An effective hybrid meta-heuristic method for the simultaneous batch production and transportation problem in additive manufacturing

One notable advancement in additive manufacturing (AM) is the mobile mini-factory, which uses a truck equipped with an AM machine to produce orders while en-route to customers' locations. This offers potential benefits such as reduced delivery times and storage expenses for companies. This study investigates a simultaneous batch production and transportation problem (denoted by SBPTP) in additive manufacturing. To solve this problem, a mixed integer linear programming (MILP) model is first formulated. Then, to solve large-scale problems, a meta-heuristic method (denoted by SA-CP) combining a simulated annealing (SA) algorithm, an ant colony optimisation algorithm (ACO) and a cutting-plane algorithm is developed, in which the assignment subproblem is dealt with the SA, the simultaneous production and transportation subproblem is dealt with the ACO, and finally the current solution is further improved by the cutting-plane algorithm. Computational experiments are conducted on both randomly generated instances and modified benchmark instances. The results demonstrate that the SA-CP is very effective since it can obtain the solutions with an average relative percentage gap 0.16% on randomly generated instances and −0.09% on modified benchmark instances within less than 180 CPU seconds, compared to those obtained by solving the MILP model directly with CPLEX within 1 h.