Generally, the product’s turn ratio (TR) is applied to the look-ahead function of the arrival time of the WIP. Nonetheless, the conditions in the factory are changing quickly and the cycle time of product’s step is varied, TR value of the product will be changed with the environment and different in every stage of product. Thus, the concept of dynamic cycle time of product step instead of TR is applied to estimate the arrival time of lot in front of cluster tool to increase the accuracy of scheduling result. Because the data is applied for the short-term scheduling only, to consider the upcoming WIP within 3 h will be satisfactory. Afterwards, the cycle time data needed to estimate the arrival time of lot will be about four steps prior to cluster tool. The cycle time of product steps include queue time and processing time eventually. The processing time is constant for each product step, but the queue time is varied by shop floor status. It exposes the importance of dynamic queue time for the accurate scheduling results. The following is the calculation and monitoring procedure of product step’s queue time.
3.1.1. Step 1. Decide the Time Span (TS) of the Data Required to Calculate the Queue Time of Equipment
Generally, the long-range and steady-state historical data is used to calculate the product’s cycle time data for long-term planning. Nevertheless, if there is a significant difference between the future product portfolio and the past’s or the shop floor status fiercely changed, it is recommended to build a simulation system or use other mathematical models to calculate the queue time of each machine. As for short-term planning, the entire production system should not be far away from the situation compares to the past few days, so it is feasible to use the recently historical data to calculate the queue time data. As the situation of shop floor is not static, the queue time of WIP will also be changed since the condition of the machine, distribution of WIP, and combination of product released are changing every single day. For short-term planning or scheduling, the accuracy of any data will seriously affect results, and cycle time is of course no exception. Therefore, in the short-term planning, the time range of the information required for the cycle time of product should not be too long, otherwise the on-site situation will be covered by the long-term trend. On the other hand, if the time span is too short, just as short as half hour, the data will also generate some bias. Therefore, it is usually recommended to calculate the queue time data based on 3–7 days.
3.1.2. Step 2. Calculate Queue Time of Equipment
The time of a job is made to wait before processing is called queue time [
27]. As mentioned in step 1, the queue time data within 3–7 days will be taken to calculate their average and standard deviation. The equations are as follows:
where,
: average queue time of workstation i within time span TS,
: queue time of lot l in workstation i at day d,
: standard deviation of queue time in workstation i within time span TS,
: the time span of queue time calculation (day).
3.1.3. Step 3. Monitor and Amend the Queue Time of Equipment
Generally, the short-term planning requires more accurate data to insure the validity of result. Although the queue time data is already a lagging indicator, it is still hoped that it will not be too far from the current and future factory conditions. Accordingly, the effectiveness of the queue time data will be monitored with the concept of a control chart. The module will set the queue time of the machine to be calculated every three hours to simplify the calculation.
As for the control chart, the average queue time in the time span TS is the center line, and the average queue time plus or minus n times of standard deviations is regarded as the upper and lower limits of the control chart. The value of n is determined by the user. In general, 3 standard deviations are used. However, if the user wants more strict control, 2 standard deviations can be used as the limit as well. When the control chart is built, the average queue time calculated every three hours can be put into the control chart to trace whether the on-site conditions are still within a tolerable range of difference. Once the average queue time within 3 h exceeds the limit range, it should go back to step 2 to recalculate the average queue time within time span TS for scheduling.
With the usable cycle time data, the WIP arrival time estimation can be estimated according to the following formula before scheduling, associates with exact date and time. The formula is as follows:
where,
,
where,
: the time of WIP w will arrive to workstation i,
: current time,
: average queue time of workstation i where WIP w at the step sk,
: processing time of WIP w at the step sk,
: the step processed on workstation i,
: current step of WIP w,
: a set of WIP where will within the next 4 steps of this WIP.
In addition, some WIPs will have the time constraint concern, including single time constraint (single TC) and time constraint loop (TC loop). The single TC means that the time constraint starts at the lot arriving the cluster tool and ends at the lot processed. TC loop stands for the time constraint covers a process segment. Due to the time constraint being covered between a process segment, the quota of time constraint can be allocated to use in the cluster tool portion which should be calculated in advance. Generally, the time constraint quota of each workstation in the loop is allocated by the ratio of its standard cycle time. A lot may be with single TC and TC loop simultaneously, these two kinds of TC will be combined and taken the small one as the only TC of this lot to increase the scheduling efficiency. The formulas of TC calculation are as follows:
where,
: remaining queue time limit of WIP w at workstation i,
: remaining queue time limit of WIP w which belongs to single TC at workstation i,
: remaining queue time limit of WIP w which belongs to TC loop at workstation i,
: single TC of WIP w at workstation i,
: TC loop of WIP w at workstation i,
: current queue time of WIP w at workstation i,
: remaining queue time limit of WIP w which belongs to TC loop,
: standard cycle time of WIP w at workstation i,
: the end workstation of TC loop.
Based on the algorithm, the flowchart of WIP arrival time estimation is showed as
Figure 2.