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Distribution & Supply Chain, as Taught by Eli Goldratt · Lesson 2 of 7

How much inventory should a point hold?

Mrs. Fernandes sells about four water heaters a week, and replenishment takes a month. Follow her through a few weeks and derive Goldratt's formula for the inventory target, then see why replenishment time is the factor that matters most, and how batching inflates it.

22 min · Not completed yet

Consumption is not enough

It seems obvious that the inventory a point holds should be proportional to its consumption. But is consumption the only factor that matters?

Mrs. Fernandes: “Customers buy about four a week, so I’ll keep four.”

First week: she sells four, and orders four more.

Second week.

Mrs. Fernandes, on the phone: “Where is my order?”

Supplier: “You know it takes a month to deliver.”

Replenishment time is as important as consumption. The longer it takes to replenish, the more inventory the point must hold.

Mrs. Fernandes: “Delivery takes a month, and I sell about sixteen a month. So I’ll order sixteen.”

Supplier: “Don’t forget, you also have to order a month in advance.”

Mrs. Fernandes: “Then I’ll order another sixteen.”

So a selling point should order to a target: consumption within the replenishment time. And the system then holds two kinds of inventory: some on the way, and some at the site.

On the way, and at the site

Replenishment time is made of three parts:

  • Order lead time: the time until an order is placed (“I’ll put in a replenishment order later…”).
  • Production lead time: processing the order, waiting in the queue to be produced, and producing it. The queue is usually the biggest part. (“If we expedite this order we can ship it in three days. But if we expedite every order, this place will be a madhouse.”)
  • Transportation lead time: moving the goods to the point of consumption.

Here is the effect of ordering more often. Instead of 16 units once a month, Mrs. Fernandes orders 4 every week.

Compare the two ways of ordering. What changes?

  • The inventory on the way
  • The inventory at the shop
  • Both

The inventory on the way is set by the forecast consumption within the supply lead time (production plus transport): 16 units either way. The inventory at the site is set by the consumption within the order lead time: up to 16 when ordering monthly, up to 4 when ordering weekly (minus what has sold). Ordering more often shortens order lead time, and that reduces the stock sitting in the shop.

Variability: be paranoid, not hysterical

Consumption varies. If Mrs. Fernandes holds exactly the average, she runs out whenever demand is above average. So she has to hold more:

To avoid shortages, order to the “maximum” forecast consumption within the average replenishment time.

“Maximum” here means paranoid, not hysterical, in proportion to the service level you need.

Replenishment time varies too. “Sorry, you didn’t specify x, y and z on your order form.” “How am I going to tell her that her order was pushed back by a more important one?” So the target must also be factored by the unreliability of the replenishment time. Again, paranoid, not hysterical.

The inventory target = “maximum” forecast consumption within the average replenishment time, factored by the unreliability of that replenishment time.

An important detail: the extra inventory added for variability, in demand or in supply, doesn’t change what is on the way. So all the safety stock ends up at the point of sale, exactly where we want it.

The key factor: replenishment time

Three parameters set the target: the level of consumption, the replenishment time, and the variability (of consumption and of replenishment time). The higher the service level, the more weight the variability carries. But replenishment time matters most, because it also acts indirectly:

  1. Forecast accuracy deteriorates with the length of time forecast, so the longer the replenishment time, the higher the variability of consumption over it.
  2. In most environments, the longer the replenishment time, the higher its variability.

Doubling the replenishment time more than doubles the inventory target.

Check yourself: Sunrise cuts the replenishment time of a product from 30 days to 15. Roughly what happens to the inventory target?

  • It halves, exactly
  • It stays the same
  • It falls by more than half

Half the time means half the average consumption to cover, and also a smaller “maximum” factor, because both the forecast and the supply are more reliable over a shorter horizon.

What inflates replenishment time? Batching

Each element of replenishment time is inflated by batching:

  • Order batching. Shops order in big lots, either because they get a discount for large quantities, or because deciding and submitting orders takes time and attention. So they wait until stock falls to a re-order point, then order an “economical order quantity”. (“Ordering one item at a time would be a waste. I prefer one big order of twenty every month.”)
  • Production batching. To look efficient by saving set-ups, the plant accumulates orders until it can run large batches.
  • Transport batching. To cut freight cost, goods wait until a full truck can be sent.

Every batch lengthens replenishment time, and so inflates the inventory needed.

An even worse effect

Long replenishment times don’t only mean high inventory. The longer the replenishment time, the slower the system reacts to actual demand, and the more its performance depends on the accuracy of the forecast. When the forecast for a product was too high, stock piles up in one place; when it was too low, it runs out in another, and the phones fill with “ship it urgently!” and hopes for a cross-shipment.

Check your understanding

Answer all five. Get four right to complete the lesson.

1. A point should order to a target of…

  • Average consumption per week
  • Consumption within the replenishment time, factored for maximum and reliability
  • Whatever the supplier suggests, based on its minimum order quantities
  • A month of sales

Replenishment time matters as much as consumption.

2. Ordering more often mainly reduces…

  • Inventory on the way
  • Production lead time
  • Transport cost
  • Inventory at the site

It shortens order lead time.

3. Safety stock added for variability ends up…

  • At the point of sale
  • On the way
  • At the plant
  • Nowhere

It doesn’t change what is in transit.

4. Doubling the replenishment time…

  • Doesn’t affect inventory
  • Exactly doubles the inventory target
  • More than doubles the inventory target
  • Halves it

Both forecast and supply get less reliable over longer horizons.

5. Which of these inflates replenishment time?

  • Daily orders
  • Waiting for a full truck
  • Small batches
  • Shorter queues

Batching in ordering, production and transport.