A manufacturing business making 50kg woven polypropylene rice sacks needs to decide how much to produce next month, but doesn't know exactly how much customers will buy.
Produce too little, and it may run out of stock, lose sales, and potentially lose customers.
Produce too much, and cash may be tied up in inventory.
So what quantity should be produced?
The problem
PrimeSack Industries Ltd. manufactures woven polypropylene sacks for rice mills, grain merchants, feed producers and agricultural distributors.
One of its important products is the 50kg plain PP woven rice sack.
The company has noticed that demand has been increasing, but it isn't constant throughout the year.
Management also knows that September tends to be a strong month.
The production manager wants to produce aggressively to avoid stockouts.
The finance manager is concerned about tying up working capital in excess inventory.
The company therefore needs to decide:
How many sacks should we produce for September 2026?
At the end of August, the company already has:
6,500 sacks in finished-goods inventory.
Normal production capacity is:
48,000 sacks per month.
Overtime can increase capacity to approximately 55,000, but at an additional ₦18 per sack.
There is also a meaningful difference between being short and being long.
The company estimates that every unfulfilled sack costs approximately ₦95 in contribution, while carrying an additional sack for a month costs approximately ₦7.50.
That difference becomes very important.
First, we need to understand demand
The company provided 30 months of historical demand.
The data showed two important characteristics.
Demand is increasing
The underlying trend is approximately:
+186 sacks per month.
Demand is seasonal
Demand tends to rise during the latter part of the year.
September and October are particularly strong months.
This means that simply taking the average of the previous 30 months would ignore important information.
Instead, I fitted a model incorporating both trend and seasonality.
The resulting September forecast was:
36,705 sacks
At first glance, we might be tempted to say:
“There we go. Produce 36,705.”
But that would be an incomplete analysis.
A forecast is not a guarantee
A forecast is our best estimate of what will happen.
It isn't what will happen.
So we also need to understand the uncertainty surrounding the forecast.
The estimated demand distribution for September was approximately:
D∼N(36,705,373)
In simpler terms:
expected demand: 36,705 sacks
estimated standard deviation: 373 sacks
The resulting 95% forecast range was approximately:
35,693 to 37,717 sacks.
That is useful information, but it still doesn't tell us exactly how much to produce.
Because there is another question:
How costly is it to be wrong?
Being short isn't the same as being long
Suppose we produce too few sacks. The company estimates that every unfulfilled sack costs approximately:
₦95
in lost contribution and associated customer consequences.
Now suppose we produce one sack too many. The estimated carrying cost for that sack for one month is only:
₦7.50.
So the business isn't equally harmed by the two errors.
Being short is much more expensive than being slightly long. That means it would be irrational to simply target the 50th percentile of demand.
We should deliberately carry some additional protection against higher-than-expected demand.
This is where the newsvendor model becomes useful.
Turning uncertainty into a production decision
The model compares the cost of underestimating demand with the cost of overestimating it.
The critical ratio is:
Cu/(Cu+Co)
where:
Cu = cost of being understocked
Co = cost of being overstocked
For PrimeSack:
95/(95+7.50)=0.9268
or approximately:
92.68%
That means the economically appropriate target isn't the average expected demand.
We're looking for approximately the 92.68th percentile of the demand distribution.
For the fitted normal distribution, that corresponds to approximately:
z=1.4526z=1.4526
Therefore:
36,705+(1.4526×373)≈37,247
So the business should aim to have approximately:
37,247 sacks available
for September.
But remember:
The company already has 6,500.
Therefore:
37,247−6,500=30,747
Recommended production: 30,747 sacks
No overtime is required.
Why isn't the recommendation 36,705?
This is where the analysis becomes interesting.
The forecast says:
We expect to need about 36,705 sacks.
The inventory decision says:
We want approximately 37,247 available because demand could be higher than expected and the cost of a stockout is much greater than the cost of carrying some additional inventory.
And the company already owns 6,500 of those sacks.
So it doesn't need to manufacture the entire forecast.
This is a subtle but important distinction:
Forecasted demand and required production are not the same thing.
Inventory that already exists is part of the supply available to satisfy that demand.
What happens if management chooses differently?
We can compare the recommended decision with several alternatives.
| Production Plan | PRoduction | Expected Cost |
|---|---|---|
| Conservative | 26,000 | 399,475 |
| Produce around forecast | 30,205 | 15,271 |
| Recommended | 30,747 | 5,317 |
| Aggresive/Overtime | 55,000 | 311,963 |
The conservative option exposes the company to substantial stockout costs.
The aggressive option eliminates most stockout risk, but creates a large excess-inventory position and incurs overtime costs.
The recommended quantity provides the best balance given the company's estimated economics.
The important thing isn't that 30,747 is universally the correct number.
It is correct for this business, given these demand characteristics and these costs.
Change the economics, and the answer changes.
What if our assumptions are wrong?
This is where I think analysis becomes much more useful than simply producing a forecast.
We tested the recommendation against several scenarios.
What if stockout costs are different?
If the true stockout cost were somewhere between ₦50 and ₦300 per sack, the recommended production quantity would only move from approximately 30,625 to 30,941 sacks.
The decision is therefore not particularly sensitive to the exact estimate of the stockout cost.
What if demand is substantially more volatile?
Even if actual demand volatility were 2–3 times the model's estimate, the recommended production quantity would rise only to approximately 31,800 sacks.
It would still remain within normal production capacity.
What if demand is 10% higher than forecast?
This is more serious.
Demand would be around:
40,400 sacks.
If the company had rigidly committed to producing only 30,747 sacks, the expected cost would rise substantially, to approximately ₦297,000, and a stockout would become highly likely.
This reveals an important operational recommendation.
Don't treat the initial production decision as the end of the analysis.
The company should review actual order flow during September.
If demand is tracking substantially above expectations, the business can use overtime production to respond.
The better strategy is therefore dynamic
The recommendation isn't really:
“Produce 30,747 sacks and forget about September.”
It's:
Before September
Produce approximately 30,747 sacks.
During September
Monitor incoming orders and demand.
If demand deviates materially from the forecast
Update the forecast and production requirement.
If necessary
Use overtime capacity to protect against an emerging shortage.
This is much closer to how a real business should use forecasting.
The forecast isn't there to predict the future perfectly.
It is there to help the business make a better decision before the future becomes known.
The real lesson
At first, the question looked simple:
“How many sacks will we sell next month?”
But that's actually not the question management needs answered.
The real question is:
“How much should we produce today, given that we don't know exactly how much customers will want tomorrow?”
Those are very different problems.
A forecast answers the first.
Decision analysis answers the second.
And that's why simply saying:
“Our forecast is 36,705, so produce 36,705”
would have been incomplete.
We had to consider:
the expected demand;
the uncertainty around that demand;
existing inventory;
production capacity;
overtime costs;
warehouse constraints;
the cost of stockouts;
the cost of excess inventory;
and how the decision could change as new information arrives.
Only then could we arrive at a production recommendation.
The forecast wasn't the decision
This is perhaps the most important lesson from the case.
Forecasting tells you what might happen.
It doesn't automatically tell you what you should do.
A business has to combine the forecast with its own economics and constraints.
For PrimeSack Industries, that meant:
Expected September demand: 36,705
Target inventory: 37,247
Existing inventory: 6,500
Recommended production: 30,747 sacks, because given the information available, it represents the economically appropriate amount of risk for this business.
And that's ultimately what good quantitative analysis should do.
It shouldn't simply give a business more numbers.
It should help the business make a better decision.