Fuzzy Flexible Delivery and Pickup Problem with Time Windows

Recently, many enterprises have incorporated reverse logistics into conventional forward-only logistics to form a closed-loop supply chain. Within such a loop, the logistics between the distribution/collection center and the customers is the most complicated part because it is related to a bi-directional logistics for delivery and pickup activities. After investigating their uncertainty properties and complexities in finding solutions, this study, based on the fuzzy credibility theory, proposes a chance constrained programming (CCP) model to describe a fuzzy flexible delivery and pickup problem with time windows (FFDPPTW).In the meantime, some test problems are generated by revising the well-known Solomon's benchmarks which are originally used for the vehicle routing problem with time windows. Cplex software is used to try to solve these problems. Three credibility confidence levels (0.5, 0.8, and 1.0) are implemented to get different results for different types of decision makers. The preliminary results reveal the phenomenon: the higher the confidence level is required, the larger the cost is paid. This observation facilitates the decision support based on the decision maker's preference.