On the hardness of maximum lot grouping problem

최대 로트 그룹핑 문제의 복잡성

We consider the problem of grouping orders into lots. The problem is modelled by a graph G = (V, E). where each node $\nu\;\in\;V$ denotes order specification and its weight $\omega(\nu)$ the orders on hand for the specification. We ran construct a lot simply from orders or single specification For a set of nodes (specifications) $\theta\;\subseteq\;V$, if the distance or any two nodes in $\theta$ is at most d, it is also possible to make a lot using orders on the nodes. The objective is to maximize the number of lots with size exactly $\lambda$. In this paper, we prove that our problem is NP-Complete when d = 2, $\lambda\;=\;3$ and each weight is 0 or 1. Moreover, it is also shown to be NP-Complete when d = 1, $\lambda\;=\;3$ and each weight is 1, 2 or 3