Research Article

Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

Table 8

Results for the first relaxation, R=1 and QCap=600.

Prob no.FCFVDCs opened ()DCs closed ()No. of open DCsUpper BoundLower Bound% GapLag iterCPU time (s)

10.70.710, 118, 145 2,023,248 2,003,836 0.97178539
20.70.8 10, 20146 2,041,897 2,022,987 0.93136329
30.70.9 10, 20146 2,056,136 2,041,066 0.74161135
40.71.0 10, 20146 2,070,318 2,056,800 0.66155534
50.71.1 10, 20146 2,085,017 2,071,114 0.67149933
60.71.220None6 2,099,931 2,089,759 0.49139731
70.71.3 10, 20146 2,116,294 2,104,572 0.56163336
80.80.710145 2,068,799 2,051,432 0.85155434
90.80.8NoneNone5 2,092,841 2,071,195 1.05182738
100.80.910145 2,109,062 2,091,839 0.82213946
110.81.0 10, 20146 2,125,723 2,109,966 0.75177539
120.81.1 10, 20146 2,140,422 2,115,810 1.16141532
130.81.220None6 2,154,840 2,144,656 0.47201544
140.81.3 10, 20146 2,171,699 2,161,893 0.45183041
150.90.710145 2,115,023 2,091,648 1.12155433
160.90.810145 2,144,384 2,114,680 1.40103622
170.90.910145 2,155,285 2,136,610 0.87178838
180.91.0NoneNone5 2,175,811 2,153,626 1.03203844
190.91.1 10, 20146 2,195,827 2,177,076 0.86168637
200.91.220None6 2,209,749 2,183,209 1.22147032
210.91.3 10, 20146 2,227,104 2,212,965 0.64168837
221.00.710145 2,161,246 2,131,154 1.41101122
231.00.8NoneNone5 2,184,295 2,155,778 1.32191040
241.00.9NoneNone5 2,202,343 2,177,796 1.13271858
251.01.02, 3, 5, 8, 14N/A5 2,221,538 2,202,020 0.89170537
261.01.120None6 2,250,748 2,218,640 1.45147432
271.01.220None6 2,264,658 2,242,602 0.98127428
281.01.3 10, 20146 2,282,509 2,263,675 0.83134330
291.10.710145 2,207,470 2,170,288 1.7192920
301.10.8NoneNone5 2,230,023 2,194,687 1.61113124
311.10.910145 2,247,732 2,219,852 1.26202243
321.11.0NoneNone5 2,267,266 2,244,557 1.01183440
331.11.11235 2,299,007 2,265,427 1.48138931
341.11.21235 2,319,104 2,289,564 1.29145232
351.11.3NoneNone5 2,331,122 2,307,567 1.02180440
361.20.710145 2,253,693 2,208,455 2.05129628
371.20.8NoneNone5 2,275,750 2,235,681 1.7993720
381.20.9NoneNone5 2,293,798 2,264,077 1.31104322
391.21.0NoneNone5 2,312,993 2,288,491 1.0795621
401.21.110145 2,346,628 2,311,584 1.52153134
411.21.2NoneNone5 2,364,918 2,336,833 1.20154834
421.21.3NoneNone5 2,376,850 2,357,551 0.82128828
431.30.7NoneNone5 2,299,884 2,247,278 2.34101122
441.30.8NoneNone5 2,321,478 2,276,995 1.95103222
451.30.9NoneNone5 2,339,525 2,300,269 1.71106422
461.31.0NoneNone5 2,358,720 2,330,384 1.22145331
471.31.110145 2,392,852 2,357,628 1.49182340
481.31.21235 2,408,450 2,382,329 1.10133729
491.31.3NoneNone5 2,422,577 2,406,503 0.67103723

(): with respect to base case, Prob no 25; N/A, not applicable.