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IE 335: Operations Research – Optimization
Fall 2020 Lab Report (2)
Due: Thursday, 03 Dec 2020 @23:59
This is a GROUP work, and each group should submit only one report
Objectives:
• To apply OR techniques and LP models for evaluating different alternatives
• To solve linear programming models using EXCEL solver and LINGO
• To interpret EXCEL and LINGO solutions
Background
A Real Estate investment company is looking to select one of two-construction sites for a new
convention center project with maximum area of 16,000m2
in total. Each of the two sites includes
properties that should be acquired if the site is selected.
The following table provides data about proposed properties in both sites together with the
acquisition cost.
Site 1 Site 2
Property Area m2 Cost (1000$) Property Area m2 Cost (1000$)
1 1,960 1,000 1 7,450 2,700
2 4,650 2,050 2 5,550 1,800
3 4,650 2,350 3 4,700 2,800
4 2,700 2,000 4 6,500 2,500
5 5,500 2,900
All the properties, except Property 1 in Site 1 can be acquired partially. Moreover, if Site 1 is
selected, at least 75% of Property 4 must be selected, and at least 50% of Property 3 must be
acquired if Site 2 has been selected.
Because of the current condition of the infrastructure, there is fixed construction costs of $17
million for Site 1 and is $21 million for Site 2. The Real Estate Company should select one of the
sites based on the minimum cost.
Tasks:

1. Read the problem carefully and formulate an LP model for each site.
   a. Write down the decision variables.
   b. Write down the LP objective functions.
   c. Write down the LP constraints.
   Hint: You need to formulate one LP model for each site separately – two models in total.
2. Solve the LP model for site (1) only using EXCEL solver (show all the steps by screenshots
   use SUM and SUMPRODUCT functions).
3. Solve the LP model for site (2) only using LINGO (sets and looping functions should be
   used).
4. Interpret the solutions you obtained for both sites, and recommend one site for the
   company to invest.
5. If partial acquisitions of properties are not allowed (i.e. property is fully selected, or not
   selected at all), and constraints related to Property 4 in site1 and Property 3 in site 2 are
   canceled, which site should selected? Use Excel to find the answer and explain it.
   Below is the laboratory report format (APA stile is required):
   o Abstract
   o Introduction
   o Methodology
   o Results and discussion
   o Conclusion
   o References (if needed)
   Grading Scheme:
6. Description and formulation of the problem (Tasks 1) 20%
7. Excel solution (Tasks 2) 20%
8. LINGO solution (Tasks 3) 20%
9. Interpretations and recommendations 15%
10. What if question (Tasks 4) 15%
11. Proper report organization 5%
12. Proper use of language 5%

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