New formulations and solution approaches for the latency location routing problem

Effective metaheuristics for the latency location routing problem

“…For the instance $$\text{Christ}\text{-}75\text{-}10$$, we found a valid lower bound equal to 2260.1, which is larger than the best solution value ($$Best=2228.4$$) reported in Nucamendi‐Guillén et al. (2022). Because of the above, these two instances were not considered in the global average results of the exact methods and of algorithm GBILS.…”

“…Note that new tighter lower bounds are reported in italic in the Tables 2–4. Furthermore, note that the value (331.9) of LB 2 reported in Moshref‐Javadi and Lee (2016) for the instance 20‐5‐1 of the Prodhon data set is larger than the proved optimal solution value 330.0 (see Nucamendi‐Guillén et al., 2022). Hence, we implemented a correct procedure and computed again the value of LB 2 for all the instances. $$BKS_0$$: Best known solution value considering algorithms RGA, MA, the five exact methods, and algorithm GBILS (i.e., the best known solution value found by the current state‐of‐the‐art algorithms).…”

“…For the instances Min‐134‐8 and Or‐117‐14 no results are reported in Nucamendi‐Guillén et al. (2022). The last line of Table 4 gives the average values (Global avg$$_{NG}$$) computed by considering only the six instances whose values are correctly reported in Nucamendi‐Guillén et al.…”

“…Each $$BKS_0$$ value proved to be the optimal solution value by Nucamendi‐Guillén et al. (2022) is presented in boldface. $$BKS$$: Best known solution value considering all the algorithms. $$Gap_{LB}$$: Percentage gap between $$BKS$$ and $$LB$$, computed as $$Gap_{LB}=100 \frac{(BKS\text{-}LB)}{LB}$$.…”

“…As pointed out in Nucamendi‐Guillén et al. (2022), the LLRP has also important applications in commercial systems where perishable products should be delivered, and in city logistics problems, where deliveries to the customers are performed by means of shared intermediate facilities.…”