Choose a seasonal order by weighing surplus against missed sales

When a business must order before demand is known and cannot replenish during the selling window, ordering the average demand is not automatically the best financial choice. A surplus unit and a missed sale have different economic consequences. Compare those consequences with the possible demand outcomes before choosing the commitment.

This is the single-period inventory problem often called the newsvendor model. MIT's supply-chain teaching material derives the decision from the cost of overage and underage. The worked example here assumes one purchase, one selling price, a stated recovery value for leftovers and no later replenishment. Different operating conditions require a different model.

Define when the selling opportunity ends and what happens to remaining stock. A holiday product with a credible clearance buyer is different from a perishable item requiring paid disposal. Obtain the recovery evidence before treating unsold units as cash that will eventually return.

Suppose an invented seasonal item sells for $60, costs $30 to acquire and can be cleared afterward for a net $6 per unsold unit. One unit too many loses $24: the $30 purchase cost less $6 recovered. One unit too few gives up $30 of contribution: the $60 sale less the $30 purchase that would have supplied it.

Under the basic model, the target demand quantile is underage cost divided by underage plus overage cost. Here it is $30 divided by $54, or about 55.56%. Choose a feasible quantity whose cumulative demand probability reaches that threshold, subject to the exact discrete distribution and any constraints.

The 55.56% is a consequence of these assumed prices and recovery values. It is not a universal inventory service target. Higher loss from a missed sale pushes the economic quantity upward; more expensive surplus pushes it downward. Include additional consequences only when they are supported and avoid counting the same lost margin twice.

Assume demand can be 80 units with probability 20%, 100 units with probability 50%, or 140 units with probability 30%. These probabilities are invented to demonstrate the calculation. Cumulative probability is 20% at 80 units and 70% at 100 units, so 100 is the first quantity reaching the 55.56% threshold.

At a 100-unit order, low demand produces $4,800 of sales plus $120 from clearing 20 units, less the $3,000 purchase cost. The outcome is $1,920. At demand of 100 or 140, all 100 units sell and the outcome is $3,000. Expected contribution is 20% of $1,920 plus 80% of $3,000, or $2,784.

An 80-unit order earns $2,400 in every listed demand outcome. A 140-unit order earns $960, $2,040 or $4,200, giving expected contribution of $2,472. The larger order benefits from the highest demand case but loses enough on surplus in the other cases to produce a lower expected result.

Average demand in the example is 108 units: 20% of 80, plus 50% of 100, plus 30% of 140. Ordering 108 would produce expected contribution of $2,721.60 under the same assumptions, below the $2,784 from ordering 100. The average is a useful demand summary, but it does not incorporate the asymmetric surplus and shortage costs.

With 100 units available, all demand is met in the 80- and 100-unit cases, giving a 70% probability of no shortage. That exceeds the 55.56% target quantile because the discrete probability distribution jumps at 100. Do not expect the achieved service probability to equal the formula exactly.

Expected units supplied are 96, compared with expected demand of 108. Their ratio is about 88.9%, a different unit-fill measure. Label whether a report means probability of avoiding a shortage, expected units filled or expected contribution. Interchanging these measures can make an order look more protective than it is.

The recovery value can change the preferred quantity sharply. If a reliable buyer paid a net $20 per leftover unit, overage cost would fall to $10 and the target quantile would rise to $30 divided by $40, or 75%. Under the same discrete demand probabilities, the first quantity reaching that level would be 140 units. Verify the recovery capacity and price before using this sensitivity to justify the larger purchase; the higher salvage value is a new commercial assumption.

Clearance proceeds should be net of the costs needed to realize them. If the $6 buyer requires extra packing and freight, subtract those amounts before using the recovery value. If only a limited quantity can be cleared, the simple constant-per-unit salvage assumption may fail at larger orders.

The 100-unit order requires $3,000 before demand is observed. A business with less available funding may need a smaller feasible commitment or different supplier terms even when 100 maximizes the modeled expected contribution. Show the cash requirement and the lower-demand loss exposure beside the expected result.

Case packs, order minimums, price breaks and storage limits can restrict the feasible quantities. Evaluate those actual quantities directly. A formula-derived quantity is a candidate for review; the business still needs to check the commercial terms and operating limits attached to that purchase.

Estimate demand from relevant selling periods and retain the events that changed exposure, price or availability. Stockout-limited sales may understate demand, while a launch promotion may overstate ordinary demand. A finely calculated quantile cannot repair an unsupported distribution.

Where probabilities are uncertain, compare how the order changes under plausible alternative distributions. Identify whether one uncertain high-demand case drives the larger commitment. A decision that changes sharply with a small probability revision deserves more attention to evidence or a more flexible purchasing option.

After the season, preserve the original order rationale, observed sales, availability, surplus and net recovery. Do not equate one shortage with a bad decision or one sellout with proof of success. The review should ask whether the assumptions and feasible alternatives were reasonable, then use the outcome to improve the next commitment.