Newsvendor Order Quantity & MOQ Calculator
Estimate the order quantity for a seasonal, perishable, or one-time buy when demand is uncertain. The calculator shows the classical newsvendor optimum, then compares the feasible MOQ and case-pack choices by expected profit.
Recommended feasible order1,068
- Unconstrained optimal order
- 1,063.73
- Critical ratio
- 62.5%
- Stockout probability
- 36.69%
- Expected units sold
- 949.64
- Expected leftover units
- 118.36
- Expected unmet demand
- 50.36
- Expected profit
- $17,572.60
- Supplier-constraint profit impact
- $0.55
Feasible order comparison
| Candidate | Order | Expected profit | Stockout probability |
|---|---|---|---|
| Continuous optimum | 1,063.73 | $17,573.15 | 37.5% |
| Lower case pack | 1,056 | $17,571.33 | 38.97% |
| Upper case pack | 1,068 | $17,572.60 | 36.69% |
Assumes one ordering opportunity, normally distributed demand, no replenishment, and no fixed order cost.
How to use this calculator
- Enter the forecast mean demand and the standard deviation for the same selling period.
- Enter the selling price, landed unit cost, leftover recovery value, and any measurable stockout penalty.
- Add the supplier minimum order and case-pack multiple that your purchase order must follow.
- Compare the recommended feasible order with expected leftovers, unmet demand, and profit impact.
How the order quantity is calculated
The newsvendor model is a single-period inventory model. It is used when you place one order before demand is known, then sell, clear, or discard what remains at the end of the period. The tradeoff is between ordering too little and losing margin or goodwill, and ordering too much and recovering less than cost on leftovers.
The calculator first converts commercial inputs into the two costs used by the model:
Cu = p - c + g, the underage cost of being one unit short.Co = c - v, the overage cost of having one unit left over.
Here p is selling price, c is purchase cost, v is salvage or recovery value, and g is any extra stockout cost. The critical ratio is CR = Cu / (Cu + Co). For normally distributed demand, the unconstrained order is Q* = max(0, mean + standard deviation x inverseNormal(CR)).
Supplier rules are applied after that. The effective MOQ is the first case-pack multiple at or above the stated minimum order. The calculator evaluates the neighboring feasible case-pack quantities around Q*, after applying that effective MOQ, and recommends the one with higher expected profit.
What moves the recommendation most
The price-cost spread, salvage value, stockout penalty, and demand uncertainty drive most of the result. A high salvage value lowers the cost of leftovers, so the model orders more. A high stockout penalty raises the cost of shortage, so the model also orders more. Higher demand standard deviation spreads the possible outcomes wider, which makes the critical ratio more visible in the final order.
MOQ and case packs can matter even when the continuous optimum is well estimated. A high MOQ may force a purchase above the profit-maximizing quantity. A coarse case pack can make the lower multiple better than the upper one, especially when leftover cost is high.
What this calculator leaves out
The estimate assumes one ordering opportunity, no replenishment during the period, and normally distributed demand. It does not include fixed order costs, storage capacity, quantity discounts, taxes, financing cost, price-dependent demand, or multiple markdown stages. The normal model can also be a poor fit for sparse, highly skewed, censored, or strictly low-volume demand.
Worked example
Suppose forecast demand is 1,000 units with a 200-unit standard deviation. The selling price is $40, landed cost is $20, leftover recovery value is $8, there is no extra stockout penalty, no MOQ, and the case pack is 12 units.
The underage cost is $20 and the overage cost is $12, so the critical ratio is 62.5%. The normal quantile gives an unconstrained optimum of 1,063.73 units. The neighboring case-pack choices are 1,056 and 1,068 units; their expected profits are about $17,571.33 and $17,572.60. The calculator recommends 1,068 units, with expected sales of 949.64 units, expected leftovers of 118.36 units, expected unmet demand of 50.36 units, and a stockout probability of 36.69%.
Common questions
What is the newsvendor model?
The newsvendor model is a single-period inventory model for one buying decision before uncertain demand is known. It balances the cost of ordering too little against the cost of ordering too much.
When should I use this instead of EOQ?
Use this model for seasonal, perishable, event, fashion, promotional, or one-time inventory where there is no normal replenishment cycle during the selling period. EOQ is for repeat ordering with ongoing demand and replenishment.
How do MOQ and case-pack rules change the answer?
The classical model returns a continuous optimum that may not be purchasable. This calculator rounds the supplier minimum up to a case-pack multiple, then compares the feasible case-pack quantities around the optimum by expected profit.
What should I include in stockout cost?
Include only costs you can reasonably tie to an unmet unit, such as expediting, contractual penalties, lost add-on margin, or a quantified goodwill estimate. Do not add vague dissatisfaction twice if it is already reflected in the selling margin.
What if demand is not normally distributed?
The normal-demand result is a useful approximation when demand is reasonably symmetric and the mean is not near zero. For sparse, censored, highly skewed, or intermittent demand, use a distribution or simulation that matches the item better.