Multi$-$Echelon Supply Chain Optimization

A company has two manufacturing plants, three distribution centers, and five retail stores. The goal is to determine the optimal transportation plan that minimizes total shipping costs while adhering to the following constraints:

$-$ Each plant has a maximum production capacity.

$-$ Each distribution center has a maximum throughput capacity.

$-$ Each retail store has a specific demand requirement.

Shipping Costs:

Plant Capacities:

$-$ Plant A: $700$ units

$-$ Plant B: $600$ units

Distribution Center Capacities:

$-$ Distribution $1$: $500$ units

$-$ Distribution $2$: $800$ units

$-$ Distribution $3$: $600$ units Multi$-$Echelon Supply Chain Optimization

Shipping Costs to Retail Stores:

Retail Store Demands:

$-$ Retail $1$: $200$ units

$-$ Retail $2$: $300$ units

$-$ Retail $3$: $400$ units

$-$ Retail $4$: $250$ units

$-$ Retail $5$: $350$ units Multi$-$Echelon Supply Chain Optimization

$1.$ Formulate the problem as a linear programming $($LP$)$ model, including:

$1.$ Decision variables for the number of units shipped from plants to distribution centers and from distribution centers to retail stores.

$2.$ Objective function $($minimize total transportation costs$).$

$3.$ Constraints $($plant capacities, distribution center capacities, and retail store demands$).$

$2.$ Write a Python script to solve the problem using the PuLP library.

$3.$ Output the results, including:

$1.$ Number of units shipped from each plant to each distribution center.

$2.$ Number of units shipped from each distribution center to each retail store.

$3.$ Total transportation cost.