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.

Bidding price decision is a key issue for the contractors and construction companies. The success/failure of the contractors in competitive biddings is directly dependent on their bidding strategy. This paper aims to develop a hybrid statistical and mathematical modeling approach for determining the optimum bidding price in construction projects. By statistical analysis of historical data, some uncertain parameters like the number of competitors and the cost of the project are estimated. Then, a scenario-based mathematical model for bidding price decision is proposed. In order to present a model in more accordance with the real-world situations, factors like risk, minimum acceptable rate of return (MARR) and opportunistic behavior are taken into account. In order to achieve an insensitive solution to the change in the realization of the input data from the scenarios, a robust mathematical model is used. The performance of the model is evaluated through some numerical problems. Furthermore, sensitivity analysis of the key parameters and robustness evaluation of the model against uncertain parameters are conducted. To evaluate the model's effectiveness in real-world situations, a case study is analyzed by the proposed approach. Numerical results show that the proposed approach reduces the cost estimation errors and increases the average expected profit, which validates the applicability of the model in a real-world situation.