With one patient per batch, pooling disappears and safety stock stops being an available instrument, so the only buffers left are capacity, time and slack in the schedule. Three separate calendars have to line up for every patient, and the one that usually binds is apheresis at a small number of qualified centres rather than the manufacturing suite everyone models. Vein-to-vein time is dominated by queueing rather than by processing, and Kingman's 1961 approximation says the waiting term roughly triples when suite utilisation moves from 80% to 92%. Manufacturing failures generate fresh demand for both a collection and a slot, so reserved retry capacity belongs in the plan. The cryogenic shipper fleet is a closed loop whose size follows from Little's law, and it becomes the binding constraint more often than anyone expects.
The apheresis slot was booked for Tuesday. The manufacturing slot was booked seventeen days out on the strength of it. On Monday the patient's lymphocyte count came back too low to collect, the physician deferred by a week, and now there is a suite reserved for cells that do not exist.
Nobody else can use that slot. Two other patients are waiting for capacity four weeks out and neither of them has been collected either, because their collections were scheduled against the slots they were already given. The suite will sit idle, the deferred patient will go to the back of a queue, and none of this will appear in a capacity report that counts suite days rather than patient journeys.
The unit of supply is one named patient
Almost every technique in planning depends on things being interchangeable. Pooling reduces variability because demand for one unit can be met by any unit. Safety stock works because you can hold inventory before you know who wants it. Aggregation improves forecast accuracy because errors cancel across items that substitute for each other.
An autologous cell therapy has none of that. The starting material comes from one patient, the product returns to the same patient, and the identity link is carried through every step by a coding standard such as ISBT 128 that exists precisely to make substitution impossible. A batch that fails is not replaced from stock, because there is no stock, and there never can be.
What that removes is the instrument planners reach for first. The buffering logic covered elsewhere assumes you can hold units against uncertainty. Here the only things you can hold are capacity you have not sold, time you have not committed, and slack in a schedule. Every buffering decision has to be expressed in one of those three currencies, and the arithmetic is different for each.
Three calendars have to line up, and the one you model is rarely the one that binds
The slot people talk about is the manufacturing slot: a suite, a trained operator team, and the QC resource that will release the product at the end. That is the capacity most planning models represent, usually as a weekly start rate.
Two other calendars have equal standing. Apheresis capacity sits at the treating centre, which has a finite number of collection chairs, a qualification status for your product, and a schedule already committed to other therapies. Infusion capacity sits at the same centre and carries a further constraint, since lymphodepleting chemotherapy has to be given in a fixed window before the product arrives, which means the infusion date has to be settled before the product has been released.
The three calendars have to intersect inside a window measured in days, for each patient, individually. That makes this a scheduling problem with sequencing and resource constraints, the shape that job shop methods address, and the model has to represent all three resources or it will publish plans that the sites cannot execute. In practice the collection calendar binds more often than the suite, because qualified centres are few and their apheresis units serve stem cell transplant programmes that were there first.
The diagnostic is simple enough to run. For the last three months, count how many manufacturing slots went unused and record the reason. If most of the reasons trace back to collection scheduling rather than to demand, the capacity you have been arguing about is the wrong one.
Vein-to-vein time is mostly queueing
Break the interval into six segments: collection to shipment, outbound transit, waiting for a slot, manufacture, QC release and disposition, and return transit through thaw and infusion.
Two of those are fixed. Manufacture takes what the biology takes. QC release is bounded from below by the assays, and the long pole is usually sterility, since the compendial test in USP <71> runs a fourteen day incubation unless a validated rapid method has been put in place. Neither segment responds to management attention.
The waiting segment does, and it is where the variability lives. Little's law, from Little (1961), gives the relationship between the three quantities that matter: with four starts a week and an average five weeks in the system, there are twenty patients in process at any moment. That number tells you how much identity tracking, sample storage and coordination load the operation is carrying, and it grows with cycle time even when volume is flat.
Kingman's 1961 heavy traffic approximation is the one that changes decisions. The waiting term scales with utilisation divided by one minus utilisation. At 80% utilisation that factor is 4. At 92% it is 11.5. Pushing a suite from comfortably busy to nearly full multiplies the queueing component of vein-to-vein by roughly three, and it does so without any change in the process itself. The same convexity that a separate post describes for berth queues applies here, with the difference that the thing waiting is a patient with a defined clinical window.
The planning conclusion follows directly. A facility sized to run at high utilisation cannot hold a vein-to-vein commitment, and a commitment made in a commercial contract will be broken by arithmetic rather than by anyone's failure to execute.
Manufacturing failure generates its own demand
A run that misses specification consumes a slot, produces nothing, and creates fresh demand for both a new collection and a new slot. That makes failure a demand signal with a lead time attached rather than a yield adjustment on the end of a calculation.
Work the numbers. Four starts a week gives 208 runs a year. At an 8% failure rate that is roughly seventeen events, each requiring an apheresis appointment, a shipper, a slot, and a place in a queue the patient has already waited in once. Since the retry is clinically urgent, it takes priority, which means it displaces a scheduled start rather than filling a gap. Seventeen displacements a year is a meaningful share of a 208 slot calendar, and it is entirely predictable in aggregate while being unpredictable in timing.
The failure distribution is also correlated with the thing you would least like it to be correlated with. Starting material quality tends to be poorest in heavily pre-treated patients, and those are the patients whose clinical window is shortest. Failures cluster where the consequence of a delay is highest.
The policy that follows is to reserve capacity for retries explicitly rather than letting them displace scheduled starts. Hold a defined fraction of slots unsold on a rolling horizon, release them to new starts inside a short window if unused, and report the reserve as a named line in the capacity plan so that a commercial team asking for more starts can see what they are asking to spend. There is also a question to settle before any of this is planned, which is whether a run that misses one specification can still be supplied through a separate authorisation route. The answer changes the size of the reserve, and it is a regulatory affairs answer rather than a planning one.
Sizing the cryogenic shipper fleet as a closed loop
Dry vapour shippers are returnable assets moving round a cycle: dispatch to the collection site, hold there until the collection happens, loaded return, inbound receipt and queue, reconditioning and recharge, requalification, back into the pool. The fleet size follows from Little's law applied to that loop, using the full door to pool cycle rather than the transit leg.
Four outbound and four return movements a week with a three week end to end cycle puts around twenty four shipper legs in flight at any moment. Add cover for variance in the return leg, which is the least controlled part of the loop because it depends on a hospital shipping department, and add the units sitting in requalification. Buy twenty and the fleet becomes the binding constraint on start rate, which will show up as collections deferred for reasons that never enter a capacity model built around suites.
The static hold rating creates a second constraint that is easy to miss. A shipper rated for ten days of hold that arrives at a centre on a Thursday and waits through a weekend has consumed a third of its charge before anything is loaded into it. Dispatch timing is therefore part of the schedule rather than a logistics detail, and the planning system needs the dispatch date as a dependent task rather than a fixed offset. Temperature excursion handling once material is moving is a separate discipline covered elsewhere.
Chain of identity removes the optimiser's main move
When a constrained plan cannot be met, the standard move is to reallocate: take supply committed to a low priority demand and give it to a higher one. That move is unavailable here in both directions. The product is legally and physically bound to one patient, and the coding standard exists to enforce it.
The remaining degrees of freedom are dates and sequence. You can move which slot a patient occupies, defer a collection, expedite a release, or change the order in which runs enter the suite. You cannot change who gets what. Any planning model that represents this as a constrained allocation problem will produce plans that look feasible and cannot be executed, because the allocation variable it is optimising over does not exist in reality.
The data model consequence is worth stating plainly. The planning object is a patient journey with linked appointments sharing one identifier, rather than a stock keeping unit at a location with a quantity on it. Systems that cannot represent that will end up with the real schedule living in a spreadsheet next to them, which is where it usually is. Resolution of genealogy after a quality event is handled elsewhere.
Allogeneic gives inventory back and adds a different constraint
Off the shelf allogeneic products restore the instruments the autologous case removed. There is inventory, so there is safety stock, and demand at a treatment centre can be met from any dose in the pool.
The constraint that replaces identity is the donor lot. A lot yields a finite number of doses, carries its own potency profile and its own expiry, and lots are not identical to each other. The problem becomes allocation across a small number of large, non-interchangeable lots with a shelf-life disposition question attached, which is the territory a separate post covers. Demand at the site level stays intermittent, so the forecasting methods that suit sparse series apply, and a separate post covers those.
Where this stops
With a hundred treated patients a year, there is no statistical demand forecast worth having. The variance is dominated by site activation dates, referral patterns at individual centres, and reimbursement decisions in individual countries, and none of those appear in shipment history. The honest forecast is a bottom-up model of the site pipeline with clinician judgement in it, reviewed monthly, and it will be wrong at the site level even in the months when the national total comes out close.
The failure rate that sizes the retry reserve is estimated on a small denominator. Three failures in forty runs supports a range rather than a point, and a reserve built on it should be presented as a range with the sample size next to it. Anyone quoting a failure rate to one decimal place from fewer than a hundred runs is describing noise.
The queueing arithmetic carries an assumption of its own. Kingman's approximation describes a system in steady state, and a product in launch ramp is not in steady state. During a ramp the arrival rate is climbing and the queue behaves worse than the formula suggests, which argues for planning the ramp at lower utilisation than the steady state target and letting utilisation rise as arrivals stabilise.
What planning can do here is narrower than what it does elsewhere, and predicting enrolment sits outside it. The work that pays is making the binding constraint visible, keeping the three calendars honest with each other, and turning a vein-to-vein promise into a number somebody has checked against the arithmetic.
Instrument the six segments of vein-to-vein for your last fifty patients and plot the distribution of each segment rather than its mean, because the segment with the widest spread is the one setting the promise you can safely make.
More on this in industry on the DemandLabs platform.
