This paper presents a mathematical model for a single depot, time-dependent vehicle routing problem with backhaul considering the first in first out (FIFO) assumption. As the nature of the problem is NP-hard, variable neighborhood search (VNS) meta-heuristic and mat-heuristic algorithms have been designed. For test problems with large scales, obtained results highlight the superior performance of the mat-heuristic algorithm compared with that of the other algorithm. Finally a case study at the post office of Khomeini-Shahr town, Iran, was considered. Study results show a reduction of roughly 19% (almost 45 min) in the travel time of the vehicle.

In this paper, the authors proffer a novel mathematical model for the simultaneous optimization of facility location and network design in the presence of uncertainty, with the aim of minimizing operational and transportation costs. The proposed model constitutes a departure from conventional methods in its consideration of probable events in the real world and the incorporation of uncertainty assumptions into the mathematical framework. An algorithm based on simulated annealing is then advanced for the solution of the problem, and the performance of the algorithm is evaluated through comparison with exact methods for problems of modest size, as well as with a basic simulated annealing algorithm for larger problems. The results of these comparisons demonstrate the superiority of the proposed meta-heuristic algorithm. Finally, the robust approach is compared with four other approaches in the presence of uncertainty, with a thorough analysis of the results obtained from each of the methods conducted in a suite of sample problems.

In this paper, a novel multi-objective robust possibilistic programming model is proposed, which simultaneously considers maximizing the distributive justice in relief distribution, minimizing the risk of relief distribution, and minimizing the total logistics costs. To effectively cope with the uncertainties of the after-disaster environment, the uncertain parameters of the proposed model are considered in the form of fuzzy trapezoidal numbers. The proposed model not only considers relief commodities priority and demand points priority in relief distribution, but also considers the difference between the pre-disaster and post-disaster supply abilities of the suppliers. In order to solve the proposed model, the LP-metric and the improved augmented ε-constraint methods are used. Second, a set of test problems are designed to evaluate the effectiveness of the proposed robust model against its equivalent deterministic form, which reveales the capabilities of the robust model. Finally, to illustrate the performance of the proposed robust model, a seismic region of northwestern Iran (East Azerbaijan) is selected as a case study to model its relief logistics in the face of future earthquakes. This investigation indicates the usefulness of the proposed model in the field of crisis.