GATE 2024 ME – Question 65
In a supplier-retailer supply chain, the demand of each retailer, the capacity of each supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain.
| Retailer I | Retailer II | Retailer III | Retailer IV | Capacity | |
|---|---|---|---|---|---|
| Supplier A | 11 | 16 | 19 | 13 | 300 |
| Supplier B | 5 | 10 | 7 | 8 | 300 |
| Supplier C | 12 | 14 | 17 | 11 | 300 |
| Supplier D | 8 | 15 | 11 | 9 | 300 |
| Demand | 300 | 300 | 300 | 300 |
The optimal cost of satisfying the total demand from all retailers is _____ rupees (*answer in integer*).
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Correct answer: 12300
Explanation
Every capacity and every demand is 300, so the problem is an assignment problem in blocks of 300: the optimum sends each supplier's whole 300 to one retailer. Trying the 24 possible assignments, the cheapest is A to I (11), B to III (7), C to II (14) and D to IV (9), a total of $11 + 7 + 14 + 9 = 41$ rupees per unit, so the cost is $41 \times 300 = 12300$ rupees.