Safety Stock Simulation
When the Formula Is Enough, and When to Run It Over Time

The safety stock formula is a good first answer for one item at one site. It gets less reliable as lead times vary, demand gets lumpy and stock sits at more than one tier. Simulation takes over where the formula’s assumptions stop holding.

The formula and what it assumes

The textbook formula sets safety stock from demand variation over the lead time:

SS = z · σd · √L

Here z comes from the service level you want, σd is the standard deviation of daily demand, and L is the lead time in days. A version with variable lead time adds a second term for lead-time spread. Both rest on the same assumptions:

• demand is roughly normal and independent from one day to the next;
• the lead time is known, or varies in a simple, stable way;
• the site reorders continuously, the moment stock crosses its order point;
• the site stands alone, with a supplier that always has stock.

For a steady item at a single site those are fair, and the formula is quick and good enough.

Where the formula breaks down

Lumpy or seasonal demand

A few large orders, a promotion or a season don’t look like a normal curve. The formula sizes stock for an average week and misses the week that matters.

Review periods and order sizes

Most sites review stock weekly or on a schedule, and order in cases, pallets or full trucks. Stock can fall well below the order point before anyone looks, and a big order quantity changes how often the site is exposed at all.

More than one tier

A regional DC’s lead time depends on whether the central DC has stock when it orders. If the central DC runs short, every DC below it waits longer. The formula treats each site on its own and can’t see that chain.

Plant, central DC or regional DC?

The biggest safety stock decision in a network is often where to hold it, not how much. Holding it upstream, at the plant or a central DC, pools variation. A slow week in one region and a busy week in another partly cancel out, so one pooled buffer can be smaller than the sum of several. Holding it downstream puts stock next to customers and cuts the time to recover from a surprise, but each site has to cover its own swings.

Multi-echelon optimization weighs those against each other across the whole network. The Safety stock demo shows saved output from one such optimizer on a three-tier US network: a plant, a central DC and three regional DCs, with three products. In that network the optimizer holds all of the safety stock at the regional DCs and none at the plant or the central DC. The highest-value product takes the largest share of the budget. A different network, with different lead times and costs, can come out the other way.

Where to pack, and where to hold stock

Where stock sits also depends on what form it’s in. The postponement case study is a consumer goods network that asked whether to pack at the plant or at the DCs, and where cycle stock should sit. Packing downstream helped some product categories and not others, and the model separated them product by product. It’s a reminder that the answer is rarely one rule for the whole network.

Test the policy over time

An optimizer or a formula gives you a number. A simulation shows what that number does. Run the network through a year of demand with the policy in place, with real review periods, order sizes and lead-time variation, and watch stock at every site against its order point.

• Does stock at each site stay above zero through the peak, or does it drain before the replenishment lands?
• When the central DC runs low, how long do the DCs below it wait?
• Is some of the stock never touched, which means it can come down?

Run the same demand against two or three candidate policies, so the only difference between runs is the policy. The Simple supply chain demo shows what that view looks like, with stock at each location plotted against its order point through a threefold demand spike.

A practical sequence

1. Start with the formula for a first estimate by item and site.
2. Decide where stock should sit across tiers, with a multi-echelon optimizer if the network has more than one.
3. Validate the model against a period of history. How to know your supply chain model is right covers how.
4. Simulate the policy through a year that includes your worst season, and adjust where stock drains or sits idle.