Inputs and planning rule
Use one illustrative cost unit for all costs and the same count unit for all quantities. Under fixed annual demand D, cost per order S and annual holding cost per item h, compare C(Q)=DS/Q+hQ/2. The positive continuous minimum is sqrt(2DS/h). This model assumes immediate replenishment, no shortage or discount and constant costs. Supplied pack/minimum/maximum constraints determine feasible quantities.
Worked example
| Order units | Order cost | Holding cost | Total cost |
|---|---|---|---|
| 100 | 600 | 150 | 750 |
| 200 | 300 | 300 | 600 |
| 400 | 150 | 600 | 750 |
With D1200,S50,h3 and packs of60, is180 or240 cheaper under this model?
Show the worked answer
180 costs 1810/3, about 603.333; 240 costs 610. Choose 180 as the lower feasible model cost. An explicit minimum 300 instead makes 300 the constrained choice at 650, with no real supplier claim.
When the result is held
Zero demand has no positive demand recommendation. Zero ordering or holding cost has no positive interior optimum; do not report a unique positive EOQ. Blank inputs, negative costs and no feasible pack multiple are held. Use annual demand and annual holding cost per item, one common illustrative cost unit and one count unit; numeric fields do not identify periods or currencies. All quantities are whole and bounded at 1,000,000; costs have two decimals. Exact rational feasible costs drive selection, including tied minima. The plotted continuous value is approximate and no supplier price or accounting result is claimed.