I agree 100% with Lawrence’s recommendations of using a ROP technique, estimating an EOQ, tracking actual stockouts and doing what you can to minimize daily demand variation.

Let’s see if I’ve properly understood your posts so far:
• Lead time = 1 day (24 hours from replenishment signal to replenishment).
• Replenishment interval = your choice; maximum (ROP + ROQ) is limited by dispensing-machine capacity, minimum can be as little as 1 day.
• Target service level = 95% = 1.645 z-value

Perhaps I could ask several more questions about your situation:
• Does each of the 25 dispensing machines hold all 400 different items? Or, does each dispensing machine hold about 16 items, so that 16 * 25 = 400?
• How often do you want the pharmacy to make a replenishment visit to each of the 25 dispensing machines (once per day, twice per week, etc.)?
• Do you have cost estimates for pharmacy replenishment? Cost per trip to the facility that has the 25 dispensing machines? Cost per trip to a dispensing machine? Cost per replenishment of each item in a dispensing machine?
• Is your week (and the pharmacy’s week) a 7-day week?
• Does the pharmacy always replenish within 24 hours? Or is this an expedite-only lead time? If so, what’s the non-expedite lead time?
• What happens during the 5% of the time when a drug is not available for a nurse? Does the drug get expedited immediately?

FYI – with daily average demand = 3.67, and std dev = 3.74, your example item definitely does not have a normal distribution of demand. Instead, it is doubtless right-skewed, and its demand is probably sporadic (some days have no demand). This is important, because your z-value service-level multiplier assumes a normal distribution. When you use a normality-based z-value with a distribution that is right-skewed, you run the risk of substantially understating the safety stock that’s included in the kanban or ROP calculation.

I’ve made some uneducated (and probably wrong) guesses about your example item’s demand distribution, and some other (probably wrong) assumptions, just for the sake of illustration. I ran my guesses through our proprietary safety-stock model, and came up with these example results for your item with average demand = 3.67 and std dev = 3.74:
Replenish once every 14 days: ROP = 53, ROQ = 53, Safety Stock = 0, Avg Qty On Hand = 28.0
Replenish once every 7 days: ROP = 27, ROQ = 27, SS = 0, AQOH = 16.6
Replenish twice per week: ROP = 14, ROQ = 14, SS = 0, AQOH = 11.9
Replenish once every two days: ROP = 10, ROQ = 8, SS = 2, AQOH = 10.7
Replenish once per day: ROP = 12, ROQ = 4, SS = 8, AQOH = 10.7

Notice that with the longer replenishment intervals, ROP = ROQ. This is because the ROQ itself is providing “de facto” safety stock that achieves the 95% target service level with 95% confidence, without additional calculated safety stock in the ROP.

As replenishment interval (RI) gets smaller, two days or less in this example, ROP > ROQ. This is because the ROQ does not provide sufficient “de facto” safety stock, so the ROP must include additional calculated safety stock.

The “de facto” safety stock provided by larger ROQs is not efficient, in terms of inventory performance. That’s why AQOH drops significantly from the 14-day RI to the 7-day RI, and somewhat less significantly from the 7-day to the 3.5-day. However, from the 3.5-day RI to the 2-day RI, AQOH drops very little, and it doesn’t drop at all from the 2-day RI to the 1-day RI. This supports your intuitive conclusion that there’s no value in replenishing every item every day. These AQOH values are an important component of an EOQ calculation.

I’ll be happy to perform our correct, comprehensive safety-stock analysis on up to 30 of your items as a free trial, just as I’ve offered at http://www.resourcesystemsconsulting.com/blog/blog (about the third posting down from the top). Feel free to contact me at http://www.topdownleansystems.com/contact.php.

Also emphasizing Lawrence’s suggestion, you may also be able to correlate demand to predictive factors such as flu season, etc., and adjust ROPs and ROQs accordingly. The more you can do this, the less you need to depend on a static safety-stock level (whether calculated or “de facto”) to achieve your target service level.

David McPhetrige, TopDown Lean Systems

You might also look at why your standard deviation is so high and if there is anything you can do to dampen or level load. As a rule of thumb I generally avoid kanban when Cv > 1.0 where the Coefficient of Variation is the standard deviation divided by the mean (or average).

Also, demand can change over time, so you will want to regularly recalculate your order points and order quantities.

Good luck!

thoughts?

again thanks for the help!

Perhaps rather than kanban you need to figure out a reorder point, or as you call it “low stock level”. If restocking is truly only 24 hours from warning system alert then you would set your reorder point at AD + (SF* SD) or (3.67 + (1.65 * 3.74)), or 9.84 or rounded up to 10. When stock in the machine falls to 10 you order more.

How much more? Two weeks worth, or something less? You can look into Economic Order Quantity to optimize inventory carrying cost, order filling cost, and service level. Or you can use a fixed order quantity with kanban, but you need to rethink the bin quantity of 50, which I suppose is the quantity that your machine will hold?

Also as far as your math goes – your bin quantity of 50 is a variable not a constant! You can make the bin quantity (or what I call Standard Container Quantity any number you want.

So OK, lets do some math … # Kanban = ((AD * R) + (SF * SD))/ SCQ

#K = ((3.67 * 1) + (1.65 * 3.74))/50
#K = 0.19 which doesn’t make sense. If you change SCQ to say 5 then the number of kanban you need is 1.968.

You certain your replenishment time is 24 hours?

This is great information … however I seem to be getting stuck on symantics. I tend to use the formula with standard deviation. If I have an average daily usage of 3.67 parts, a standard deviation of 3.74, a 24 hour replenishment time, and I want to use a z factor of 1.645 … I seem to be getting a kanban of 9.8. The bin can hold 50 parts, but I do not think it makes since to put 50 parts into the bin and my supply can supply whatever quantity I ask for. So how can I tell what my reorder point and quantity should be?

Equation I use:

Number of Kanban = ((Average Daily Demand * Replenishment Time) + Safety Stock)/Standard Container Quantity

So #Kanban = ((2000 * Replenishment Time) + 100)/100