Formula Versus Plan - Inventory: The EOQ and Lot-Sizing, Honestly

The final lesson separates two exact tools by their assumptions. EOQ is a formula for a continuous steady-demand model; Wagner-Whitin is a plan for a pinned lumpy-demand instance.

highlighted = computed this step

Formula Scope

The EOQ formula gives quantity 8 and model cost 8. Motivation: a closed-form formula is useful when the smooth-demand assumptions really describe the model.

Q^*=8\quad C^*=8

Plan Scope

The Wagner-Whitin plan has cost 15 for the lumpy instance. Why: it is an exact DP optimum for the discrete horizon, not an EOQ cost.

F(T)=15

Recomputed Comparison

If period 3 demand is changed to 2, the exact DP recompute has cost 17 and places orders in periods 1 and 3. Interpretation: changed lumpy demand changes the exact plan without changing the flagship instance.

\text{comparison }F(T)=17\quad q_{\text{second}}=6

Honest Choice

Use the formula for smooth steady demand and the plan for known lumpy demand. Interpretation: both are exact only inside their own assumptions.

\text{formula scope differs from plan scope}

Diagram note

Honesty note: EOQ is exact only for the idealized continuous constant-demand model: known steady demand, infinitely divisible order quantity, zero lead time, and no capacity. Wagner-Whitin is exact for this pinned finite discrete demand instance. EOQ plot segments interpolate between exact evaluated points; only the marked points are recomputed. Pixel positions are rounded for layout; every number shown is exact.

\text{exact model arithmetic stops at the model boundary}