Mathematical Problems in Engineering / 2016 / Article / Tab 8

Research Article

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
()

16518010818 (788)1367
57071535987 (948)1376
897015711264 (1220)1381
15649901451536 (1492)1381
26193102011696 (1652)1381
29630302542080 (2036)1381
38603002902240 (2196)1381
47869603202512 (2468)1381
59642003212779 (2736)1380
73979703672939 (2896)1380

(b)

Mathematical programming
MILP
()

1651808480117 (79204)47426
57071575280117 (79204)50626
897015724880117 (79204)53826
161345360080117 (79204)57026
269972060080117 (79204)60226
300331060080117 (79204)63426
406295060080117 (79204)66626
509240060080117 (79204)69826
654345060080117 (79204)73026
821345060080117 (79204)76226

(c)

DHIP
HM
()

19359017829 (800)1384
64131545999 (960)1394
1000770821276 (1232)1399
16772901981548 (1504)1399
26382702341708 (1664)1399
30462502982092 (2045)1399
39708203112252 (2208)1399
48546803452524 (2480)1399
60349604012791 (2748)1398
74759804532951 (2908)1398

(d)

DHIP
HM
()

16518011821 (792)1371
57071538991 (952)1381
897015741268 (1224)1386
15649901511540 (1496)1386
26310902041700 (1656)1386
29989502602084 (2040)1386
39454302962244 (2200)1386
47962503212516 (2472)1386
60047503782783 (2740)1385
76524904212943 (2900)1385

(e)

DHIP
HM
()

1651809801 (772)1266
57071531971 (922)1276
897015671240 (1196)1381
15716001341504 (1460)1381
26346201981664 (1620)1381
30003102342032 (1988)1381
40277402872192 (2148)1381
49167403112456 (2412)1381
59782203182715 (2672)1380
74759803322875 (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.