## 3 Method
### Determine Buffer Time of Bottleneck Activities
[PERSON] [47] and [PERSON] [44] pointed out three buffer times in manufacturing system constraint buffer, assembly buffer and shipping buffer. The buffer time would be reduced if the operation completion time exceeds predetermined. If the activities can be done as expected and made no idle time in the following activities, it would be helpful to the project managers to arrange as well as the capital input and use of project resources. Additionally, on the other hand, the occurrence of risk has probably a negative impact on the completion as expected of the project. Therefore, impact caused by risk exists in between pessimistic completion time and expected completion time of the activity. Therefore, the buffer time can be calculated according to the following Equations (1)-(3). \[CB_{c}=\frac{T_{cb}-T_{ce}}{2},c\in S_{CB} \tag{1}\]  
\[AB_{a}=\frac{T_{ab}-T_{ae}}{2},a\in S_{AB} \tag{2}\]  
\[SB_{s}=\frac{T_{sb}-T_{se}}{2},a\in S_{SB} \tag{3}\]  
where  
\(CB_{c}=\) Constraint buffer (CB) time;  
\(AB_{a}=\) Assembly buffer (AB) time;  
\(SB_{s}=\) Shipping buffer (SB) time;  
\(T_{cb}=\) Pessimistic duration all predecessor activities of constraint buffer;  
\(T_{ce}=\) Expected duration of all predecessor activities of constraint buffer;  
\(T_{ab}=\) Pessimistic duration of all predecessor activities of assembly buffer;  
\(T_{ae}=\) Expected duration of all predecessor activities of assembly buffer;  
\(T_{sb}=\) Pessimistic duration of all predecessor activities of shipping buffer;  
\(T_{se}=\) Expected duration of all predecessor activities of shipping buffer;  
\(S_{CB}=\) Set of predecessor activities of constraint buffer;  
\(S_{AB}=\) Set of predecessor activities assembly buffer;  
\(S_{SB}=\) Set of predecessor activities shipping buffer. Constraint buffer (CB) is a set before the bottleneck operation activities. The purpose is to provide a protective effect produced by the bottleneck, so that the bottleneck resource can reach the goal of predetermined output in terms of progress schedule.The bottleneck buffer must be placed in front of the critical path activity to minimize the resource limit and maximize the duration reliability [15]. Assembly buffer (AB) ensures that the bottleneck is not delayed by postponement of other activities when it is formed by joining componentstogether. The PERT and CPM have a confluence of activities that give rise to duration variation, resulting in an increase in project duration uncertainty. AB is therefore added to the assembly node where the bottleneck and non-bottleneck are merged. Shipping buffer (SB) is established in the product shipping area and aimed to protect production to satisfy the order delivery date, in order to prevent the influence of uncertain factors in the production process that may delay the project delivery date. The traditional production process in the CPM or PERT scheduling belongs to the push system. Once the bottleneck duration is extended, the postponed duration causes a breach of the contract, which is why the shipping buffer occurs after a bottleneck. The measurements of three buffer times are similar, but have different numbers of predecessor activities of bottleneck, so the buffer time varies. Equations (4)-(6) distribute each activity buffer time in accordance with the ratios of expected duration of predecessor activity of the buffer to expected project duration.