# Buffer Allocation via Bottleneck-Based Variable Neighborhood Search
## 1 Introduction
Search methods select suitable locations to allocate buffers using some guide information. Their main disadvantage is that it is extremely difficult to achieve a balance between solution quality and computation time for different production line topologies. Some previous studies [16; 17; 18; 19; 20] achieved buffer allocation based on search methods. Specific parameters are used to rapidly determine suitable locations for buffer allocation. However, these methods are applicable to limited production line topologies such as serial topologies. Other studies [5; 6] focused on various production line topologies and proposed buffer allocation approaches with effective guide information to allocate buffers. However, the computation time needs to be further decreased under the constraint of solution quality requirements if such approaches are to be used for efficient buffer allocation. Although previous studies achieved buffer allocation with high solution quality, a long computation time is usually required to achieve the high solution quality, which does not meet computation time requirements of efficient buffer allocation. Hence, there is a need for a buffer allocation approach that can rapidly allocate buffers to the production line with acceptable solution quality. The objective of this study is to develop an efficient buffer allocation approach that achieves a good balance between solution quality and computation time. The solution quality of the buffer allocation should be higher than previous methods in available computation time. Furthermore, from the perspective of industry practical application, the proposed approach can be applied to a production line with 50 buffers and servers, which can be regarded as a large-scale production line; the available computation time of buffer allocation for this production line typically lies within 8 h.  
In the study, a throughput calculation approach that can yield the state probability of a production line is adopted to evaluate the effectiveness of candidate buffer allocation solutions efficiently. The bottleneck-based variable neighborhood search algorithm is proposed to generate the candidate buffer allocation solutions efficiently. Based on state probability, the active probability index as a bottleneck indicator is proposed to search suitable buffer updating locations, which facilitates efficient buffer allocation by decreasing invalid buffer allocation attempts. Moreover, the variable neighborhood search algorithm is used to maintain acceptable solution quality using a proper additional neighborhood structure in the case no satisfactory solution is generated in the initial neighborhood structure. Finally, numerical examples are provided to evaluate the effectiveness of the proposed approach for a production line with a different topology and topology scale. The remainder of this article is organized as follows. Section 2 presents the problem statement. The solution methodology is described in Section 3. Section 4 provides numerical examples to verify the effectiveness of the proposed solution methodology. The article ends with some conclusions and the scope for future work, in Section 5.