Problem 3
Consider a scenario in which a company operating in the Sultanate of Oman manages multiple factories,
each with a designated supply capacity. These factories play a crucial role in providing goods to various
distribution centers scattered across the country, each having specific demand requirements. The
transportation costs incurred while moving goods from different factories to diverse distribution centers
vary based on the distances between them. The factories are strategically situated at different locations in
Oman, identified as F1, F2, ..., Fm, with m representing the total number of factories. Each factory,
denoted as Fi, possesses a distinct supply capacity denoted as Si. Similarly, the distribution centers are
dispersed throughout Oman, labeled as D1, D2, .., Dn, with n representing the total number of distribution
centers. Each distribution center, denoted as Dj, has a specified demand denoted as Dj. The distance
between a factory Fi and a distribution center Dj is symbolized as Dij. The cost associated with
transporting one unit of goods from factory Fi to distribution center Dj is directly proportional to the
distance Dij. The objective is to determine the optimal distribution plan that satisfies the demands at the
different distribution centers at minimum cost, without violating either the supply or demand constraints.
This involves deciding how many goods to transport from each factory Fi to each distribution center Dj.
Required:
Provide a network representation for this transportation problem.
Complete the problem description and provide the data assumptions to create a specific instance of
this transportation problem. (Refer to the hint below)
Formulate a Linear Programming (LP) Model applicable to determining the optimal distribution plan.
(Write the Mathematical Model using the Word Math Editor)
Use Excel Solver to solve the Linear Programming Model. Present the optimal solution output and the
sensitivity analysis report. Submit the Excel file containing both the solution and the sensitivity
analysis report along with the project report.
Use the Python CVXPY Optimization Library to solve the Linear Programming Model. Implement
the LP model in both explicit and matrix forms.
Hint:
To derive an instance of this transportation problem, the following data assumptions need to be made:
Supply Capacity: Each factory Fi has a known supply capacity Si. This is the maximum amount of
goods that the factory can produce.
Demand: Each distribution center Dj has a known demand, Dj. This is the amount of goods that the
distribution center needs.
Distances: The distances Dij between factories and distribution centers are known and do not change.
The distances can be obtained directly from Google Maps or calculated based on the Euclidian distance
between each factory Fi and each distribution center Dj.
Transportation Cost: The cost of transporting one unit of goods from factory Fi to distribution
center Dj is directly proportional to the distance Dij between them. This assumes that the cost
increases linearly with distance, and that the cost per unit distance (e.g., kilometers) is known.
Problem 3
Consider a scenario in which a company operating in the Sultanate of Oman manages multiple factories each with a designated supply capacity.These factories play a crucial role in providing goods to various distribution centers scattered across the country, each having specific demand requirements. The transportation costs incurred while moving goods from different factories to diverse distribution centers vary based on the distances between them.The factories are strategically situated at different locations in Oman, identified as F1, F2,., Fm, with m representing the total number of factories. Each factory denoted as Fi, possesses a distinct supply capacity denoted as Si. Similarly, the distribution centers are dispersed throughout Oman,labeled as Dl,D2,..,Dn,with n representing the total number of distribution centers.Each distribution center, denoted as Dj, has a specified demand denoted as Dj. The distance
between a factory Fi and a distribution center Dj is symbolized as Dij. The cost associated with
transporting one unit of goods from factory Fi to distribution center Dj is directly proportional to the distance Dij. The objective is to determine the optimal distribution plan that satisfies the demands at the
different distribution centers at minimum cost, without violating either the supply or demand constraints This involves deciding how many goods to transport from each factory Fi to each distribution center Dj.
Required:
1.Provide a network representation for this transportation problem. 2. Complete the problem description and provide the data assumptions to create a specific instance of this transportation problem.Refer to the hint below 3. Formulate a Linear Programming (LP) Model applicable to determining the optimal distribution plan (Write the Mathematical Model using the Word Math Editor) 4. Use Excel Solver to solve the Linear Programming Model. Present the optimal solution output and the sensitivity analysis report. Submit the Excel file containing both the solution and the sensitivity analysis report along with the project report. 5. Use the Python CVXPY Optimization Library to solve the Linear Programming Model. Implement the LP model in both explicit and matrix forms.
Hint: To derive an instance of this transportation problem,the following data assumptions need to be made
Supply Capacity: Each factory Fi has a known supply capacity Si. This is the maximum amount of goods that the factory can produce. Demand: Each distribution center Di has a known demand.Dj.This is the amount of goods that the distribution center needs Distances: The distances Dij between factories and distribution centers are known and do not change The distances can be obtained directly from Google Maps or calculated based on the Euclidian distance between each factory Fi and each distribution center Di Transportation Cost: The cost of transporting one unit of goods from factory Fi to distribution
center Dj is directly proportional to the distance Dij between them. This assumes that the cost increases linearly with distance, and that the cost per unit distance (e.g., kilometers) is known.
