A continuous‑review replenishment policy that issues an order to raise inventory to an upper level S whenever on‑hand inventory falls to or below a reorder point s; the order quantity is variable and equals S minus the inventory position at ordering time. It governs timing (trigger s) and quantity (raise to S) under stochastic demand and lead times.

Principle

A two‑parameter (s,S) rule separates the decision of when to order (threshold s) from how much to order (replenish to S); the pair s and S together balance ordering costs, holding costs and stockout risk under uncertainty.

Demonstration

Illustrative scenario → A small distributor monitors on‑hand stock continuously. Recognition → On‑hand level drops to s after a sale. Action → The system places an order that brings the position to S. Consequence → Order frequency and average order size adjust endogenously: low s raises frequency and reduces order size; high S raises average inventory but reduces stockout probability.

Misapplication

Confusing (S,S) with fixed‑quantity policies (Q,R): treating S−s as a fixed Q regardless of current pipeline. The semantic error is assuming order size is independent of inventory position or that orders always equal a preset Q.

Consequence

Correct application yields adaptive order sizes that can reduce total cost when economies of scale in ordering are limited; missetting s or S yields either excessive holding costs (S too high) or frequent stockouts (s too low).

Reversal

When fixed ordering costs are large and batching is economically beneficial, a fixed‑quantity Q policy may outperform (S,S); likewise, in periodic review contexts a (s,S) continuous policy is infeasible and periodic order rules apply.

Boundary

Clearly within: single‑item, continuous‑review systems where replenishment can restore position to S and order size may vary. Boundary case: modest minimum order quantities where S must be constrained. Clearly outside: fixed Q continuous policies (Q,R) where order quantity is predetermined, or periodic review policies.

Semantic Tension

Flexibility versus predictability: (S,S) adapts order size to current pipeline (flexible, lower stockouts) but produces variable order quantities that complicate supplier scheduling (less predictable).

Synthesis

The (S,S) policy operationalizes the separation of timing and magnitude: by choosing a trigger s and a target S, the manager converts uncertain demand realizations into variable replenishment quantities that directly reflect the current inventory position and outstanding orders.