##  [(S,S) Inventory Policy](/ss-inventory-policy-0) 

 Definition

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

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

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

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

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

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

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

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

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.