A method for designing minimum‐cost multisource multisink network layouts

Systems engineers are equipped to design complex networked systems such as infrastructures. A key goal is cost minimization over a vast solution space. However, finding a minimum‐cost system while comprehensively satisfying different stakeholders is challenging and lacks proper methodological support. Stakeholders often employ their own expert estimations for lack of suitable decision‐support methods. In these settings, systems engineers typically require mid‐fidelity, easy‐to‐use methods. We present a rigorous method that quickly finds minimum‐cost solutions for networks with multiple sources and sinks, focusing on pipeline topology, length, and capacity. It can serve as a discussion tool in multiactor design processes, to demarcate the design space, indicate sources of uncertainty, and provoke further analyses, different designs, or contractual negotiations. It is applicable to a wide variety of cases, including many prominent infrastructures needed to mitigate CO₂. We prove that the optimal layout is a minimum‐cost Gilbert tree, and develop a heuristic based on the Gilbert‐Melzak method. We demonstrate the method's efficacy for a case set regarding solution quality, computational time, and scalability. We also show its efficiency and usefulness for systems engineers in real‐world settings. Systems engineers can use the generated cost‐optimal system designs to benchmark any design changes in real‐world negotiation processes.