Inventory and Allocation
Inventory and Allocation
The newsvendor balance
For one-period perishable inventory:
- underage cost : consequence of one unit too few;
- overage cost : consequence of one unit too many.
The optimal demand quantile under the classical assumptions is
This is a decision rule, not a forecast accuracy metric.
HarborMart fresh meals
Selling price is £8, purchase cost £5, end-of-day salvage £2, and an estimated service loss of £1 accompanies a stockout.
Critical fractile is . Forecast demand distribution:
| Demand | Probability | Cumulative probability |
|---|---|---|
| 80 | 0.20 | 0.20 |
| 100 | 0.30 | 0.50 |
| 120 | 0.30 | 0.80 |
| 150 | 0.20 | 1.00 |
The first quantity whose cumulative probability reaches 0.571 is 120 meals.
Audit the newsvendor quantity
The calculation depends on the forecast distribution and cost assumptions. If salvage, substitution or goodwill estimates change, so can the order.
From forecast to inventory system
The one-period model omits:
- multi-period carryover and shelf life;
- lead time and order frequency;
- pack sizes and supplier minimums;
- substitution and lost-sales observation;
- capacity shared across products;
- demand affected by stock visibility or price.
For multi-period inventory, distinguish cycle stock, safety stock, reorder trigger and service measure. “95% service” could mean cycle-service probability or fill rate; define it.
Allocation under scarcity
When supply is fixed, allocate by expected incremental value, not historical sales alone. For each destination, consider:
- probability of sale before expiry;
- contribution and substitution;
- stockout/service consequence;
- transport and handling;
- minimum fair/service constraints;
- forecast and parameter uncertainty.
A high-demand store may already have enough inventory; the next unit’s marginal value can be higher elsewhere.
Current frontier
The modern “predict then optimise” literature asks whether statistical errors matter equally to the downstream decision. Smart Predict, then Optimize trains with optimisation structure, while the 2025 contextual optimisation survey maps several frameworks and their assumptions. These are extensions after a transparent baseline, not permission to hide costs and constraints.
Quick check
Two demand models have identical MAE. Model A is best near the median; Model B estimates the 80th percentile better. Under critical fractile 0.80, which evidence matters most?