Batch Delivery Reliability Calculator
How does the number of sources change the odds that a batch arrives on the promised date? Work it out from your own on-time rate — the answer is a range, not a single number.
Calculator
How the number of sources changes the odds that a batch arrives on the promised date — with the correlation uncertainty shown as a range rather than hidden.
Result
The calculation runs entirely in your browser; nothing you type is sent to our servers.
Worked example
Opened with its default case — How many separate sources does one batch come from today?: 5 · On-time delivery rate of those sources (%): 90 · Number of sources after consolidation: 1 — the calculator returns the figures below. The headline result is 59% – 90% (batch on-time probability today). They are written out here so the output is readable without running JavaScript: in print, with scripts disabled, or by a search engine.
| Input | Value |
|---|---|
| How many separate sources does one batch come from today? | 5 |
| On-time delivery rate of those sources (%) | 90 |
| Number of sources after consolidation | 1 |
| On-time rate of the remaining supplier (%) | 90 |
| Is partial shipment allowed? | No — the batch must arrive complete |
| How many batches (delivery rounds) per year? | 24 |
| Typical delay of a late shipment (days) | 6 |
| Result | Value |
|---|---|
| Batch on-time probability today | 59% – 90% |
| After consolidation | 90% |
| Mathematical floor (shared capacity) | 50% → 90% |
| Change | +0 pts … +31 pts |
| Late batches per year | 2.4 – 9.8 → 2.4 batches/year |
| Delay days per year | 14.4 – 59 → 14.4 days/year (lower bound) |
| Effect of partial shipment | Off — the batch waits for its slowest source |
| Verdict | At best consolidation gains +31 pts, at worst it changes nothing — which of the two depends on whether your delays share a cause. Even where the gain is real, it is not kept unless partial shipment is written into the order. |
Change any field above and the calculator recomputes; this table is the default case only.
How does buying from a single supplier affect the delivery schedule?
A batch is only complete when every line has arrived. So its duration is not the sum of the line lead times but the longest one, and its probability of arriving on time is the product of the individual probabilities. Five sources that are each 90% reliable give a batch that is 59% reliable, not 90%.
Batch on-time probability = p₁ × p₂ × … × pₙ when delays are independent. If they all share one cause the result moves towards the smallest p; if the sources share one vehicle or one weekly capacity it can fall below the product. That is why this tool prints a range and, separately, the mathematical floor.
The gain is not automatic. If the single supplier collects the lines internally and ships once, the same wait simply moves. What locks the gain in is one written line: partial shipment is permitted.
Why a product, not an average
Lead time for a batch is usually built from the wrong arithmetic: the line lead times get averaged. A batch is not finished by the average line, it is finished by the last one. If two of three lines arrive in three days and one takes fourteen, the batch takes fourteen days — not six and a half.
Batch lead time = the maximum of the line lead times
Batch on-time probability = the product of the individual probabilities
The second line follows from the first. If the batch was on time then every line was on time, and the probability that several independent things all happen is their product. The counter-intuitive consequence: a batch built from individually reliable sources becomes unreliable quickly as sources are added, because numbers below one shrink when multiplied.
The 90%, 95% and 98% figures below are example assumptions, not a measured industry average. Read them with your own measured rate substituted in.
| Independent sources | Each 90% on time | Each 95% | Each 98% |
|---|---|---|---|
| 1 | 90.0% | 95.0% | 98.0% |
| 3 | 72.9% | 85.7% | 94.1% |
| 5 | 59.0% | 77.4% | 90.4% |
| 8 | 43.0% | 66.3% | 85.1% |
| 12 | 28.2% | 54.0% | 78.5% |
These are the direct output of pⁿ, valid where delays are independent; they are arithmetic, not measurements. Read the bottom row: even at a very good 98% source reliability, a twelve-source batch is late more often than one in five.
Independent or correlated? What the range means
The product rule has a condition that is rarely fully met in practice: the delays must be independent of each other. In reality they share causes — the same public holiday, the same customs backlog, the same raw material shortage, sometimes even the same sub-manufacturer behind different brands.
| Structure of the delays | Batch on-time probability | Delivery gain from consolidating |
|---|---|---|
| Negatively dependent — sources share one capacity | max(0, Σp − (n−1)) — the mathematical floor | High, but for a different reason |
| Fully independent | The product (pⁿ) — a point inside the range, never its floor | High |
| Fully shared cause | The smallest p — the highest value | Almost none |
The ordering of the last two looks backwards at first: more shared cause means a higher chance the batch is on time, because all-or-nothing behaviour stops independent risks from stacking. That is not good news — it only means the spread setup is less bad than it looks, and consolidation therefore less good.
“More shared cause raises the probability” holds only while the individual on-time rates stay unchanged. In practice a strike or a rule change raises the correlation and lowers every source’s own rate — and then the result falls below the independent case.
The product is not the floor
The commonest mistake is to read the product as the worst case. It is not: the product is only the independent case. The mathematical floor for a joint probability is the Fréchet–Hoeffding lower bound, and it sits far below:
Mathematical floor = max(0, p₁ + p₂ + … + pₙ − (n − 1))
| Sources | Independent (pⁿ) | Mathematical floor |
|---|---|---|
| 2 | 81.0% | 80.0% |
| 5 | 59.0% | 50.0% |
| 8 | 43.0% | 20.0% |
| 12 | 28.2% | 0.0% |
At twelve sources the independent calculation says “28.2% at worst”; the real floor is zero. That is the concrete measure of how badly the independence assumption understates downside risk.
This floor is not a curiosity. Negative dependence comes from shared capacity and is ordinary in supply: one vehicle, one shipping window, one customs slot, one week of production. If a supplier can only finish one of two orders this week, sending one on time is what delays the other, and the two stop being independent. Each order is still 90% on its own, but the chance of both arriving is pushed down towards 80% rather than the 81% independence predicts. A setup that looks reassuring (“they are never both late”) is, for a batch, worse than independence.
Put last year’s late deliveries on a calendar. If they cluster in the same weeks, the shared cause is strong and most of the delivery gain you expect from consolidation will not arrive. If they are scattered through the year, the independence assumption largely holds and the gain is real.
What consolidation does and does not speed up
Cutting the number of suppliers shortens no manufacturer’s production time. What changes is not the durations but how they combine. Consolidation does not sell faster supply; it sells fewer waits stacked on top of each other.
| Consolidation improves this | It does not improve this |
|---|---|
| How many separate risks the batch depends on | The production and transit time of any one line |
| The number of shipments and goods receipts to track | Raw material shortages, customs, seasonal peaks |
| Who has to fix a delay — one counterpart instead of five | Risk inside the supplier’s own sub-sources |
| Paperwork and reconciliation on partial arrivals | Your own internal approval cycle |
The last item on the right is the one most often forgotten: internal approval time does not change with supplier count and is a material share of total lead time in most organisations. Keep it separate, or you will try to fix a delay that is not the supplier’s with a change of supplier.
Going to one supplier does not remove risk, it moves it. If your supplier collects the same lines in parallel from its own sub-sources, your five-source problem becomes its five-source problem. What decides whether the risk was really transferred is a written lead time commitment and a stock-holding obligation; without those it has only become invisible.
Partial shipment: the clause that locks the gain
Everything above rests on one assumption: that the batch has to arrive complete. Remove the assumption and the model changes. With partial shipment allowed, the question is no longer whether the batch is on time; each line arrives on its own date and only the late line is late. The unit of measurement drops from the batch to the line.
Partial shipment off: batch = its slowest line
Partial shipment on: each line = its own lead time
Under Turkish law the default here is the opposite of what most buyers assume, and it rests on two separate provisions that are easy to confuse. Early performance is the debtor’s option, not the creditor’s right: under article 96 of the Turkish Code of Obligations, headed “Early performance”, the debtor may perform before the term expires unless the contract or the circumstances show otherwise — so nothing obliges the supplier to send the ready lines ahead of the order date. Article 84, headed “Partial performance”, answers a different question again: it lets the creditor refuse partial performance once the whole debt is certain and due, so it protects the buyer rather than entitling the buyer to be served in parts — and its “certain and due” condition keeps it out of the early-shipment argument altogether. Neither article is mandatory, and neither creates a right to partial delivery — which is exactly why that right has to be written into the order.
Its twin applies at the goods-receipt desk. Article 23/1(a) of the Turkish Commercial Code provides that where the buyer has accepted partial delivery without reservation, the buyer may exercise its rights only in respect of the undelivered part. The practical consequence is a single sentence: write the missing lines and your reservation on the delivery note.
- Put “partial shipment permitted” in the order — without it the default is to wait.
- Settle who pays the freight on a partial shipment in the same line, or the supplier will sensibly wait and send once.
- Separate the lines that stop the job from those that can wait; partial shipment only helps if priority is defined.
- Record the confirmed delivery date and the revision procedure — “about two weeks” is not a commitment.
- Make the reservation wording part of your goods-receipt instruction (Commercial Code art. 23/1(a)).
- Do not confuse early performance with partial performance: article 96 says the debtor may discharge the whole obligation sooner, not that it may divide it.
Measuring your own on-time rate
Every number on this page starts from one input you have to supply: p, the probability that a single source delivers on time. (The second driver — how far your delays share a common cause — is what the printed range stands for.) The example values of 90%, 95% and 98% are placeholders. Your own figure is not hard to produce, since it is already in your goods-receipt records, but it is easy to produce wrongly.
| Decision | The two options | Which one to take |
|---|---|---|
| Which date counts as “promised” | The date on the order, or the date the supplier confirmed | The confirmed date. Measuring against your own wish measures your planning, not their reliability |
| Which date counts as “delivered” | Arrival at the gate, or acceptance after inspection | Gate arrival, for a number going into this calculator: the model measures the supplier, and your inspection queue sits outside it by design. Keep acceptance as a second number if you need it, and never mix the two inside one rate |
| What a partial delivery counts as | On time if anything arrived, or on time only if complete | Count the order, not the truck, and score it on time only if complete — that is the case this model prices. Where partial shipment is permitted the unit drops to the line, exactly as in the section above, and each line is scored against its own confirmed date |
| How wide a window is “on time” | Exact day, or a tolerance of a day or two | State it explicitly, because the tolerance sets the answer: if a tenth of your deliveries land one or two days late, a two-day tolerance lifts the measured rate by exactly those ten points, and an unstated tolerance makes two sites’ numbers incomparable |
Whatever you decide, write it down next to the number. A rate without its definition cannot be compared with next year’s.
p = on-time deliveries ÷ total deliveries, counted for one source under one written definition
Twenty deliveries is the practical minimum, and even then the figure is wide: 18 on time out of 20 reads as 90%, but the rates consistent with that count run from roughly 70% to 97%. Thirty narrows it to about 74–97%, and telling a 90% source apart from a 95% one takes well over a hundred. Use the number to rank sources and to run this calculator at an optimistic and a pessimistic end — not to defend a decimal point.
One refinement is worth the effort once the basic number exists: measure per source, not per company. A distributor that ships stock items from its own shelf and special orders from a factory has two very different rates hidden inside one average. If a single batch draws on both, count them as two sources in the first field and enter the weaker of the two rates. The tool takes one rate for all sources, so the weaker figure keeps the estimate on the cautious side: it is exact at the shared-cause end, and deliberately low at the independent end.
Start by measuring forward rather than reconstructing backwards. Add two columns to the goods-receipt sheet — confirmed date and actual date — and the count builds itself. Twenty deliveries is the milestone, not the calendar: at two orders a month that is under a year, at two a week it is a couple of months. Until you get there, run this calculator twice, once at an optimistic p and once at a pessimistic one, and make the decision only if it survives both.
Four things this calculation cannot see
The model is deliberately small: it converts a set of individual on-time rates into a batch on-time rate. Four things sit outside it, and each of them can matter more than the effect the model measures.
| What the on-time rate cannot show | Why it matters | Where to handle it |
|---|---|---|
| How late a late delivery is | The probability figure scores a one-day delay and a one-month delay identically; the delay-days line closes that gap only roughly, because it works from a single average and prints a lower bound | Keep the spread of your delays, not just their average — the tail is what stops a job |
| Your own internal time | Approval, budget release and specification rework sit before the order and can rival or exceed the supplier’s own lead time | Measure the request-to-order interval as its own number |
| Correlation you cannot observe | Two “different” suppliers may sit behind one factory, port or vehicle — the shared causes set out under “Independent or correlated?” | Ask where the goods actually originate before treating sources as independent |
| What consolidation costs | One supplier means one point of failure, less price tension and a weaker position at renewal | Decide it as a commercial question; the delivery arithmetic is only one input |
The honest summary: this page tells you how much delivery reliability a consolidation could buy. It cannot tell you whether that is worth what consolidation costs — that comparison needs your own figures for the cost of a late batch.
One further limit is worth stating plainly, because it is the one most often missed. The calculator asks for the remaining supplier’s rate separately for a reason: nothing guarantees it stays what it is today. A source that suddenly carries five times the volume, or a line that moves from a stocked item to a special order, has a different rate from the one you measured. Whatever you enter for the after case is a forecast, not a measurement — re-measure once the new arrangement has produced twenty deliveries of its own, rather than assuming the predicted number arrived.
Frequently Asked Questions
Does buying from one supplier make delivery faster?
Not directly. No manufacturer’s production time shortens because you changed how many suppliers you use. What changes is how many separate risks the batch depends on at once: because a batch is complete only when every line has arrived, its on-time probability is the product of the individual probabilities. Five sources at 90% each give a 59% batch. Going to one removes that product — but only if the delays were independent. If they all share a cause, the gain is close to nothing.
How is batch lead time calculated?
Take the maximum of the line lead times, not the sum or the average. The batch finishes with its last line. If two lines take three days and one takes fourteen, the batch takes fourteen. Add your own internal time — request, approval, order creation — separately, because it does not change with supplier count.
Is partial shipment something a buyer can demand?
Not by default, and the reason is usually cited from the wrong article. Article 96 of the Turkish Code of Obligations decides the point: early performance is the debtor’s option, so the supplier is free to hold the ready lines until the order is complete. Article 84 protects the buyer from the opposite move — it lets the creditor refuse partial performance once the whole debt is certain and due — but it does not entitle the buyer to be served in parts. Neither article is mandatory, so the parties may agree otherwise, which is exactly why partial shipment belongs in the order or the contract. Settle the freight cost of the extra shipment in the same clause, or it will stay on paper.
What should I watch when accepting an incomplete delivery?
Write the missing lines and your reservation on the delivery note. Under article 23/1(a) of the Turkish Commercial Code, a buyer who has accepted partial delivery without reservation may exercise its rights only in respect of the undelivered part. The same article allows termination where the missing part destroys or materially weakens the purpose of the contract — but that argument is far harder after an unqualified signature.
Why is the range so wide?
Because a second thing that drives the answer has not been measured yet: whether your delays share a common cause. One end assumes they are fully independent, the other that they always move together. To narrow it, put last year’s late deliveries on a calendar — clustered in the same weeks means the real value sits near the shared-cause end.
Is the product the worst case?
No, and this is the commonest error. The product is only the independent case. The mathematical floor for a joint probability is max(0, Σp − (n−1)), which is far lower: with twelve sources at 90% each, the product says 28.2% while the floor is 0%. That floor is reached through shared capacity — one vehicle, one shipping window, one week of production — and the tool shows it on its own line.
Are the results sent to your servers?
No. The calculation runs entirely in your browser; the rates and batch counts you type are never sent anywhere or stored.
Sources
- Method note — this tool uses no benchmark on-time delivery rate. Published figures sit either behind paid research or inside software vendors’ marketing, so nothing of that kind is embedded. The calculation runs only on the rate you measure yourself; the pre-filled values exist so the form does not open empty and are not a standard. The model itself is standard probability: the joint probability of independent events is their product, and a joint probability is bounded by the Fréchet–Hoeffding limits, max(0, Σp − (n−1)) and min(p). The product is a point inside that interval, not its floor
- Turkish Code of Obligations (Law no. 6098) art. 96, headed “Early performance” — same Official Gazette. Unless the contract or the circumstances show a contrary intention, the debtor may perform before the term expires. Early performance and partial performance are different things: the first is the whole obligation discharged sooner, the second is the obligation divided
- Turkish Code of Obligations (Law no. 6098) art. 84, headed “Partial performance” — Official Gazette 4 February 2011, no. 27836. Where the whole debt is certain and due, the creditor may refuse partial performance; if the creditor accepts it, the debtor may not withhold the part it has acknowledged. The provision is not mandatory
- Turkish Commercial Code (Law no. 6102) art. 23/1(a) — Official Gazette 14 February 2011, no. 27846. Where the buyer accepts partial delivery without reservation, its rights may be exercised only in respect of the undelivered part; termination remains available where the missing part destroys or materially weakens the purpose of the contract
How we choose sources, verify figures and date our pages is set out in how we source and verify what we publish. Spotted an error? Write to info@aksco.com.tr — verified errors are corrected.
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