736)
1380
7397970
367
2939 (2896)
1380
(b)
Mathematical programming
MILP
()
165180
84
80117 (79204)
47426
570715
752
80117 (79204)
50626
897015
7248
80117 (79204)
53826
1613453
600
80117 (79204)
57026
2699720
600
80117 (79204)
60226
3003310
600
80117 (79204)
63426
4062950
600
80117 (79204)
66626
5092400
600
80117 (79204)
69826
6543450
600
80117 (79204)
73026
8213450
600
80117 (79204)
76226
(c)
DHIP
HM
()
193590
17
829 (800)
1384
641315
45
999 (960)
1394
1000770
82
1276 (1232)
1399
1677290
198
1548 (1504)
1399
2638270
234
1708 (1664)
1399
3046250
298
2092 (2045)
1399
3970820
311
2252 (2208)
1399
4854680
345
2524 (2480)
1399
6034960
401
2791 (2748)
1398
7475980
453
2951 (2908)
1398
(d)
DHIP
HM
()
165180
11
821 (792)
1371
570715
38
991 (952)
1381
897015
74
1268 (1224)
1386
1564990
151
1540 (1496)
1386
2631090
204
1700 (1656)
1386
2998950
260
2084 (2040)
1386
3945430
296
2244 (2200)
1386
4796250
321
2516 (2472)
1386
6004750
378
2783 (2740)
1385
7652490
421
2943 (2900)
1385
(e)
DHIP
HM
()
165180
9
801 (772)
1266
570715
31
971 (922)
1276
897015
67
1240 (1196)
1381
1571600
134
1504 (1460)
1381
2634620
198
1664 (1620)
1381
3000310
234
2032 (1988)
1381
4027740
287
2192 (2148)
1381
4916740
311
2456 (2412)
1381
5978220
318
2715 (2672)
1380
7475980
332
2875 (2832)
1380
: the optimal value of Fc (objective function). : time for finding solution (in seconds). The feasible value of the objective function after the time . Calculation was stopped after 600 s. (): the number of decision variables (integer decision variables). : the number of constraints. MILP: the implementation in the MP-based environment - MILP model. MILP_T: the implementation in the declarative hybrid implementation framework (DHIF) MILP model after transformation. HM: implementation in the declarative hybrid implementation framework (DHIF) model after transformation.
