Throughput Accounting at a Furnace Bottleneck: Product Mix, Special Order and Capacity Purchase
Apex Alloy Forgings runs a single heat-treatment furnace that constrains the whole plant; 3,500 furnace hours are available each month and no subcontracting is possible. Three products share the furnace. Product X sells at ₹900, uses ₹320 of material and ₹180 of other variable cost, and needs 0.5 furnace hours; monthly demand is 2,000 units. Product Y sells at ₹1,400, uses ₹560 of material and ₹260 of other variable cost, and needs 1.0 furnace hour; demand is 2,500 units. Product Z sells at ₹1,900, uses ₹820 of material and ₹300 of other variable cost, and needs 1.25 furnace hours; demand is 1,600 units. Total factory operating expense is ₹28 lakh a month and is treated as fixed. The marketing head has always ranked products by contribution per unit and is puzzled that the profit the plant actually reports is far below his plan. A customer has also asked for 400 units of Y at ₹1,150 with a modified specification.
1. Determine the optimum monthly product mix and profit under throughput accounting, and reconcile the result with the mix the marketing head would choose on contribution per unit.
Read the worked answer
Throughput per unit and per furnace hour (throughput = sales less material only; all factory cost treated as fixed):
- X: 900 − 320 = 580; ÷ 0.5 h = ₹1,160 per hour
- Y: 1,400 − 560 = 840; ÷ 1.0 h = ₹840 per hour
- Z: 1,900 − 820 = 1,080; ÷ 1.25 h = ₹864 per hour
Ranking: X, then Z, then Y. Allocate 3,500 hours: X 2,000 × 0.5 = 1,000 h; Z 1,600 × 1.25 = 2,000 h; 500 h remain for 500 units of Y.
Throughput = (2,000 × 580) + (1,600 × 1,080) + (500 × 840) = 11,60,000 + 17,28,000 + 4,20,000 = ₹33,08,000. Less ₹28,00,000 = profit ₹5,08,000.
Marketing head's mix ranks by contribution per unit: Z (1,080), Y (840), X (580). Z 2,000 h, then Y 1,500 units = 1,500 h, X nil. Throughput = 17,28,000 + 12,60,000 = ₹29,88,000, profit ₹1,88,000.
The throughput policy is better by ₹3,20,000 because it maximises throughput per scarce hour, not per unit sold. Robustness check: deducting the other variable costs before ranking gives X 800, Z 624, Y 580 per hour - the same order - so the conclusion holds even if power and consumables are treated as variable.
2. Evaluate the request for 400 units of Y at ₹1,150, given two production options: the modified specification needs 1.4 furnace hours per unit; alternatively a cheaper substitute material (₹120 less per unit) can be used, but it needs 1.6 furnace hours.
Read the worked answer
The test is throughput per bottleneck hour against the value of the hours displaced, not the price per unit.
Option A - modified specification: throughput = 1,150 − 560 = ₹590 per unit; per hour = 590 ÷ 1.4 = ₹421 per hour. Option B - cheaper material: material 560 − 120 = 440, so throughput = 1,150 − 440 = ₹710; per hour = 710 ÷ 1.6 = ₹444 per hour.
Value of the displaced hours. The plant is capacity-constrained and Y is the marginal product (500 of 2,500 units are being made). Every hour given to this order displaces Y production worth ₹840 of throughput per hour.
- Option A: 400 × 1.4 = 560 h; loss = 560 × (840 − 421) = ₹2,34,640
- Option B: 400 × 1.6 = 640 h; loss = 640 × (840 − 444) = ₹2,53,440
Recommendation: reject both. The ₹1,150 price looks attractive against Y's normal ₹1,400, but the rework consumes the scarce resource faster than the price premium compensates. If management insists on accepting for strategic reasons (new customer, future volume), Option A is the less damaging route and the shortfall should be disclosed as a deliberate ₹2.3 lakh investment, not reported as profit. Accept only if the furnace has genuinely idle hours in the delivery window.
3. The furnace supplier offers 500 additional hours next month for a fixed charge of ₹2,90,000. Advise whether to take it, and state the conditions attached to your advice.
Read the worked answer
Cost per incremental hour = 2,90,000 ÷ 500 = ₹580.
The hours would go to Y, the only product with unmet demand (2,000 of 2,500 units are currently unserved). Y generates ₹840 of throughput per furnace hour, so each purchased hour adds 840 − 580 = ₹260.
Gain = 500 × 260 = ₹1,30,000 for the month - accept.
Conditions that must hold before signing:
- Y demand is real and firm at ₹1,400; if the customer negotiates, the ₹840 per hour falls and the margin with it. At a price below ₹1,140 the extra hours cease to pay.
- The hours are genuinely additional and available in the month in which Y demand exists; unusable hours are a ₹2,90,000 loss.
- Y must not be constrained by a second resource (forging press, skilled welders, inspection). If it is, the true gain is set by that resource, not by the furnace.
- The ₹2,90,000 is a one-off fixed charge, not the first instalment of a lease; if it recurs or carries a commitment period, evaluate it over the whole term against expected Y demand.
- Capacity bought to serve one product should not become a reason to keep loss-making products in the mix later; the furnace will again become the constraint.
If the extra capacity is expected to be available permanently and Y demand is durable, buying capacity alters the long-run mix decision and should be reviewed together with pricing - the ₹1,30,000 is the one-month answer, not necessarily the strategic one.