Module6

Question 1

Capacitated Plant Location Model

Answer 1

• (decides on?) Location and capacity allocation of facilities.
• Parameters:
  – Fixed and variable costs.
  – Capacities and demands.
  – Transportation costs.
• Decision Variables:
  – Binary indicator for facility status (open/closed).
  – Quantities shipped between facilities and regions.

Question 2

SunOil Problem

Answer 2

Scenario:
- SunOil explores centralisation vs decentralisation for petrochemical plants.
- Options:
- Large plants for economies of scale.
- Regional plants to minimise transport costs.

Costs: Include production, inventory, and transportation.
Capacities: Low (10M units) or high (20M units).

Question 3

Capacitated Plant Location with Single Sourcing

Answer 3

Key Features:
- Assign each demand region to a single plant.
- Objective: Minimise total fixed, production, and transportation costs.
- Constraints:
- Each region served by one plant.
- Plant capacity limits.

Question 4

Gravity Location Model

Answer 4

Approach:
- Use grid points as potential facility locations.
- Objective: Minimise transportation costs by finding the gravity centre.

Inputs:
- Customer coordinates and demand.
- Distance and shipping cost per unit.

Question 5

Minimum Spanning Tree Problem

Answer 5

Objective: Minimise total length of links in a network.
Applications:
- Telecommunications and transportation networks.
- Power lines and pipeline systems.
Algorithm:
1. Start with the cheapest link.
2. Add links to unconnected nodes until all nodes are connected.

Question 6

Travelling Salesman Problem (TSP)

Answer 6

Objective: Find the shortest route visiting each location exactly once and return to the start.

Heuristic Methods:
- Nearest neighbour: Select the closest unvisited node iteratively.
Challenges:
- NP-complete problem with factorial growth in routes.