443. Base Stock

443.1. (S−1, S) Policy — base stock / one-for-one

The simplest continuous-review policy: every consumed unit triggers an immediate replenishment of one unit. Sometimes called the base-stock policy.

Decision rule: maintain inventory position at exactly . As soon as one unit is sold, place an order for one unit.

Equivalently: trigger an order at (whenever inventory dips below ). Hence the name.

Single parameter:

• = base-stock level (the only decision)

443.1.1. When does this make sense?

Use base-stock when fixed ordering cost is negligible (or items are too critical to risk by batching):

• Spare parts and critical components: stockouts are catastrophic, individual items are cheap to order.
• High-value, low-volume items: holding cost dominates; ordering one-at-a-time is fine.
• Vendor-managed inventory with continuous data exchange: ordering happens automatically per consumption.

Don’t use base-stock if you have meaningful per-order setup costs — the EOQ logic says batch up.

443.1.2. Inventory position vs. on-hand

In (S−1, S):

• Inventory position = on-hand + on-order = always (just before each consumption).
• On-hand = .
• An outstanding order is one consumed within the past time units that hasn’t yet arrived.

If demand during lead time is , outstanding orders just before the next consumption is exactly . So:

Stockouts occur when .

443.1.3. Set — Newsvendor style

Choose to balance holding cost vs. shortage cost.

For Poisson lead-time demand :

Critical ratio: where is shortage cost per unit, is holding cost per unit per cycle.

For a cycle service-level requirement (probability of no stockout in lead time = ):

For Poisson: , so .

443.1.4. Average inventory

Steady-state expected on-hand:

where is the standard normal loss function (see [expected_profit.typ](../newsvendor/expected_profit.typ)).

Annual holding cost: .

443.1.5. Final formulas