The location routing problem with simultaneous pickup and delivery and fuzzy time window (LRPSPDFTW) is a complex combinatorial problem with many real world applications in distribution logistics. The multi-objective LRPSPDFTW seeks to minimize total cost and maximize customers’ service level by locating the depots and designing the vehicle routes that satisfy customer’s pickup and delivery demand simultaneously. However, literature on location-routing problem addressed the location and vehicle routing decisions with a common assumption of no requirement on customer time window, though the requirement of customer time window is often more significant than the routing cost in distribution service. This paper proposes a problem formulation for the multi-objective LRPSPDFTW in which a fuzzy membership function is used to characterize customers’ satisfaction on service time. Furthermore, we proposed two heuristic approaches based on tabu search and simulated annealing respectively, in which a forwards push procedure is applied to determine the adjustment of customers’ service time. Through comparing heuristics performances on solving the medium-size problems, the experimental results demonstrate that the effectiveness and efficiency of our proposed model and algorithm in solving multi-objective LRPSPDFTW.
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