We consider the problem of consolidating compatible orders for a batch production process where its downstream process differentiates its output to yield final products that are characterized by p different attributes. In particular, we consider the case where the customer orders are considered to be compatible enough to be processed together in the same batch when their difference in each attribute is no more than a specific tolerence. In such case, the compatibility relationship among orders can be represented by the graph known as the graph with cubicity p . We show that the problem of optimizing the batch production in this case is NP-hard even when we have only two attributes. Then, we develop a simple optimal algorithm for the case with a single attribute. This result also shows, for the first time, that the K r packing is solvable in polynomial time on the graph with cubicity 1 which is also knonw as the unit interval or indifference graph.

Jae Jung Kim

Soo Young Chang

Woo-Lahm Kwak

International journal of industrial engineering

该杂志强调使用工程设计和分析，并努力保持研究和应用之间的平衡。该杂志涵盖工业工程的各个方面，特别是：数据挖掘和计算智能；生产计划与控制；运筹学；服务工程（医疗保健等）；可持续性（能源、环境等）；信息系统和技术；技术管理；制造业;工作测量、人为因素和人体工程学；质量、可靠性、维修工程；供应链管理;物流和物料搬运；产品设计与开发；统计分析;建模与仿真；国土安全（国防、防灾等）

The journal emphasizes the application of engineering design and analysis, striving to maintain a balance between research and practice. It covers various aspects of industrial engineering, with particular focus on the following areas: data mining and computational intelligence; production planning and control; operations research; service engineering (such as healthcare); sustainability (energy, environment, etc.); information systems and technology; technology management; manufacturing; work measurement, human factors, and ergonomics; quality, reliability, and maintenance engineering; supply chain management; logistics and material handling; product design and development; statistical analysis; modeling and simulation; and homeland security (defense, disaster prevention, etc.).

该杂志强调工程设计与分析的应用，并致力于研究与实践之间的平衡。它涵盖了工业工程的各个方面，特别关注以下领域：数据挖掘与计算智能、生产计划与控制、运筹学、服务工程（如医疗保健）、可持续性（包括能源与环境）、信息系统与技术、技术管理、制造业、工作测量、人因工程与人体工程学、质量、可靠性与维修工程、供应链管理、物流与物料搬运、产品设计与开发、统计分析、建模与仿真，以及国土安全（如国防与防灾）。

Category	Quartile
工程技术	4
工程技术, 工程工业	4
工程技术, 工程制造	4

ORDER CONSOLIDATION PROBLEM ON GRAPHS WITH CUBICITY P

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info

Category	Quartile
ENGINEERING, MANUFACTURING	4