NP-hardness proof for the assembly problem with stationary setup and additive holding costs

In this paper we answer a long-standing open question regarding the computational complexity of one of the core problems in inventory management, the assembly problem. In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NPNP-hard, this fundamental question was left unanswered. In this paper, we provide a proof that the problem is indeed NPNP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.