Make-or-Buy and Constraint Analysis at a Kigali Beverage Plant
Umurava Beverages produces bottled juice. Its bottling line is the bottleneck, with 12,000 machine-hours available per month. Three products share the line:
| Product | Selling price (RWF) | Variable cost (RWF) | Machine hours per unit | Monthly demand (units) |
|---|---|---|---|---|
| Mango | 1,200 | 700 | 0.5 | 15,000 |
| Pineapple | 1,800 | 1,100 | 1.0 | 10,000 |
| Passion | 2,500 | 1,600 | 2.0 | 6,000 |
A contractor has offered to supply up to 8,000 units of Mango at RWF 850 per unit, freeing the bottling line. Fixed costs are RWF 4,000,000 per month and are unavoidable. The sales director wants to accept the offer because the contractor price (850) is below the current selling price.
1. Using a throughput (contribution per constraint) approach, determine the optimal production plan and whether the contractor offer should be accepted.
Read the worked answer
Step 1 - Contribution per unit and per machine hour:
| Product | Contribution/unit | Hours/unit | Contribution/hour | Demand hours |
|---|---|---|---|---|
| Mango | 500 | 0.5 | 1,000 | 7,500 |
| Pineapple | 700 | 1.0 | 700 | 10,000 |
| Passion | 900 | 2.0 | 450 | 12,000 |
Total hours demanded = 29,500; available = 12,000. The line is the binding constraint.
Step 2 - Rank by contribution per hour: Mango (1,000) > Pineapple (700) > Passion (450).
Step 3 - Allocate 12,000 hours:
- Mango: 7,500 hours → 15,000 units, contribution 15,000 × 500 = RWF 7,500,000
- Remaining 4,500 hours → Pineapple: 4,500 units, contribution 4,500 × 700 = RWF 3,150,000
- Passion: 0 units
- Total contribution = RWF 10,650,000
Step 4 - Evaluate the contractor offer: Buying Mango at 850 instead of making it saves 0.5 hours per unit. The relevant comparison is the cost of buying versus the cost of making plus the contribution forgone from the freed hours.
- Make: variable cost 700 + opportunity cost of 0.5 hours used on the next-best product (Pineapple at 700/hour → 350) = 1,050 effective cost.
- Buy at 850 < 1,050, so buying Mango is beneficial - but only because the freed hours can produce Pineapple.
Optimal plan with contractor: Buy 8,000 Mango (cost 850 each), freeing 4,000 hours. Make remaining 7,000 Mango (3,500 hours), then Pineapple with 8,500 hours → 8,500 units (capped by 10,000 demand).
Contribution: Pineapple 8,500 × 700 = 5,950,000; Mango made 7,000 × 500 = 3,500,000; Mango bought: resale contribution 8,000 × (1,200 − 850) = 2,800,000. Total ≈ RWF 12,250,000 - an improvement of RWF 1,600,000 over making all Mango.
Key judgement: The sales director's reasoning (850 < 1,200) is wrong because it ignores the constraint. The correct test is buy price versus make variable cost plus opportunity cost of the bottleneck.
2. Suppose the contractor can only supply 3,000 units. Recalculate the optimal plan and explain how the answer changes.
Read the worked answer
Constraint: Contractor supply limited to 3,000 Mango units, freeing 1,500 hours.
Re-optimise:
- Buy 3,000 Mango → make 12,000 Mango (6,000 hours), leaving 6,000 hours.
- Pineapple: 6,000 units (6,000 hours).
- Passion: 0.
Contribution:
- Mango made: 12,000 × 500 = 6,000,000
- Mango bought: 3,000 × (1,200 − 850) = 1,050,000
- Pineapple: 6,000 × 700 = 4,200,000
- Total = RWF 11,250,000
Compare with no contractor (RWF 10,650,000): still an improvement of RWF 600,000.
Why the answer changes: With limited contractor supply, the freed hours are fewer, so less high-ranking Pineapple can be produced. The marginal value of each freed hour remains 700 (Pineapple contribution/hour), so each bought Mango unit is worth buying as long as 850 < 700 + 350 = 1,050. The limit simply caps the gain.
General rule: Accept contractor supply up to the point where the buy price equals the make variable cost plus the contribution per hour of the next-best use of the freed hours. Here that ceiling is RWF 1,050 per Mango unit.