A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty

• Presenting a new model for pollution routing problems with pickup and delivery.
• Introducing a new robust counterpart of the MILP model to handle uncertainty.
• Integrating time window constraints into pollution routing problems.
• Comparing proposed deterministic and robust mathematical programming in detail.

Organizations have recently become interested in applying new approaches to reduce fuel consumptions, aiming at decreasing green house gases emission due to their harmful effects on environment and human health; however, the large difference between practical and theoretical experiments grows the concern about significant changes in the transportation environment, including fuel consumptions, carbon dioxide (CO2) emissions cost and vehicles velocity, that it encourages researchers to design a near-reality and robust pollution routing problem. This paper addresses a new time window pickup-delivery pollution routing problem (TWPDPRP) to deal with uncertain input data for the first time in the literature. For this purpose, a new mixed integer linear programming (MILP) approach is presented under uncertainty by taking green house emissions into consideration. The objective of the model is to minimize not only the travel distance and number of available vehicles along with the capacity and aggregated route duration restrictions but also the amount of fuel consumptions and green house emissions along with their total costs. Moreover, a robust counterpart of the MILP is introduced by applying the recent robust optimization theory. Computational results for several test problems indicate the capability and suitability of the presented MILP model in saving costs and reducing green house gases concurrently for the TWPDPRP problem. Finally, both deterministic and robust mathematical programming are compared and contrasted by a number of nominal and realizations under these test problems to judge the robustness of the solution achieved by the presented robust optimization model.