A multi-objective mixed integer linear programming model for supply chain planning of 3D printing

TL;DR

This paper tackles the problem of scheduling and allocating parts to multiple identical 3D printers under two competing goals: minimize delivery earliness and tardiness and maximize printer utilization, while optimizing each part's orientation (height) in the build. It introduces a multi-objective mixed-integer linear programming (MOMILP) model and employs the epsilon-constraint method to generate Pareto fronts, along with a linearization scheme to keep the model tractable. A numerical example with two printers and nine parts demonstrates a clear trade-off between area utilization and completion time and shows that allowing height-based orientation can substantially reduce lead times. The findings offer practical guidance on printer provisioning, orientation strategies, and sensitivity to process parameters, with data and code available on request.

Abstract

3D printing is considered the future of production systems and one of the physical elements of the Fourth Industrial Revolution. 3D printing will significantly impact the product lifecycle, considering cost, energy consumption, and carbon dioxide emissions, leading to the creation of sustainable production systems. Given the importance of these production systems and their effects on the quality of life for future generations, it is expected that 3D printing will soon become one of the global industry's fundamental needs. Although three decades have passed since the emergence of 3D printers, there has not yet been much research on production planning and mass production using these devices. Therefore, we aimed to identify the existing gaps in the planning of 3D printers and to propose a model for planning and scheduling these devices. In this research, several parts with different heights, areas, and volumes have been considered for allocation on identical 3D printers for various tasks. To solve this problem, a multi-objective mixed integer linear programming model has been proposed to minimize the earliness and tardiness of parts production, considering their order delivery times, and maximizing machine utilization. Additionally, a method has been proposed for the placement of parts in 3D printers, leading to the selection of the best edge as the height. Using a numerical example, we have plotted the Pareto curve obtained from solving the model using the epsilon constraint method for several parts and analyzed the impact of the method for selecting the best edge as the height, with and without considering it. Additionally, a comprehensive sensitivity and scenario analysis has been conducted to validate the results.

Figures (12)

• Figure 1: Adapted from kucukkoc2019milp, allocation of parts to 3D printers and sequencing of jobs
• Figure 2: Adapted from oh2018production, combination 1. Parts $P_2$ and $P_4$ determine the completion of the job while the other parts have been completed earlier. This can cause delays and inefficiency in the utilization of the printers.
• Figure 3: Adapted from oh2018production, combination 2. This figure demonstrates a case in which the problem mentioned in Figure \ref{['fig:2']} has been tackled by the correct combination of parts in a job.
• Figure 4: Adapted from oh2018production, part orientation
• Figure 5: Pareto Front Diagram