Facility Location Optimization Project

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Problem

Simple facility location model: given a set of plants and a set of warehouses, with transportation costs between them, this example finds the least expensive set of plants to open in order to satisfy product demand. This example demonstrates the use of MIP starts — the example computes an initial, heuristic solution and passes that solution to the MIP solver.

Objective

Aim to minimize the combined fixed and transportation costs by deciding which of five plants to keep open while satisfying four warehouses’ demands.

What to Do

By considering data Gather input data: plant capacities, fixed opening costs, warehouse demands, and per-unit transport costs.

Formulate a mixed-integer programming model:

1. Binary “open” variables for each plant

2. Continuous “transport” variables for shipments from plants to warehouses

3. Objective: minimize fixed costs + transport costs

Constraints:

1. Each warehouse’s demand must be exactly met

2. Shipments from a plant cannot exceed its capacity if it’s open

3. Provide a warm start by closing the highest-cost plant initially.

4. Solve the model with an MIP solver (e.g., Gurobi) and inspect the solution.

Result

Total minimum cost: $210,500

Closed plant: 2

Open plants and shipping plan:

Plant 0 → Warehouse 2 (14k), Warehouse 3 (6k)

Plant 1 → Warehouse 0 (14k), Warehouse 3 (8k)

Plant 3 → Warehouse 0 (1k), Warehouse 1 (18k)

Plant 4 → Warehouse 3 (6k)