Bi-objective covering tour location routing problem with replenishment at intermediate depots: Formulation and meta-heuristics

- A bi-objective ILP model of location covering routing problem is presented.
- The epsilon-constraint method is offered to solve the model optimally by GAMS with Cplex solver.
- For large scale instances, three heuristic algorithms based on NSGAII are presented.
- NSGAII-FFI algorithm outperformed the others based on the determined performance metrics.

The Covering tour Location Routing Problem with Replenishment at intermediate depots (CLRPR) is an extension of location routing problem with service time restriction, replenishment at intermediate depots, and customer mobility in a predefined walking distance. Among the different applications of the problem, this study concentrates on the post-earthquake relief distribution system. This paper represents a new bi-objective integer linear programming model that minimizes the total weighted waiting time and the total amount of lost demands. The mathematical model is coded in GAMS software and solved optimally by Cplex solver with epsilon-constraint method. In order to cope with the NP-hardness feature of the problem, the NSGAII multi-objective algorithm with two distinct improvements are proposed as heuristic solution procedures. The results of 36 randomly generated test problems were analyzed in terms of quality, quantity, diversity and spread of Pareto front solutions.