# A New Self-Balancing Assembly Line Based on Collaborative Ant Behavior
## 1 Introduction  
A common assembly system consists of \(m\) workers (or workstations) arranged along a production line. The components are fed into the line and progressively assembled as they move down from station to station. At a workstation \(k\) (\(=\) 1,..., \(m\)), a worker performs a set of assembly tasks, \(S_{k}\), repeatedly. It takes station time, \(t(S_{k})~{}=~{}\sum_{j\in S_{k}}t_{j}\) to complete all the tasks assigned to workstation \(k\) where \(t_{j}\) is the assembly time for task \(j\) (=1,..., \(n\)). The cycle time, \(c\), of the assembly line is determined by a bottleneck station whose station time is the largest, i.e., \(c~{}=~{}max_{k}~{}t(S_{k})\). The capacity of the assembly line is 1/\(c\). When an assembly line is operated in a full capacity, station \(k\) with \(t(S_{k})\) < c has an idle time of \(c-t(S_{k})\) in each production cycle. Line balance efficiency \(E\) is defined by \(E~{}=~{}\frac{T}{mc}\) where \(T~{}=~{}\sum t_{j}\). The assembly lines are widely employed in various industries for the production of standardized products. One of the important decisions in the assembly line involves the work assignment regarding how much work to assign to each worker. Decisions about assembly task assignments are made through assembly line balancing (ALB) techniques whose key objective is to obtain a balanced assembly line by assigning assembly tasks to each worker as evenly as possible. The existing studies on ALB problems are well summarized in survey papers [1; 2; 3; 4]. Most existing studies on ALB problems deal with a static line-balancing solution with which the workers perform a pre-assigned set of assembly tasks from cycle to cycle. In general, the ALB decisions are made at the early stage of the assembly line design process in which assembly time for an individual task is assumed to be constant. However, the real industrial environment is often different from the situations on which the ALB decisions are based. Manufacturing systems undergo various types of uncertainties including a machine breakdown, different workerskills, rework requirements, and quality problems. With the uncertainties, the assembly time fluctuates over time so that the assembly lines often fail to achieve the performance as expected [5]. When a new product is introduced, which frequently happens in today's fast-moving market, the assembly systems should be reconfigured. The frequent reconfiguration results in low performance in the traditional assembly line with a static task assignment. Moreover, it is common that the workers have different work speeds and each worker cannot perform assembly tasks at a constant speed throughout a day. When uncertainties are common, it has become more important for production systems to have the flexibility to respond quickly to uncertainties. Assembly cells have been introduced to solve these problems of assembly lines (e.g., [6; 7; 8; 9]). A long assembly line is reconfigured into several small assembly cells in each of which a small number of workers (or a single worker in an extreme case) perform the entire range of assembly tasks for a final product. The assembly cells are now widely implemented in industries because they provide better manufacturing performance than traditional assembly lines in terms of productivity, product quality, and customer responsiveness. However, the assembly cell still has a workload balancing problem, especially under system uncertainty. To solve the balancing problems associated with static task assignments, a new assembly line control method has been introduced where the idea of a bucket brigade (BB) is used as control logic in assembly lines [10; 11; 12; 13; 14]. The BB-based assembly cell imitates a cooperative behavior of ants in nature, as shown in Figure 1a. When some ant colonies find a large amount of food in one place, they move the food items to their nest in a collaborative way as follows [15]: An ant carries her food item along the trail.