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We study a new variant of the vehicle routing problem, called the Mobile Production Vehicle Routing Problem (MoP-VRP). In this problem, vehicles are equipped with 3D printers, and production takes place on the way to the customer. The objective is to minimize the weighted cost incurred by travel and delay of service. We formulate a Mixed Integer Programming (MIP) model and develop an Adaptive Large Neighbourhood Search (ALNS) heuristic for this problem. To show the advantage of mobile production, we compare the problem with the Central Production Vehicle Routing Problem (CP-VRP), where production takes place in a central depot. We also propose an efficient ALNS for the CP-VRP. We generate benchmark instances based on Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances, and realistic instances based on real-life data provided by the Danish Company 3D Printhuset. Overall, the proposed ALNS for both problems are efficient, and we solve instances up to 200 customers within a short computational time. We test different scenarios with varying numbers of machines in each vehicle, as well as different production time. The results show that these are the key factors that influence travel and delay costs. The key advantage of mobile production is flexibility: it can shorten the time span from the start of production to the delivery of products, and at the same time lower delivery costs. Moreover, long-term cost estimations show that this technology has low operation costs and thus is feasible in real life practice.