In short: A forecourt is a small set of tanks with a random drain, so fuel retail supply is the decision of when to send a compartmented vehicle and what to put in each compartment. The compartment constraint breaks generic inventory logic, because a delivery is a set of indivisible compartment loads rather than a freely chosen quantity. Delivery economics are dominated by a fixed cost per stop, which is what sets the real trade-off between run-out risk and cost per litre. The problem has a name and two decades of literature behind it, the petrol station replenishment problem in operations research.
The site ran dry on premium diesel at four on a Friday afternoon. The order had been placed for Saturday morning, which was the site's usual day, and the tank had four days of cover when the order went in. Thursday was warm, a competitor two junctions away went up by three pence, and the site sold half again its normal volume for two days running.
The emergency drop cost more than the margin on everything the site sold that week. The scheduling team's report for the month shows a run-out rate inside target and a delivery cost per litre that improved slightly, which is the normal pattern: the two numbers are managed by different people and they trade directly against each other.
A forecourt is a tank with a random drain
Strip a site to its planning object and it is a small set of tanks, each with a usable capacity considerably smaller than its nameplate, draining at a rate that varies day to day.
Take a 30,000 litre diesel tank. Below the pump suction level there is a retain of perhaps 1,500 litres that cannot be sold, partly because of the suction geometry and partly because you do not want to pull water and sediment through the filters. At the top, the fill limit sits around 95 percent to leave vapour space. Usable volume is therefore about 27,000 litres rather than 30,000, and that 10 percent difference matters because it comes straight out of the cover calculation.
The site sells 6,000 litres a day on average with a standard deviation of 1,400. Full to empty is 4.5 days of cover at the mean. At two standard deviations of demand over four days, the cover falls to about 3.5 days, and that is before any of the demand shifts that actually cause run-outs, which are competitor pricing moves, weather, roadworks, a local event, or a nearby site closing for maintenance.
The point of the arithmetic is that a forecourt has a very short buffer. Four days of cover in a consumer goods business would be tight; here it is normal, and it means the replenishment decision is made against a forecast with a horizon of days, at a site level, where the variance is large relative to the mean.
Demand at this granularity has strong day-of-week structure, weather sensitivity, and a price-position effect against local competition that can move volume by double digits within a day. Any site-level forecast that ignores the competitor price differential is missing one of its largest regressors.
The compartment constraint that breaks the tidy answer
Here is the constraint that makes fuel delivery different from almost every other replenishment problem, and it is the one that generic inventory logic gets wrong.
A road tanker is divided into compartments. A 40,000 litre vehicle might carry two compartments of 13,000 and two of 7,000. Each compartment holds one product, and it is filled at the terminal and discharged at the site. Part-loading a compartment is possible in some operations and prohibited or impractical in others, and even where it is allowed, the metering and reconciliation get harder.
So the deliverable quantity to a site is a sum of compartment sizes rather than a continuous number. You cannot deliver 21,400 litres of diesel because that is what the tank has room for. You can deliver 20,000 as 13,000 plus 7,000, or 26,000 as two thirteens, and the second one overfills.
That converts the loading decision into an assignment problem nested inside the routing problem: which compartments carry which product, to which sites, in which order, given that discharge order is constrained by how the vehicle is loaded and by the tank capacities waiting at the other end. Solving the route without solving the load produces schedules that the driver cannot execute, which is the fastest way to lose a planning system's credibility with an operations team.
The practical consequence for anyone specifying a system is that compartment structure has to be a first-class input. A tool that plans in litres and leaves the compartment allocation to the terminal is doing about half the job.
What a drop actually costs, per litre
The economics of delivery frequency are dominated by a fixed cost per stop, and the arithmetic is worth having on hand for the recurring argument about service levels.
Take a fully loaded cost of 180 per stop, covering the drive leg, the connection, the discharge time, the paperwork and the vehicle's share of the day. Deliver 27,000 litres and the cost is 0.67 per thousand litres. Deliver 13,000 and it is 1.38. Halving the drop size roughly doubles the delivery cost per litre.
Scale that to a site selling 2.2 million litres a year. At full drops it takes 81 deliveries a year, costing about 14,600. At half drops it takes 169, costing about 30,400. The difference is 15,800 a year on one site, and on a network of 200 sites it is over three million.
Against that sits the run-out cost, which has three parts and is usually estimated at only the first. Lost fuel margin during the outage, which on 1,500 litres at 6 pence is small. The emergency delivery, which carries a premium and disrupts the rest of the day's plan. And the shop basket and repeat visit effect, where a driver who found the site dry buys their coffee somewhere else this week and possibly next week too. That third term is the largest and the hardest to measure, and where a retailer has loyalty data it is measurable rather than guessable.
The two costs make a standard trade-off with an interior optimum. Cover too thin and you pay in run-outs and emergency drops; cover too generous and you pay in stops. What makes the fuel version awkward is that the optimum is a joint decision across sites, because the delivery cost per stop depends on which other sites are on the run.
The problem has a name and a literature
The combination of compartmented vehicles, tank capacities and consumption rates at each station has been studied under its own name for two decades. In the operations research literature it is the petrol station replenishment problem, formulated as delivering a divisible product from depots to stations over a planning horizon, and treating it as a generic routing exercise with fuel-shaped inputs throws away most of what is known about it.
Cornillier, Boctor, Laporte and Renaud published a heuristic for the multi-period version in the European Journal of Operational Research in 2008, and the broader family, where the supplier decides both the quantity and the timing rather than responding to orders, is the inventory routing problem surveyed by Coelho, Cordeau and Laporte in Transportation Science in 2014 under the title Thirty Years of Inventory Routing.
Three things from that literature transfer directly to an operating network.
The value is in the joint decision. Deciding how much each site needs and then routing the deliveries produces worse answers than deciding both together, because the quantity at one site changes which other sites fit on the run. The published gap between sequential and joint approaches is consistently material.
Deliberate early deliveries are efficient. An inventory routing solution regularly tops up a site well before it needs anything, because the vehicle was passing and the marginal cost of the stop is small. That behaviour looks wasteful to anyone monitoring days of cover and it is the source of much of the saving.
Consistency has a cost and it can be priced. Fixing drivers to territories and sites to delivery days makes execution easier and costs efficiency. The literature on consistent vehicle routing quantifies that trade-off, so the decision to run fixed days can be made with a number attached rather than by preference.
Where the supplier takes over the replenishment decision from the site entirely, the operating model questions that raises are covered in K2, and the underlying routing method is covered in X1.
Fixed delivery days are a decision with a price
Most networks run something close to a fixed pattern: this site gets Tuesdays and Fridays. It is easy to manage, drivers know the sites, and site staff know when to expect the vehicle.
The cost shows up in two places. Sites whose demand runs above pattern have to be topped up with smaller drops between scheduled visits, and sites below pattern receive part-loads that waste compartment capacity. Both erode the drop size economics computed above.
Quantify it on your own data before changing anything. Take a quarter of actual deliveries, compute the average fill ratio, meaning delivered volume as a share of available ullage at the moment of delivery, and look at the distribution. A network running at an average fill ratio of 70 percent is paying roughly 40 percent more in delivery cost per litre than one running at 95, and the gap between those two numbers is what dynamic scheduling is competing for.
Then look at the tail. The sites with the lowest fill ratios are usually a small group with either an unsuitable delivery pattern or a tank configuration that no longer matches their sales mix, and fixing the pattern on those alone captures a large share of the available saving without touching the rest of the network.
Wet stock reconciliation is the gate on all of it
Everything above assumes you know how much fuel is in each tank, and that number is less reliable than it looks.
The site's stock position is reconciled from three measurements: delivered volume from the tanker's meter or the delivery note, dispensed volume from the pump meters, and the tank gauge. The three rarely agree, and the variance gets investigated when it exceeds a threshold, on the assumption that a persistent loss means a leak or theft.
A large share of apparent variance is temperature. Fuel is bought and often sold on a volume basis, and volume changes with temperature. Diesel expands by roughly 0.083 percent per degree Celsius. A delivery loaded at a terminal at 20 degrees and dipped in a cold underground tank at 10 degrees will appear to have shrunk by about 0.83 percent, which on a 27,000 litre drop is 224 litres. That is larger than many leak detection thresholds, and it repeats on every delivery in the cold months.
So the first step in any wet stock programme is temperature compensation, converting all volumes to a standard reference temperature before comparing them. Without it, the reconciliation generates alarms with a seasonal pattern and the investigation effort goes into a physical phenomenon rather than into the sites that actually have a problem.
Once compensated, the residual variance is worth acting on. A persistent 0.3 percent unexplained loss on 2.2 million litres a year is 6,600 litres, which is a real number and a genuine signal of a meter calibration issue, a leak or a loss of product elsewhere.
The limit
Optimised replenishment schedules assume the network executes them. Sites have delivery time windows imposed by planning consent or by traffic, some sites cannot take a full vehicle at all because of access, drivers' hours are a hard legal constraint, and terminal loading racks have their own queues and operating hours. A plan that ignores any of those produces a saving on paper and a rota nobody can work.
The forecast is the other limit and it is the harder one. Site-level daily demand has a large irreducible component, because the events that move it, a competitor's price change, a road closure, weather, are either unobserved or observed too late. Improving the forecast helps up to a point and then stops, and after that the way to reduce run-outs is to make the replenishment system responsive rather than to make the forecast better: shorter lead times from terminal to site, live tank telemetry rather than daily dips, and the ability to re-plan the afternoon's runs at midday.
Telemetry is worth being specific about, because it is often the binding constraint on everything in this piece. A network with daily gauge readings is planning on information up to 24 hours old at a site with four days of cover. Hourly readings change the problem qualitatively, and the cost of retrofitting them is small against the numbers computed above.
Take a quarter of delivery records, compute delivered volume as a share of the ullage available at the moment each delivery started, and look at which sites sit in the bottom decile.