The Batch-Size Trap at Corran Foods
Corran Foods produces a single chilled sauce in batches of 500 litres. Each batch incurs a setup cost of $1,800 (mostly cleaning and line changeover labour) and the annual demand is steady at 60,000 litres. Holding cost is $4.50 per litre per year, based on warehouse space and spoilage risk. The production manager currently runs 100 batches a year because 'smaller batches keep us flexible,' but the operations director argues the setup cost is being wasted. Separately, the finance team notes that the current 100-batch policy means average inventory of 250 litres plus a safety buffer of 200 litres. A supplier has offered to deliver pre-mixed base sauce at $0.60 per litre more, which would eliminate setup entirely but raise variable cost. The plant has spare capacity and no other use for the line.
1. Calculate the economic batch quantity and quantify the annual saving from moving to it, then assess whether the supplier's pre-mixed offer is financially preferable at the EBQ level of output.
Read the worked answer
EBQ = sqrt(2 × D × S / H) = sqrt(2 × 60,000 × 1,800 / 4.50) = sqrt(48,000,000) = 6,928 litres per batch (≈ 8.66 batches/year).
Current policy (100 batches):
- Setup cost = 100 × $1,800 = $180,000
- Average inventory = 500/2 + 200 = 450 litres → holding cost = 450 × $4.50 = $2,025
- Total relevant cost ≈ $182,025
At EBQ (8.66 batches):
- Setup cost = 8.66 × $1,800 = $15,588
- Average inventory = 6,928/2 + 200 = 3,664 litres → holding = $16,488
- Total ≈ $32,076
Saving ≈ $149,949 per year. The current policy is far from optimal; the manager's 'flexibility' argument has no quantified benefit here because demand is steady and capacity is spare.
Supplier offer: extra variable cost = 60,000 × $0.60 = $36,000. It removes setup ($15,588) and the cycle-stock holding cost but the safety buffer of 200 litres remains ($900). Net cost of the offer ≈ $36,000 − $15,588 − $15,588 ≈ +$4,824 worse. So at EBQ the supplier is not preferable; it only becomes attractive if setup costs rise or flexibility has real value. Recommend adopting EBQ and rejecting the offer, but test sensitivity to the $1,800 setup estimate.
2. The production manager claims smaller batches improve responsiveness. Under what conditions would that argument overturn the EBQ recommendation, and what data would you request to test it?
Read the worked answer
The EBQ model assumes deterministic, level demand and ignores stockout or changeover-response value. The flexibility argument holds only if:
- Demand is volatile or seasonal, so cycle stock cannot be planned - then the cost of stockouts (lost contribution, retailer penalties) may exceed extra setup cost.
- Shelf life is short enough that large batches cause spoilage before sale - check actual wastage rates by batch size.
- Changeover time creates a bottleneck: if the line is capacity-constrained, large batches may delay other products (not applicable here - single product, spare capacity).
Data to request: weekly demand variance and forecast error; spoilage/wastage records by batch size; any customer service-level penalties; actual setup time and whether it can be reduced (SMED) to lower S. If setup cost can be halved to $900, EBQ falls to ~4,899 litres, moving toward the manager's instinct - so the real lever is setup reduction, not batch policy alone.