Table 2: Comparison of CPLEX results with the proposed algorithms for small-sized instances.

𝑛 𝑚 CPLEXMWCSA VNS
ObjectiveTimeObjectiveRPDObjectiveRPDTime
value (gap)(sec)valuevalue(sec)

625821.485820.00%5820.00%0.36
33602.473702.78%3600.00%0.30
82859103.55 8590.00%8590.00%0.52
3513122.20 5130.00%5130.00%0.46
102128424632.09 13081.87%12840.00%0.72
31190144761.59 12161.59%11900.00%0.72
*the deteriorating date with the interval 𝑈 ( 0 , 𝐷 0 . 5 ]
624301.504300.00%4300.00%0.30
33922.053920.00%3920.00%0.30
8283580.70 8350.00%8350.00%0.46
3590233.25 5900.00%5900.00%0.47
102118617676.28 11860.00%11860.00%0.71
379462828.11 7990.63%7940.00%0.72
*the deteriorating date with the interval 𝑈 [ 𝐷 0 . 5 , 𝐷 ]
624461.634460.00%4460.00%0.30
33351.923350.00%3350.00%0.31
82934102.61 9390.54%9340.00%0.47
3486205.08 4911.03%4860.00%0.47
102116122216.36 11932.76%11610.00%0.72
363851367.00 6380.00%6380.00%0.70
*the deteriorating date with the interval 𝑈 ( 0 , 𝐷 ]

Average  0.62% 0.00%