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Introduction
Published in Joseph Y.-T. Leung, Handbook of SCHEDULING, 2004
[7] J.J. Hwang, Y.C. Chow, F.D. Anger, and C.Y. Lee. Scheduling precedence graphs in systems with interprocessor communication times. SIAM Journal on Computing, 18(2):244-257, April 1989.
Research on balancing and sequencing problems of flexible mixed model assembly lines with alternative precedence relations
Published in International Journal of Production Research, 2022
Yunfang Peng, Lijun Zhang, Beixin Xia, Yajuan Han
Precedence constraint which guarantees task to be performed only if all the predecessor tasks are completed is very important to balance assembly lines. Generally, a precedence graph is used to represent the precedence relations between tasks. However, when the precedence relation between tasks is optional, a single precedence graph cannot fully describe the problem. Hence, Koc, Sabuncuoglu, and Erel (2009) used an AND/OR graph, and Topaloglu, Salum, and Supciller (2012) applied If–then rules, instead of a precedence diagram to represent the process sequence. Table 1 summarises the basic alternative precedence relations which are described by different tools, including precedence graphs, AND/OR graphs, and If–then rules. When the OR relations exist, a set of alternative precedence graphs need to be listed. The number of alternative precedence graphs is increased with the number of OR relations. In the AND/OR graph, when more than two arcs are directed to the same node, a short curve connecting these arcs is added to represent the AND relation. Otherwise, the arcs without connection represent the OR relation. The different representations of ‘(1 and 2) → 6’ (AND relation) and ‘(1 or 2) → 7’ (OR relation) are shown in Table 1. However, the AND/OR graph is complicated when the number of OR relations increases. Compared with the graph-based modelling, the rule-based modelling is easier to be deduced from precedence relations. And If–then rules can be simply described by logical expression in the CP model. More complex precedence relations can be deduced from the basic relations described in Table 1.