442. Overview
442.1. Policy dimensions
Stochastic-demand inventory policies sit at the intersection of five design choices. The choices made along these dimensions name the policy.
442.1.1. 1. Inventory review
- Periodic review (R-policies): inventory checked at regular intervals . Orders are placed only at review points.
- Continuous review (s-policies): inventory monitored continuously. Orders are triggered immediately when the level falls below a threshold.
442.1.2. 2. Order quantity
- Fixed order quantity (Q): a predetermined, constant quantity is ordered each time (lot-for-lot replenishment).
- Order-up-to level (S): inventory replenished up to a pre-defined maximum , adapting to the current stock gap.
- Reorder-point shorthand (s): the trigger level — used in both Q-style and S-style policies.
442.1.3. 3. Flexibility
- Q-policies: rigid — order size is always the same.
- S-policies: responsive — order size adapts to the actual inventory level.
442.1.4. 4. Lead time
- Constant: time between placing an order and receiving it is fixed.
- Variable: lead time fluctuates, requiring extra safety stock (see [stocks/safety_stock.typ](../stocks/safety_stock.typ)).
442.1.5. 5. Demand
- Deterministic: known and constant — yields the EOQ family.
- Stochastic: random — yields the policies in this section.
442.1.6. Policy comparison table
| Policy | Review type | Trigger | Order size |
| — see [q_r.typ](q_r.typ) | Continuous | Inventory | Fixed batch |
| — see [s_S.typ](s_S.typ) | Continuous | Inventory | Order-up-to |
| — see [nQ_r.typ](nQ_r.typ) | Continuous | Inventory | Smallest above |
| — see [base_stock.typ](base_stock.typ) | Continuous | Every consumption | One unit (one-for-one) |
| — see [R_S.typ](R_S.typ) | Periodic (every ) | Always at review | Order-up-to |
| — see [R_s_S.typ](R_s_S.typ) | Periodic (every ) | If inventory at review | Order-up-to |
| — see [R_nQ_s.typ](R_nQ_s.typ) | Periodic (every ) | If inventory at review | Smallest above |
A policy is named by listing its parameters in sorted order: review interval (if periodic), reorder point or , target level , fixed quantity , with for integer multipliers.
The (s, Q) policy is also widely written (Q, r) — same thing, different naming convention. Likewise (R, s) is a family (specifies trigger but not order rule); concrete instances are (R, s, Q) and (R, s, S).