OR4023

Group Project

Spring 2024

Each group is required to give an optimization model for solving the problem, write a computer program and solve the problem numerically if necessary. Submit your report together with your program source file. Submit your written report and code via the designated link on iSpace by 11:59am, 9 June 2024.

Your written report should consist of the following parts

•   Abstract

•   Problem restatement

•   Model (including assumptions)

•   Methodology (including algorithms, if any)

•   Results and Discussions

•   Conclusion

•   References

We plan to build two refineries on one side of a railway line and add a new station on the railway line to transport refined oil. Due to the general nature of this mode, the oil field design institute hopes to establish a general mathematical model and method to minimize pipeline construction costs.

1. Propose your design scheme for various scenarios of distances between the two refineries and the railway line, and the distance between the two refineries. When designing the scheme, consider cases where the shared pipeline costs are the same as or different from the non-shared pipeline costs.

2. The design institute currently needs to conduct a specific design for a more complex scenario. The specific locations of the two refineries are shown in the attached figure, where Refinery A is located in the suburbs (Area I in the figure), and Refinery B is located in the urban area (Area  II in the figure). The boundary between the two areas is indicated by a dotted line in the figure. The  distances represented by the letters in the figure (unit: kilometers) are a = 6, b = 10, C = 18, l = 22.

If the cost of laying all pipelines is  80,000 yuan per kilometer. Additional costs  for laying pipelines in urban areas include demolition and engineering compensation fees. To estimate these additional costs, three engineering consulting companies were hired (Company One has a Class A qualification, and Company Two and Company Three have Class B qualifications). The estimated results are shown in the table below:

Please provide the design institute with a pipeline layout scheme and the corresponding costs.

3. In this actual problem, to further save costs, suitable oil pipes can be selected according to the production capacity of the refineries. In this case, the pipeline laying costs will be reduced to 60,000 yuan per kilometer for transporting finished oil from Refinery A, 64,000 yuan per kilometer for transporting finished oil from Refinery B, and 80,000 yuan per kilometer for shared pipelines. Additional demolition and other costs remain the same as above. Please provide the optimal pipeline layout scheme and the corresponding costs.