The Vehicle Routing Problem (VRP) is a critical component of many logistics systems involving the routing and scheduling of vehicles from a depot to a set of customer nodes. The Vehicle Routing Problem with Time Window (VRPTW) is one of the most studied versions of VRP, in which each customer must be visited within a specific time interval known as a time window. It has previously been demonstrated that VRPTW is an NP-hard problem, which means that finding optimal solutions for large problems is computationally difficult. As a result, a number of heuristics and metaheuristics have been proposed. This study aims to develop a new relaxation scheme that loosens the constraints of the time window, resulting in a feasible and good solution. Furthermore, as an alternative model for VRPTW that is time dependent and involves multiple suppliers, this research will develop a discrete optimization model. This study will also create a metaheuristic algorithm with an initial solution defined by relaxing the time window.

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