MF5001: Four Trucks Will Be Used For Transporting Products From One Plant To Four Storage Facility: Mathematical Modelling In Supply Chains Assignment, UOL, Ireland

 Problem 1:

Four trucks will be used for transporting products from one plant to four storage facilities (labeled A, B, C, D). Any of the products can be shipped by any of these four tracks. However, because of differences in the trucks and product types, various loading/unloading, handling, and transporting costs are incurred resulting in different total costs for the different truck warehouse combinations.

The objective is to minimize the total cost of assigning the most suitable trucks to ship products to the storage facilities. a) Formulate this problem as an assignment LP model. b) Solve the developed LP model using Microsoft Solver.

Problem 2:

A company wants to move some products (medical supplies) from Pittsburgh (Node 1) and Staunton (Node 2) to hospitals in Nodes3 to Node7. Figure 1 provides the details of this network. The shipping costs of all routes are provided below each arc. Please note that there is a vehicle capacity limitation of maximum of 800 units for all routes. That means, for instance, no more than 800 units of products (medical supplies) can be shipped from a city to another one.

b) Solve the model in (a) using MS Solver.

c) Reformulate the model in (a) assuming that the vehicles are now changed to a different one with more capacity up to 1000 products between any two cities. d) Solve the model in (c) using MS Solver and compare your results with (b).

Problem 3:

Company 1 and Company 2 are two European producers of a demanding medical component. Company 1 has plants in Germany, France, and Italy, whereas Company 2 has plants in Ireland and UK. The markets are in North America and have four geographical zones, i.e. north, east, west, and south. Table 2 provides all required information about these plants and markets. Table 2. Information for problem 3.  Demand (millions of units) 15 20 30 20 a) Company 1 and 2 are merging and will serve the markets (supply products) collectively, what is the minimum total cost if none of the plants is shut down? Formulate this problem using Integer Programming (IP) and solve using MS solver. Clearly show your model and discuss results. b) After the merger, what is the minimum total cost of plants that can be shut down (assume that a shutdown saves 100% of the annual fixed cost of the plant)? Formulate this problem using Integer Programming (IP) and solve using MS solver. Clearly show your model and discuss results.

The requirement for this assignment is:

1. A . PDF file containing answers for the three questions above (.PDF file can be written using a computer or can be a scanned hand-written one).

2. Three excel files containing the spread-sheet model used for solving these three questions.

3. Rename all. PDF and excel files as “family name-Question number-Student ID”.