Simultaneous Production and Transportation Problem: A Case of Additive Manufacturing

Additive manufacturing (AM) promises considerable advantages over conventional manufacturing to meet the growing demand for customized products and faster delivery times. Consider a mobile mini-factory, that is, a vehicle equipped with an AM facility, which can simultaneously produce and transport the final products to the customers. The overlapping of production and transportation processes allows potential savings on customer delivery lead times and inventory holding costs, thereby facilitating on-demand fulfillment of the orders of intricate products. Based on this situation and motivated by a recent Amazon patent, we introduce a novel routing optimization problem called Simultaneous Production and Transportation Problem (SPTP) in this study. Given a set of customers and their respective orders with associated production time and delivery due dates, SPTP minimizes the trip time for the AM installed vehicle while meeting the customers’ stipulated due dates for all deliveries. We formulate the problem using a mixed integer linear program, discuss several valid inequalities to strengthen the formulation, and discuss a cutting-plane-based exact solution approach. We also design a variable neighborhood search metaheuristic to solve larger instances of SPTP very efficiently. The effectiveness of the exact and heuristic solution approaches is demonstrated using extensive computational experiments. The study also explores the interaction between production and travel times in SPTP and how the problem compares with the traveling salesman problem and the single machine scheduling problem, each of which may be viewed as special cases of SPTP. Further, the problem involves a trade-off between the total trip time and the tardiness of the deliveries. Therefore, an extension of the proposed formulation is also proposed with interesting managerial insights on identifying appropriate trip time-tardiness combinations using an illustrative example.