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ECON7322
Assignment 2 - Part 1
Question 1. (Total 100 marks)
SpaceXYZ is a multiplanetary corporation that is trying to optimize its Interstellar transportation business. The corporation delivers high-value super-rare chemical elements from three different planets in Galaxy A to different ports on the Planet B (Earth), where such elements are not available and extremely valuable for advanced technology production and human health. These elements need to be transported in specially designed safe-boxes (to preserve their high value) and there are strict limits on the safe-boxes feasible for each month at each planet. The business involves three phases:
Phase 1: The safe-boxes are delivered from the three planets (call them A1, A2 and A3) of Galaxy A by spaceships to different space-ports on Planet B (call them B1, B2, B3, B4). The shipping & handling costs (mln.$/safe-box) between each of the origin in Galaxy A and destination ports on Planet B, and the available number of the safe-boxes are as follows:
Phase 2: Upon arrival to the ports on Planet B, the space-boxes are unloaded from the spaceships, treated and uploaded onto within-planet-super-large drones and transported to different Hubs that are spread out across the different regions of the Planet B. At each Port and each Hub there are limits on the number of safe-boxes they can handle (per month). The shipping & handling costs (mln.S/safebox) between each of the ports and the hubs on Planet B and the handling capacity of the safe-boxes are as follows:
Phase 3: Upon arrival to the hubs, the space-boxes must be then distributed across five different factories (call them Factory 1, Factory 2, Factory 3, Factory 4, Factory 5) that are spread out in different regions across the Planet B.
The shipping & handling costs (mln.$/safe-box) between each of the Hub and the Factories on the Planet B and the demand of the safe-boxes per month are as follows:
a. Formulate a mathematical programming model for optimizing the shipments from eachplanet to the factories (via ports and hubs) to minimize the total shipping & handling costs.(60 marks)
b. Solve your model with Excel QM, present and explain your results, and make relevant recommendations.(40 marks)
Question 2. (100 marks)
SpaceXYZ is planning to deploy special giant robots to search, excavate, process and package the highvalue super-rare chemical elements on the different planets. They have three of such robots, each authorized to be deployed on any of the three planets. Each robot has different productivity on different planets, so that it does better on some planets than on others due to different environments. The times required by the robots to do the task on each planet are as follows:
SpaceXYZ wants to optimize its business by assigning one type of robot to each planet to minimize the total operating time for all three robots.
a. Formulate a linear programming model for this problem. (25 marks)
b. Solve the model by using the computer and report the solution. (25 marks)
c. Before the deployment of the robots, SpaceXYZ was offered a new robot, Robot 4, which is more adaptive to various environments and can perform the required task in 25 hours on any of the three planets. Should SpaceXYZ lease this new robot? If so, instead of which one? Justify your answer by formulating the updated mathematical programming model given this new information, solve the model by using the computer, report the solution and make relevant recommendations. (50 marks)