This research presents an extension of the Vehicle vehicle Routing routing Problem problem with Time time Wwindows (VRPTW), namely,called the path covering problem with time windows (PCPTW). In order to be more applicable in a real-world setting, this research presents a problem that always has been faced by a many company companies which that does not have their own a vehicle at allfleet, or do not have enough vehicles its feel is inappropriate or inadequate to satisfy the demand. and have to be delivered in relatively short times to a set of customers. PCPTW is NP-hard since its variant of the well-known VRPTW is NP-hardvehicle routing problem with time windows. Thus, this research formulated a mathematical models for PCPTW and , performed a numerical study usinged CPLEX to solve small and largePCPTW benchmark instances. In addition, this study and developed a simulated annealing with restart strategy (SA_RS) algorithm to solving large PCPTW instances, which that are generated from Solomon’s VRPTW benchmark instances. At the end, this research cComputational result shows that the proposed SA_RS performed performs well on solving PCPTW.

This research presents an extension of the Vehicle vehicle Routing routing Problem problem with Time time Wwindows (VRPTW), namely,called the path covering problem with time windows (PCPTW). In order to be more applicable in a real-world setting, this research presents a problem that always has been faced by a many company companies which that does not have their own a vehicle at allfleet, or do not have enough vehicles its feel is inappropriate or inadequate to satisfy the demand. and have to be delivered in relatively short times to a set of customers. PCPTW is NP-hard since its variant of the well-known VRPTW is NP-hardvehicle routing problem with time windows. Thus, this research formulated a mathematical models for PCPTW and , performed a numerical study usinged CPLEX to solve small and largePCPTW benchmark instances. In addition, this study and developed a simulated annealing with restart strategy (SA_RS) algorithm to solving large PCPTW instances, which that are generated from Solomon’s VRPTW benchmark instances. At the end, this research cComputational result shows that the proposed SA_RS performed performs well on solving PCPTW.

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