Health Camp Catering Contract Under Demand Uncertainty
A community health camp expects between 450 and 650 visitors, with the organising committee estimating a 20% chance of 450, a 50% chance of 550, and a 30% chance of 650. Two caterers have submitted bids. Vendor A charges a fixed ₹18,000 for setup and ₹85 per meal prepared. Vendor B charges a fixed ₹9,000 and ₹120 per meal prepared. The camp must guarantee a meal count in advance; unused meals incur a ₹30 disposal charge, while any shortfall costs ₹150 per meal in emergency arrangements. The committee has a hard budget ceiling of ₹75,000 and wants to avoid visible shortages. The camp runs a single day, and registration closes 48 hours before the event, leaving little room to revise the guaranteed count. The finance volunteer has to recommend a vendor and a guaranteed meal count, and then defend the recommendation to a treasurer who dislikes both waste and public shortages.
1. Compare the two vendors at an attendance of 550 and find the attendance level at which the cheaper vendor changes. Show the equations.
Read the worked answer
At 550 meals:
- Vendor A: ₹18,000 + 85 × 550 = ₹18,000 + ₹46,750 = ₹64,750
- Vendor B: ₹9,000 + 120 × 550 = ₹9,000 + ₹66,000 = ₹75,000
Vendor A is cheaper by ₹10,250 at 550.
Set the costs equal to find the switch point:
18,000 + 85q = 9,000 + 120q
9,000 = 35q
q = 257.14
So Vendor B is cheaper only below about 258 meals; Vendor A is cheaper above that. Because every plausible attendance figure here is at least 450, the fixed-cost advantage of Vendor B is overwhelmed by its higher variable cost. The recommendation should therefore start from Vendor A and focus on the guarantee quantity.
2. Using Vendor A and the probability estimates, calculate the expected total cost for guaranteed counts of 450, 550 and 650. Recommend a guarantee and check the budget.
Read the worked answer
For any guarantee q, the base cost is ₹18,000 + 85q. Add expected waste at ₹30 per unused meal and expected shortfall at ₹150 per missing meal.
| Guarantee | Base cost | Expected penalty | Expected total |
|---|---|---|---|
| 450 | ₹56,250 | 0.5×100×150 + 0.3×200×150 = ₹16,500 | ₹72,750 |
| 550 | ₹64,750 | 0.2×100×30 + 0.3×100×150 = ₹5,100 | ₹69,850 |
| 650 | ₹73,250 | 0.2×200×30 + 0.5×100×30 = ₹2,700 | ₹75,950 |
A guarantee of 550 has the lowest expected total cost, ₹69,850, and it remains under the ₹75,000 ceiling. A guarantee of 450 is cheaper in base cost but creates a 50% chance of a 100-meal shortfall and a 30% chance of a 200-meal shortfall, which is operationally risky for a health camp. A guarantee of 650 nearly eliminates shortage risk but exceeds the budget on an expected basis and creates waste in 70% of scenarios. Recommend 550 meals with Vendor A.
3. Suppose the committee insists on a guarantee of 650 to avoid any shortage. What is the expected cost and the trade-off? Is that insistence justified?
Read the worked answer
At q = 650, the expected total is ₹75,950, which is ₹950 above the hard ceiling. The expected disposal penalty is ₹2,700, and the probability of at least some waste is 0.2 + 0.5 = 0.7.
Compared with q = 550:
- Extra base cost: ₹73,250 − ₹64,750 = ₹8,500
- Expected shortfall falls from ₹4,500 to ₹0, a saving of ₹4,500
- Expected waste rises from ₹600 to ₹2,700, an extra cost of ₹2,100
- Net expected increase: ₹8,500 − ₹4,500 + ₹2,100 = ₹6,100
So the 650 guarantee buys protection against a 100-meal shortage in the 650-visitor scenario, but it does so at a net expected cost of about ₹6,100 and breaches the budget. It is not justified unless the committee treats any visible shortage as unacceptable at almost any cost. Even then, the decision should be recorded as an explicit risk choice, not presented as the cost-minimising option.