GATE ME 2024 Set 1 — Question 65
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Industrial Engineering → Operations Research → Transportation & Assignment
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Question
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.
The optimal cost of satisfying the total demand from all retailers is _____ rupees (answer in integer).
| 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 |
Correct answer
12300 to 12300
Solution
This is a balanced transportation problem where total capacity () equals total demand (). Since each supplier's capacity and each retailer's demand are identical (300 units), this problem is equivalent to an assignment problem where we need to assign one supplier to exactly one retailer to minimize the sum of unit costs.Using the Hungarian method or inspection to find the minimum unit cost sum:Unit Cost Matrix:Let's test the assignment:
Total Optimal Cost = rupees.
- Supplier A to Retailer I: Cost = 11
- Supplier B to Retailer III: Cost = 7
- Supplier C to Retailer II: Cost = 14
- Supplier D to Retailer IV: Cost = 9
- Supplier A to Retailer I: Cost = 11
- Supplier B to Retailer II: Cost = 10
- Supplier C to Retailer IV: Cost = 11
- Supplier D to Retailer III: Cost = 11
- Supplier B to Retailer I: Cost = 5
- Supplier D to Retailer IV: Cost = 9
- Supplier C to Retailer II: Cost = 14
- Supplier A to Retailer III: Cost = 19
Total Optimal Cost = rupees.
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