Paediatric Paracetamol: Two Pack Options, One Budget
The paediatric ward of your hospital has 45 children on the current chart, and the ward protocol fixes paracetamol at 180 mg per dose, four doses a day, for four days, for every one of them. The store has two possible packs. Option 1: paracetamol suspension 120 mg/5 mL in 60 mL bottles at ₹42 per bottle. Option 2: paracetamol suspension 250 mg/5 mL in 100 mL bottles at ₹95 per bottle. The pharmacy applies a 5 per cent buffer on every ward issue for spillage and breakage, and always rounds up to whole bottles. Only 5 mL oral syringes graduated at 0.2 mL intervals are available. Separately, the average hospital consumption of the 60 mL bottle is 900 bottles a month, the supplier's lead time is 12 days, the pharmacy holds a safety stock of 150 bottles, and 300 bottles are on the shelf today. The annual indent is being prepared.
1. Work out the volume per dose and per child, then decide which pack is cheaper for the full ward course, including the 5 per cent buffer.
Read the worked answer
Option 1 - 120 mg/5 mL.
- Dose volume = 180 ÷ 120 × 5 = 7.5 mL per dose.
- Per child per day = 7.5 × 4 = 30 mL.
- Per child for four days = 30 × 4 = 120 mL, which is exactly two 60 mL bottles.
- Ward total = 45 × 2 = 90 bottles; with a 5 per cent buffer, 90 × 1.05 = 94.5, rounded up to 95 bottles.
- Cost = 95 × ₹42 = ₹3,990.
Option 2 - 250 mg/5 mL.
- Dose volume = 180 ÷ 250 × 5 = 3.6 mL per dose.
- Per day = 14.4 mL; for four days = 57.6 mL, so one 100 mL bottle covers each child.
- Ward total = 45 bottles; with buffer, 45 × 1.05 = 47.25, rounded up to 48 bottles.
- Cost = 48 × ₹95 = ₹4,560.
Decision: Option 1 is cheaper by ₹570 for this course, and it avoids leaving roughly 42 mL of unused suspension per child, which is a real waste and a temptation for unsupervised re-use at home. Practical caveat: 7.5 mL needs two draws or a 10 mL syringe, whereas 3.6 mL is measurable exactly on the 5 mL syringe, since 3.6 is a multiple of 0.2. If the ward only has 5 mL syringes, measure 7.5 mL as 5 mL plus 2.5 mL rather than eyeballing it.
2. Calculate the reorder level for the 60 mL bottle and state how many bottles should be indented, showing the assumption behind the indent quantity.
Read the worked answer
Reorder level. Daily usage = 900 ÷ 30 = 30 bottles. Lead-time demand = 30 × 12 = 360 bottles. Reorder level = lead-time demand + safety stock = 360 + 150 = 510 bottles.
Interpretation. When the shelf stock falls to 510 bottles, a fresh order must already be on its way; below 510 the pharmacy is eating into the safety stock and is one delayed delivery away from a stock-out.
Indent quantity. A common and defensible convention is to indent enough to cover the review period plus the lead time, plus safety stock, less what is on hand. Taking one month as the review period: required = 900 (one month's usage) + 360 (lead-time usage) + 150 (safety stock) − 300 (on hand) = 1,110 bottles.
Why the assumption must be stated. The figure depends entirely on the review period. If the store reviews stock fortnightly, the indent becomes 450 + 360 + 150 − 300 = 660 bottles. Presenting 1,110 without saying "one-month review" would be an unjustified number, and in an audit the assumption is the first thing that will be questioned. Note also that 300 bottles is already below the reorder level of 510, so the order should be treated as urgent rather than routine.
3. A colleague claims that Option 1 needs 45 bottles and Option 2 needs 90 bottles. Identify the error in that reasoning.
Read the worked answer
The colleague has inverted the two answers and has also ignored the buffer.
Correct figures without buffer: Option 1 needs 90 bottles (two per child × 45 children); Option 2 needs 45 bottles (one per child × 45 children).
Where the inversion comes from. The colleague is probably comparing the strengths (120 mg/5 mL against 250 mg/5 mL) and reasoning that the weaker preparation must need twice as many bottles - that part is right - but then attaching the doubled figure to the stronger pack. A second likely error is dividing the total dose by the bottle strength in mg per bottle and then halving once too often.
A safe check. Total paracetamol needed by the ward = 180 mg × 4 doses × 4 days × 45 children = 129,600 mg. Option 1: 95 bottles × 60 mL × 24 mg/mL = 136,800 mg, comfortably above the requirement. Option 2: 48 bottles × 100 mL × 50 mg/mL = 240,000 mg, far more than needed - which is precisely why it is wasteful. Whenever two packs are compared, computing the total milligrams required and the total milligrams purchased is the fastest way to expose an inverted answer.