I have been wondering if my code is wrong or something. But why can't I get the optimality with only 16 nodes (I have clustered it so the max now becomes 16 from a total of 54 nodes)? My model was based on VRP Time Windows by Paschos 2014. I've tried it by using Lingo and Gurobi. The formulation is this:
$$
\text { Minimize } \sum\_{k=1}^{m} \sum\_{\left(v\_{i}, v\_{j}\right) \in \mathcal{A}} c\_{i j} x\_{i j k}
$$

Constraint:
$$
\begin{array}{ll}
\sum\_{k=1}^{m} \sum\_{v\_{j} \in \mathcal{V}} x\_{i j k}=1 & \begin{array}{r}
k=1\left(v\_{i}, v\_{j}\right) \in \mathcal{A} \\
v\_{i} \in \mathcal{V} \backslash\left\{v\_{0}\right\}
\end{array} \\
\sum\_{v\_{i} \in \mathcal{V}} x\_{i \ell k}=\sum\_{v\_{j} \in \mathcal{V}} x\_{\ell j k} & v\_{\ell} \in \mathcal{V} \backslash\left\{v\_{0}\right\}, 1 \leqslant k \leqslant m \\
\sum\_{v\_{j} \in \mathcal{V} \backslash\left\{v\_{0}\right\}} x\_{0 j k}=1 & 1 \leqslant k \leqslant m \\
\sum\_{v\_{i} \in \mathcal{V} \backslash\left\{v\_{0}\right\}} x\_{i 0 k}=1 & 1 \leqslant k \leqslant m \\
\sum\_{v\_{i} \in \mathcal{V} \backslash\left\{v\_{0}\right\}} \sum\_{v\_{j} \in \mathcal{V}} q\_{i} x\_{i j k} \leqslant Q & 1 \leqslant k \leqslant m
\end{array}
$$

$$
\begin{aligned}
&a\_{i} \sum\_{v\_{j} \in \mathcal{V}} x\_{i j k} \leqslant u\_{i k} \leqslant b\_{i} \sum\_{v\_{j} \in \mathcal{V}} x\_{i j k}, \quad v\_{i} \in \mathcal{V}, 1 \leqslant k \leqslant m \\
&u\_{i k}+s\_{i}+t\_{i j}-u\_{j k} \leqslant T\left(1-x\_{i j k}\right), \quad\left(v\_{i}, v\_{j}\right) \in \mathcal{A}, 1 \leqslant k \leqslant m \\
&u\_{i k} \geqslant 0, \quad v\_{i} \in \mathcal{V}, 1 \leqslant k \leqslant m
\end{aligned}
$$

The weird thing is when I tried to solve it with 10 nodes, the lingo solver was able to return the optimal solution in under 1 minute. But when I tried with real data, even for 10 hours running, the solver is still running.

**EDIT:**

```
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 2 physical cores, 4 logical processors, using up to 4 threads
Optimize a model with 168 rows, 768 columns and 2976 nonzeros
Model fingerprint: 0x460da4ce
Model has 630 general constraints
Variable types: 48 continuous, 720 integer (720 binary)
Coefficient statistics:
  Matrix range     [1e+00, 8e+01]
  Objective range  [1e+00, 5e+01]
  Bounds range     [1e+00, 1e+00]
  RHS range        [1e+00, 1e+03]
  GenCon rhs range [1e+01, 4e+01]
  GenCon coe range [1e+00, 1e+00]
Presolve added 1272 rows and 210 columns
Presolve time: 0.17s
Presolved: 1440 rows, 978 columns, 11136 nonzeros
Variable types: 258 continuous, 720 integer (720 binary)

Root relaxation: objective 2.700000e+01, 67 iterations, 0.03 seconds (0.00 work units)

    Nodes    |    Current Node    |     Objective Bounds      |     Work
 Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time

     0     0   27.00000    0   30          -   27.00000      -     -    0s
     0     0   30.02381    0   37          -   30.02381      -     -    0s
     0     0   35.00000    0   36          -   35.00000      -     -    0s
     0     0   43.00000    0   31          -   43.00000      -     -    0s
H    0     0                     281.0000000   43.00000  84.7%     -    0s
     0     0   43.00000    0   31  281.00000   43.00000  84.7%     -    0s
     0     0   43.00000    0   31  281.00000   43.00000  84.7%     -    1s
     0     0   43.00000    0   30  281.00000   43.00000  84.7%     -    1s
     0     0   43.00000    0   30  281.00000   43.00000  84.7%     -    1s
     0     0   43.00000    0   30  281.00000   43.00000  84.7%     -    1s
     0     2   43.00000    0   26  281.00000   43.00000  84.7%     -    1s
H   29    35                     198.0000000   43.00000  78.3%  21.5    1s
H   88    99                     168.0000000   43.00000  74.4%  14.0    1s
*  119   123              50     127.0000000   43.00000  66.1%  12.4    1s
H  456   391                     125.0000000   43.00000  65.6%  10.3    2s
H  463   379                     119.0000000   43.00000  63.9%  10.4    2s
   817   658   43.15451   22   27  119.00000   43.00000  63.9%  15.9    5s
H 1006   719                     118.0000000   43.00000  63.6%  16.5    5s
H 1038   692                     114.0000000   43.00000  62.3%  16.6    5s
H 1073   678                     113.0000000   43.00000  61.9%  16.6    6s
H 1705   899                     111.0000000   43.00000  61.3%  16.3    7s
  3202  1880   84.97293   66   13  111.00000   43.48152  60.8%  15.5   10s
  8845  6167   93.21239   72   10  111.00000   44.28152  60.1%  15.6   15s
 14423  9889 infeasible   64       111.00000   45.12155  59.3%  14.7   20s
 19007 13198   51.85990   38   12  111.00000   45.74524  58.8%  14.4   25s
 20856 14247   67.91148   60   30  111.00000   46.00000  58.6%  14.5   31s
 20886 14267   86.76100   43   54  111.00000   46.00000  58.6%  14.4   35s
 20987 14336   46.00000   36   33  111.00000   46.00000  58.6%  14.8   40s
 22171 14926  100.20962  115   23  111.00000   46.00000  58.6%  15.1   45s
 26640 16889 infeasible   69       111.00000   47.53714  57.2%  15.0   50s
 32818 19229   69.72771   59   26  111.00000   51.16970  53.9%  14.8   55s
 38186 21010   59.97461   45   34  111.00000   53.16667  52.1%  14.9   60s
 42489 22265   90.33333   49   14  111.00000   54.63747  50.8%  14.9   65s
 47836 24148   89.49744   77   31  111.00000   56.00000  49.5%  14.9   70s
 53826 25927   65.11477   60   34  111.00000   56.79788  48.8%  14.8   75s
 59884 27894   78.77307  154   23  111.00000   57.41955  48.3%  14.9   80s
 65719 30032  101.20672   60   24  111.00000   58.09387  47.7%  14.9   85s
 71150 33633 infeasible  115       111.00000   58.72779  47.1%  14.9   90s
 74887 36114   64.05556   52   27  111.00000   59.09387  46.8%  14.9   95s
 79892 39307  109.30875   49   24  111.00000   59.51082  46.4%  14.9  100s
 83720 41742   71.64684   51   22  111.00000   59.91729  46.0%  15.0  105s
 88446 44919   98.25571   45   10  111.00000   60.10905  45.8%  15.0  110s
 93592 48237   85.96847   48   24  111.00000   60.43274  45.6%  15.1  115s
 98541 51522   64.60322   51   25  111.00000   60.72943  45.3%  15.1  120s
 102845 54267   99.00000   65   16  111.00000   60.95160  45.1%  15.1  125s
 107394 57673   69.52727   64   22  111.00000   61.00000  45.0%  15.2  130s
 112444 61028   80.75000   78   18  111.00000   61.12951  44.9%  15.2  135s
 117523 64288   67.74127   75   16  111.00000   61.26834  44.8%  15.3  140s
 122741 67689   63.32275   65   19  111.00000   61.45337  44.6%  15.3  145s
 127607 70950  101.00000   49   12  111.00000   61.57306  44.5%  15.4  150s
 132756 74210   65.47593   42   31  111.00000   61.78555  44.3%  15.4  155s
 136990 76979   92.93333   77   15  111.00000   61.93750  44.2%  15.4  160s
 142582 80382  104.00000   76   17  111.00000   62.00000  44.1%  15.4  165s
 147283 83875  109.09497   64   19  111.00000   62.00000  44.1%  15.5  170s
 152753 87143  103.55460   60   10  111.00000   62.12951  44.0%  15.5  175s
 158126 90549   93.94203   55   19  111.00000   62.23102  43.9%  15.5  180s
 163038 93669     cutoff   60       111.00000   62.32400  43.9%  15.6  185s
 166698 95951   77.50173   77   15  111.00000   62.40379  43.8%  15.6  190s
 171727 98819  105.61448   56   22  111.00000   62.52864  43.7%  15.6  195s
 176952 102393 infeasible   99       111.00000   62.64973  43.6%  15.6  200s
 181955 105410   87.20043   45   11  111.00000   62.75701  43.5%  15.6  205s
 187145 108539   87.80647   75   35  111.00000   62.89160  43.3%  15.7  210s
 192246 111837 infeasible   79       111.00000   62.99708  43.2%  15.7  215s
 197389 115062   70.75900   85   13  111.00000   63.00000  43.2%  15.7  220s
 201353 117893   93.06245   75   31  111.00000   63.02439  43.2%  15.7  225s
 206195 120822   63.47779   54   24  111.00000   63.09691  43.2%  15.7  230s
 210899 123760  105.00546   61   14  111.00000   63.14964  43.1%  15.7  235s
 216382 127092  105.00000   74   14  111.00000   63.22222  43.0%  15.7  240s
 222038 130637   90.00000   68   12  111.00000   63.32452  43.0%  15.7  245s
 226492 133185   90.91646   44   13  111.00000   63.37571  42.9%  15.7  250s
 230755 136152   64.69033   64   20  111.00000   63.41868  42.9%  15.7  255s
 235252 138714   63.86574   57   31  111.00000   63.49554  42.8%  15.8  260s
 240283 141816 infeasible   50       111.00000   63.55502  42.7%  15.7  265s
 246089 145454   79.49498   48   18  111.00000   63.64156  42.7%  15.7  270s
 250670 148171   79.08612   52   12  111.00000   63.70720  42.6%  15.7  275s
 255030 150974   80.73087   37   15  111.00000   63.75478  42.6%  15.8  280s
 258930 153198   94.81954   45   16  111.00000   63.79969  42.5%  15.8  285s
 263816 156010   76.15049   45   25  111.00000   63.88839  42.4%  15.8  290s
 268782 158824   93.50000   49    8  111.00000   63.95633  42.4%  15.8  295s
 271310 160524   84.00000   52   15  111.00000   64.00000  42.3%  15.8  300s
 274848 162583   66.86667   34   27  111.00000   64.00000  42.3%  15.8  305s
 278496 165062 infeasible   87       111.00000   64.00000  42.3%  15.8  310s
 281970 167381     cutoff   59       111.00000   64.01453  42.3%  15.8  315s
 285890 169888   97.42763   61   20  111.00000   64.06042  42.3%  15.9  320s

```