The Wagner-Whitin table gives not just a cost but an order plan. Traceback names the order periods and quantities, then the baselines show what the plan improves on.

highlighted = computed this step

Traceback Plan

The first order is in period 1 for quantity 6, covering periods 1 through 3. Motivation: traceback turns the DP predecessor row into an order that covers a whole prefix block.

order period 1q=6\text{order period }1\quad q=6
optimal planordercoversqtyperiod 11-36period 44-44

Final Order

The second order is in period 4 for quantity 4. Why: the final period is cheapest as its own order in this instance.

order period 4q=4\text{order period }4\quad q=4
optimal planordercoversqtyperiod 11-36period 44-44

Rival Policies

The Wagner-Whitin cost is 15, ordering every period costs 20, and ordering once costs 22. Interpretation: the DP proves the chosen plan beats these two simple rivals for the pinned demand.

15<20<2215<20<22
policy comparisonpolicycostWW optimum15order every period20order once22

Diagram note

Honesty note: Wagner-Whitin is exact for this pinned finite discrete demand instance. Pixel positions are rounded for layout; every number shown is exact.

traceback turns the DP values into an order plan\text{traceback turns the DP values into an order plan}
optimal planordercoversqtyperiod 11-36period 44-44