Computes a stocking policy for every item, a reorder trigger (MIN), an order-up-to target (OPHQ), and an upper trigger (MAX), in two versions side by side: a faithful reproduction of a real KNIME calculation, and an improved policy that fixes the one thing the original gets wrong. The engine then measures the service level each version actually delivers, so the difference is shown, not asserted.
This is the policy layer of the network system. It sits between the demand forecasting engine, which gives it demand mean and standard deviation, and the container and transfer engines, which consume its MIN and MAX as triggers. The improved policy is the adopted implementation; the faithful engine is retained only as the reference baseline for the comparison.
- The problem and the review finding
- Architecture and the pipeline it sits in
- The faithful engine
- The improved engine
- Evaluation and results
- Limitations
- Future work
- Using the engine
- Project structure
- References
The original computed MIN, OPHQ, and MAX by transaction colorway code from a KNIME workflow and pushed them to the warehouse system monthly. The backbone is sound: it anchors the policy to lead-time demand and uses per-supplier lead time, which is right, since foreign suppliers have different lead times.
The review found one root error that explains most of the rest. The formula scales mean lead-time demand by fixed multipliers: MIN by 1.04, MAX by 1.28, and a quantity multiple by 0.84. Those three numbers are almost exactly the service-level z-scores for 85, 90, and 80 percent (1.036, 1.282, 0.842). So the intent was clearly a service level, but the z-score was multiplied against the mean instead of being applied to the standard deviation of lead-time demand. Safety stock should be z times sigma, not z times the mean. Multiplying the mean makes the buffer scale with how much you sell rather than with how uncertain it is, so two items with the same average but very different variability get the identical buffer, and the service level actually delivered drifts item by item and is neither controlled nor knowable.
Three consequences follow: demand variability is ignored, lead-time variability is ignored entirely (only mean lead time is used, which under-buffers exactly the imported items that are riskiest), and OPHQ is normalized to weekly units while MIN and MAX are in lead-time units, so nothing guarantees MIN is at most OPHQ is at most MAX.
There is one more telling detail. The service-level sheet's own callout states the correct formula in words, sigma_LT times Z times D_Avg, which is proper lead-time- variability safety stock. None of the six KNIME steps implement it; they all multiply mean lead-time demand by the z-value instead. So the document knows the right formula and the nodes compute a different one. The improved engine below implements what the callout actually asks for, and adds the demand-variability term the callout omits.
demand forecast (mean, std) --.
per-supplier lead time --------> inventory policy engine --> MIN / OPHQ / MAX per item
ABC class + service target ----' (feeds container + transfer engines)
The primary home owns a single policy. Secondary and tertiary buildings are fallback assignment ranks only, not separate policies, which reconciles the three-tier spec with the single-home decision. The MIN and MAX this engine produces are the exact triggers the transfer engine later uses: quantity below MIN pulls up to OPHQ, and quantity above MAX pushes down to OPHQ, which is reverse replenishment.
A verbatim transcription of the KNIME math nodes, now with the OHQ Service Level fields defined from the service-level sheet rather than assumed. That sheet defines three confidence levels of no stockout, each as mean lead-time demand times a z-value, and a weekly version of each:
OHQ Service Level 3 = Total Lead Time Days * daily demand * 0.84 (80% confidence)
OHQ Service Level 4 = Total Lead Time Days * daily demand * 1.04 (85% confidence)
OHQ Service Level 5 = Total Lead Time Days * daily demand * 1.28 (90% confidence)
Weekly OHQ Service Level k = (OHQ Service Level k / Total Lead Time Days) * 7
The MIN/MAX sheet then wires them together:
MIN = lead-time demand * 1.04 (equals OHQ Service Level 4)
MAX = lead-time demand * 1.28 (equals OHQ Service Level 5)
Quantity Multiple = lead-time demand * 0.84 (equals OHQ Service Level 3)
ABC Demand Value = Weekly OHQ Service Level 3 = daily demand * 7 * 0.84
OPHQ = Weekly OHQ Service Level 4 = daily demand * 7 * 1.04
Two flaws are reproduced honestly rather than fixed. The z-values multiply mean lead-time demand rather than its standard deviation, so the buffer ignores variability. And OPHQ is one week of stock while MIN is a full lead time of stock, so for any item whose lead time exceeds seven days, OPHQ falls below MIN. On the demo catalog that is 100 percent of items: the post-action target sits below the reorder trigger it is supposed to sit above, often by a wide margin.
Same backbone, corrected buffer:
- Service target per ABC class (A 98, B 95, C 90 by default, configurable), so the target is an explicit business decision rather than a hidden multiplier.
- MIN is the service-level quantile of lead-time demand. Mean lead-time demand is mu = lead_time_mean times daily_demand. Its standard deviation is sigma = sqrt(lead_time_mean times demand_var + daily_demand^2 times lead_time_var), the standard combined formula, which finally uses both the demand spread from the forecasting engine and the supplier lead-time spread. For smooth and erratic items MIN = mu + z times sigma. For intermittent and lumpy items the normal curve under-covers the right tail, so MIN is the quantile of a gamma distribution moment-matched to the same mean and variance, a standard treatment for spiky demand.
- Order quantity comes from a review-period cover, floored at MOQ and rounded up to pack, which is where the 0.84 quantity multiple actually belongs. OPHQ = MIN + Q and MAX = OPHQ + Q, so MIN is at most OPHQ is at most MAX holds by construction.
For every item the engine simulates many lead-time-demand outcomes from its true process and counts how often MIN covers demand. That realized cycle service level is compared to the item's target. Safety stock held (MIN above mean lead-time demand) is a proxy for working capital.
Results on the synthetic catalog (200 items, 8 suppliers with 5 import and 3 domestic, service targets A 98, B 95, C 90). Illustrative, from the included generator, not a claim about any real catalog:
| policy | mean realized service | spread (std) | mean gap to target | items 5+ pts below target | total safety stock |
|---|---|---|---|---|---|
| faithful formula | 0.565 | 0.017 | 0.384 | 100% | 2004 |
| improved policy | 0.950 | 0.034 | 0.004 | 0% | 32517 |
The faithful formula delivers about 56 percent cycle service uniformly, far below the 85 to 90 percent its multipliers imply, because a reorder point at 1.04 times the mean barely clears the median. Every item lands more than five points under target. The improved policy hits the target almost exactly, and by class: A 98.1, B 95.1, C 90.0.
The cost is much more safety stock, which is the honest price of real service, not a defect. Where that capital goes is the other half of the story: the improved policy places 87 percent of its safety stock on imported items, where the long and variable lead times actually create the risk, while the faithful formula spreads a thin flat buffer everywhere and protects nothing well.
The gamma quantile for intermittent and lumpy items is moment-matched to mean and variance, not fitted to full history. It respects skew without peeking at the data generator, which is the fair test, but a production version would fit the distribution to each item's demand.
The demo runs on synthetic data so the project is inspectable without proprietary inputs. Service targets, MOQ, pack, and review period are defaults, marked configurable.
- A cost-based service level: given holding and stockout costs, set each item's service level from the newsvendor critical ratio, which makes optimal holding quantity actually optimal rather than a label.
- Economic order quantity in place of a flat review-period cover, with real ordering and holding costs and pallet rounding.
- Correlated demand and lead time, which the combined-variance formula assumes are independent.
- A direct handoff to the transfer engine, feeding MIN and MAX as the forward and reverse replenishment triggers.
Standalone, on the included synthetic catalog:
pip install -r requirements.txt
python scripts/run_demo.pyAs a module:
from inventory_policy import generate, faithful_policy, improved_policy, compare
data = generate() # or supply your own items frame
faithful = faithful_policy(data["items"])
improved = improved_policy(data["items"]) # service targets configurable
table, faithful_detail, improved_detail = compare(data["items"], faithful, improved)Inputs are a per-item demand forecast (weekly or daily mean and standard deviation), an assigned supplier with lead-time mean and standard deviation, an ABC class with a service target, and pack and MOQ. The forecast comes from the demand engine; this engine produces the policy.
inventory-policy-engine/
README.md this document
requirements.txt
src/inventory_policy/
sim.py shared demand model (truth for estimation and evaluation)
classify.py ABC classification and service targets
data.py synthetic catalog generator
faithful.py verbatim reproduction of the KNIME MIN/OPHQ/MAX formula
improved.py variability-based, pattern-aware policy
evaluate.py realized service simulation and comparison
pipeline.py plan(): catalog in, policy out
scripts/run_demo.py end-to-end demo, figure and exports
tests/ formula reproduction, ordering, target attainment, allocation
assets/ generated figure
data/ sample catalog, suppliers, and policy comparison output
Chopra, S., and Meindl, P. (2016). Supply Chain Management: Strategy, Planning, and Operation, 6th ed. Pearson. (Cycle service level and safety inventory.)
Nahmias, S. (2009). Production and Operations Analysis, 6th ed. McGraw-Hill. (Reorder point and the newsvendor critical ratio.)
Silver, E. A., Pyke, D. F., and Peterson, R. (1998). Inventory Management and Production Planning and Scheduling, 3rd ed. Wiley. (Safety stock and the combined demand and lead-time variability formula.)
Syntetos, A. A., and Boylan, J. E. (2005). The accuracy of intermittent demand estimates. International Journal of Forecasting, 21(2), 303-314. (Why intermittent and lumpy demand need non-normal treatment.)