Ewing Natural Gas is a large energy company with headquarters in Dallas, Texas. The company offers a wide variety of energy products and has annual revenues of approximately $50 billion. Because of the diverse nature of the company, its Manager for Project Development, Cliff Erland, is under continual pressure to manage project proposals from the functional areas of the company. At any point in time, there might be dozens of projects at various stages requiring a wide variety of capital expenditures, promising widely varying future revenue streams, and containing varying degrees of risk. Cliff has a difficult balancing act. The companys CEO, J.R. Bayer, is very concerned about keeping capital expenditures within a fixed budget and managing risk. The heads of the companys functional areas are less worried about budgets and risks; they are most concerned that their pet projects are approved (human factors).

Cliff is currently about to meet with all parties involved to discuss project proposals for the next three years. He has proposals from the various functional areas for projects they would like to undertake. Each of these is accompanied by a schedule of capital expenditures over the next three years and a financial analysis of the expected revenue streams. These lead to an NPV for each proposal. (See the attached data file) J.R. Bayer has stated that the total of capital expenditures for the approved projects can be no more than $10 billion and that no more than $4 billion should be spent in any single year. Unfortunately, the capital expenditures for the potential list of projects is well over $10 billion, so Cliff knows that some of these very promising projects will not be approved. Each functional area wants as many of its projects to be approved as possible, but it certainly does not want to be shut out altogether.

Questions

1. Deterministic case: assuming there is no uncertainty to consider, find the best set of projects to invest for Cliff.

2. Risk evaluation: Now all of the capital expenditures in the data file shall be replaced with triangular distributions. The values in the data file should be the most likely values, and each minimum and maximum for the distribution should be, respectively, 15% below and 30% above the most likely value. The NPVs should also be modelled with triangular distributions, using the values in the data file as most likely values. However, their minimum and maximum values should be, respectively, 20% below and 15% above the most likely value. Given the set of projects selected in question 1, simulate the probability distribution of total NPV, and the probability that each budget is satisfied. For example, the results should include the fraction of iterations where total capital expenditures for the three-year period are no greater than $10 billion.

3. Recommend a set of projects to invest for Cliff under the uncertainties considered in question 2. The objective is to maximize the mean total NPV. There shall be a probability constraint on each budget: the probability that capital expenditures are within the budget should be at least 0.95. There will also be the usual (non-probabilistic) constraints that each functional area should have at least one project approved. Try to find the best set of projects and explain the solution approach you take in the report.

Project Selection at Ewing Natural Gas
Inputs			All values in $ millions
Project index	Functional Area (FA)	Capex Year 1	Capex Year 2	Capex Year 3	NPV
1	FA1	250.00	100.00	100.00	60.00
2	FA1	165.00	99.00	99.00	59.40
3	FA1	50.00	100.00	200.00	40.00
4	FA1	750.00	500.00	300.00	310.00
5	FA1	150.00	300.00	600.00	165.00
6	FA2	500.00	150.00	150.00	90.00
7	FA2	750.00	750.00	300.00	410.00
8	FA2	800.00	700.00	600.00	280.00
9	FA2	268.00	402.00	536.00	254.60
10	FA3	100.00	200.00	400.00	100.00
11	FA3	350.00	250.00	150.00	130.00
12	FA3	1500.00	400.00	400.00	340.00
Decisions			Capex for company				Capex for FA1				Capex for FA2				Capex for FA3
Project index	Undertake project?		Year 1	Year 2	Year 3		Year 1	Year 2	Year 3		Year 1	Year 2	Year 3		Year 1	Year 2	Year 3
1	1		250	100	100		250	100	100		0	0	0		0	0	0
2	1		165	99	99		165	99	99		0	0	0		0	0	0
3	1		50	100	200		50	100	200		0	0	0		0	0	0
4	1		750	500	300		750	500	300		0	0	0		0	0	0
5	1		150	300	600		150	300	600		0	0	0		0	0	0
6	1		500	150	150		0	0	0		500	150	150		0	0	0
7	0		0	0	0		0	0	0		0	0	0		0	0	0
8	0		0	0	0		0	0	0		0	0	0		0	0	0
9	1		268	402	536		0	0	0		268	402	536		0	0	0
10	1		100	200	400		0	0	0		0	0	0		100	200	400
11	1		350	250	150		0	0	0		0	0	0		350	250	150
12	1		1500	400	400		0	0	0		0	0	0		1500	400	400
Totals	10		4083	2501	2935		1365	1099	1299		768	552	686		1950	850	950
Number of projects undertaken in functional areas
	Total
FA1	5
FA2	2
FA3	3
Limits for company capital expenditures
	Year 1	Year 2	Year 3	Total
Limit	4000	4000	4000	10000
Summary of capex for projects undertaken (useful for creating chart)
	Year 1	Year 2	Year 3
Company	4083	2501	2935
FA1	1365	1099	1299
FA2	768	552	686
FA3	1950	850	950