Replenishment lead time in retail

Raj Govindarajan asked the following question:

Your blog on Safety Stock Formula was very fascinating. I work in a Retail company and I am trying to apply the safety stock formula to the retail environment. Is it fair to consider “Replenishment Intervals” as “Lead Time”? In other words, for example, I have a lead time of 7 days, but I order every day to the store; so should I consider demand variability for 7 days or 1 day?

As you may recall, I am advocating wariness in applying the formula. If you are ordering every day for delivery 7 days later, you are not using the reorder point logic the safety stock formula is based on. With a reorder point, you are only placing an order when your stock crosses a threshold, and the stock on hand at that time is supposed to carry you until the order is delivered.

The question you are faced with, for each item, is “How much do I need to order today to make sure I don’t run out 7 days from now?”  The elements you have to make that decision are as follow:

  1. The quantity on hand you have today. 
  2. The already ordered quantities that will be delivered in the next six days.
  3. Your sales forecast, with confidence interval, for the next seven days.

The tricky part is the sales forecast. The safety stock formula assumes a consumption rate that fluctuates around a constant mean. This may not fit your products. To check it out, you need to analyze sales history. Cell phones and artichokes are both retail products, but with different demand structures.

For your products, you need to know whether they are on a trend that is long-term compared to 7 days, and which kind of trend. In addition, is there a weekly pattern in sales? Do your products sell more, or less, on week-ends? Data mining on your sales history can give you the minimum on hand you can expect at the end of six days and the quantity you need to receive on the seventh to avoid running out.

And you have to keep in mind that these calculations are only valid in the absence of earthquakes, hurricanes, stock market crashes, wars breaking out, new product introductions, or any other event that can severs the connection between historical data and the near future.

Supermarket sizing

Bosch’s Taojie Hua (涛杰 华) asked the following question:

How do you define a maximum limit for a supermarket?
Especially when the customer withdraws less than planned, and the lot can not be formed as a production signal, how can I react to that “deviation” by setting a proper max limit?

The response covers the following topics:

Supermarkets in Lean

First we have to clarify what we mean by a supermarket in a Lean manufacturing context. As the term has become popular, some plants have started using it for their warehouses, which is clearly excessive. Often, it is used for any kind of buffer on the shop floor, provided it is used to implement pull. I prefer to reserve the term for buffers from which users withdraw items in smaller quantities than are brought in. If pallets come in and go out, I don’t call it a supermarket, but, if 27-bin pallets come in and withdrawals take place 1 bin at a time, I do.

On a shop floor, supermarkets are found on the edges of manufacturing islands containing a group of cells or a production line and contain either incoming or outgoing materials.  A supermarket for incoming materials has more in common with the refrigerator in your kitchen than with the supermarket you buy groceries in. You need one when your plant Materials or Logistics organization is unable to deliver materials in a form that is suitable for direct use at a production work station.

Water spider at Solectron in  Mexico (2005)

Water spider at Solectron in Mexico (2005)

The supermarket is owned by Production, and more specifically by the first-line manager in charge of the cells or lines it serves. It is replenished  by  Materials or Logistics through periodic milk runs, but parts are withdrawn by experienced members of the production team — cell leaders or water spiders — and move from the supermarket to production on hand carts, gravity flow racks, or by hand. The parts arrive in the supermarkets in bins that are too large for the line side, and leave in kit trays, small bins, or single units.

You need a supermarket for outgoing materials when your production runs are multiples of the quantities needed downstream. This happens, for example, if you only know how to paint parts in batches of 50 with the same color, while assembly alternates colors one unit at a time. In outgoing supermarkets, materials are replenished by Production and withdrawn by Materials/Logistics.

Supermarket capacity

For incoming supermarkets, replenishment by milk runs is essential because it makes lead times predictable. I am assuming here that the upstream supply chain does not cause shortages. Making it work is no small feat, but this question is specifically on supermarkets. On the withdrawal side, you want to have the smoothest possible consumption rate for all items, so that you don’t have large ups and downs to contend with, which you achieve with  heijunka (平準化)  sequencing of production. Little’s Law then tell you that you have, for means:

\overline{Quantity\, on\, hand}\left ( Item \right )= \overline{Consumption\, rate}\left ( Item \right )\times \overline{Replenishment\, lead\, time}\left ( Item \right )

If you take the minimum quantity that Materials can deliver to the supermarket, on the average the Quantity on hand will be half of it. You know the Consumption Rate.  The Replenishment lead time is a multiple of the milk run pitch, plus the time needed for Materials to act on the pull signal, which depends on when the need is identified and how the signal is passed to Materials.

Assume you consume 1 unit every 25 seconds, the milk run pitch is 30 minutes, and Materials delivers in bins of 100 units. You consume 72 parts/pitch = 0.72 bins/pitch. If the milk runs are used to convey pull signals, as happens with the two-bin system or with hardcopy kanbans, replenishment may take up to 2 pitches. In this example, the 2-bin system would cause shortages, but a Kanban loop with two cards wouldn’t, because you pull the card when you withdraw the first unit from the bin and it is still 99% full. If, instead of using cards, you issue an electronic signal when you withdraw the first unit, Materials can act on it in the next milk run, meaning at most 1 pitch later. You still need room for two bins, because the current bin will still hold at least 28 parts when the replacement bin arrives.

In this example, the mismatch between the size of the delivered bins and the consumption rate forces you to hold enough excess material that you don’t need to worry about safety stocks. If it were instead perfectly matched, you could receive a bin of 72 parts like clockwork every 30 minutes, except that fluctuations in consumption occasionally would cause shortages, and you would need some safety stock to protect yourself against it.  Coming up with a sensible plan for any one item in your supermarket is not a major task, but you need such a plan for every item.

The speed with which signals circulate adjusts itself with fluctuations in consumption. The real question is whether your “customer withdrawing less than planned” should be treated as a fluctuation or a permanent drop. In the first case, there is no action required; in the second, you need to recalculate.  In any case, you need to periodically validate the parameters of your pull system to make sure they still reflect reality. In auto parts, it should be done at least quarterly.

Further reading

For details on pull systems, see Lean Logistics, Part IV, pp. 197-330. See also the two posts on Safety Stocks: Beware of Formulas and Safety Stocks: More about the formula.