Determining the Replenishment Cycle
In Chapter 3, we determined the scheduling interval and required production parts for the production process. We will refer to this cycle as the replenishment interval . It is the smallest batch size that your process can run and still keep the customer supplied. This interval essentially tells how long it takes to produce your adjusted production requirements. The replenishment interval is a function of the time available after considering your process parameter:

Production rate

Changeover times

Downtime (both planned and unplanned )
The replenishment cycle will ultimately be determined by the time left over for changeovers after subtracting required production run time from available production time. Therefore, the length of this cycle will be a function of how long it takes to "bank" enough changeover time to make all the necessary changeovers.
These production requirements also need to account for your scrap. When the required parts include the scrap, then the term becomes your "adjusted requirements." These factors determine how many days, weeks, or months of inventory you keep on hand to supply the customer(s).
If this sounds confusing, then maybe some mathematical formulas will help. We'll start with calculating the adjusted production requirements. Adjusted production requirements are the quantity of a part that you must produce to cover the order quantity plus the system scrap. Mathematically, the equation for adjusted production requirements is shown in Figure 42.
Figure 42: Equation for Adjusted Production Requirements Using the System Scrap.
For those production processes that must also account for downstream scrap (such as for inhouse customers), then this equation changes to the equation in Figure 43.
Figure 43: Equation for Adjusted Production Requirements When Scrap is Tracked as Process Scrap and Downstream Scrap.
You will need to make this calculation for each item produced by the process. By summing the adjusted production requirement for each part you will determine the total production quantity.
Note that you may not need to make the adjusted production requirements calculation if your normally scheduled quantity accounts for scrap in your production process and downstream. In fact, if this is the case, then taking the production quantities and adjusting for scrap with the equations in Figures 42 or 43 will only incorrectly increase the amount you need to produce ”i.e., by creating overproduction.
Once you know how much you have to produce, then you must determine how long it will take and how much time you have to produce it (each day, week, or month). The answers to these two questions will allow you to determine the time available for changeovers.
To determine how long it takes to produce the adjusted production requirements, you need to determine the time required for production of each part. To determine the time required for production, multiply the adjusted production requirements by the cycle time per part and sum for all the parts produced by the process. Mathematically, the equation for available time is shown in Figure 44.
Figure 44: Equation for Production Time.
Now calculate the available production time to determine how much time you have available each day to produce parts. While this may seem ridiculous since you have twentyfour hours in a day, available time refers to the time left after considering breaks, lunches, end of shift cleanup, shift starter meetings, equipment warmup, breakdowns, kaizen activities, safety activities, PM downtime, etc. It is the time left over to produce parts. Mathematically, the equation for available time is shown in Figure 45.
Figure 45: Equation for Available Time.
Typically, most production processes have from 410 to 430 minutes of available time per shift. Once calculated, available time usually becomes a production standard.
If you operate a continuous process, then the equation for available time simply considers planned downtime for preventative maintenance/cleaning activities and breakdowns. Mathematically, the equation changes to the equation shown in Figure 46.
Figure 46: Equation for Available Time in a Continuous Process.
One source of confusion when calculating available time is how to allocate the time for events that do not occur every shift, such as safety meetings, kaizen activities, or preventative maintenance. To allocate time in the daily standard, simply determine the total time taken up by these events during a week or a month and divide by the shifts in a week or a month respectively. Once you have this number, simply subtract it from the total shift time. For example, if you allocate one hour per month for a safety meeting, one hour per week for kaizen and information meetings, and two hours per month for preventive maintenance (PM), total productive maintenance (TPM), and 5s cleaning, then the shift allocations would be calculated as shown in Figure 47.
Figure 47: Allocating Improvement and Meeting Time for Available Time Calculations.
The final result of all this calculating will be the total time available for production requirements and changeovers. To determine the total time available for changeovers, subtract the time required for production from the total available. The mathematical equation is shown in Figure 48. The example in Figures 49 and 410 should clarify these calculations.
Figure 48: Equation for Time Available for Changeovers.
Figure 49: Calculating the Time Available for Changeovers for the TwoPart Number Example in Chapter 3.
Figure 410: Calculating the Time Available for Changeovers for the TenPart Number Example in Chapter 3.
Finally, you calculate the replenishment interval by determining the total time required for changeovers and dividing this number by the time available for changeovers. Mathematically, the equation is shown in Figure 411.
Figure 411: Equation for Replenishment Interval.
Taking our Figures 49 and 410 examples further, you can calculate the replenishment intervals for both production processes. Figures 412 and 413 show these calculations.
Figure 412: Calculation of Replenishment Interval for the TwoPart Number Example.
Figure 413: Calculation of Replenishment Interval for the TenPart Number Example.
Once you have the replenishment interval and lead times established, you multiply these numbers by the adjusted production interval requirements to determine the maximum number of parts in the kanban.
To determine the number of containers in the kanban, just divide the maximum kanban quantities by each part's container capacity. The container capacity will become the smallest unit of each part that you will produce. The total number of the containers then becomes the basis for determining the scheduling level and danger level.
Essentially, you will not receive a scheduling signal until the customer uses the replenishment interval quantity. (This quantity becomes the "green" level.) You then produce parts until you reach the part's maximum quantity. These assumptions should be tailored by the size of the kanban and specifics of your process. However, the fundamental rules of kanbans must be followed:

Nothing is produced without a scheduling signal

Production stops when no more signals exist