Part I Final Project–Guggenhiem Memo

To the Guggenheim Board of Directors:

With reference to the upcoming art exhibition organized by Celeste and Valentino, three proposals were examined with respect to the several requirements both curators detailed (as seen below).

The first proposal sought to maximize the floor space while remaining with the 4 million budget allotted to this exhibition. This resulted in a total of 15 art pieces being shown at a total cost of 3,950,000. The second

The second proposal sought to minimize costs with a minimum of 20 piece shown. To minimize the 4 million dollar budget 20 pieces were selected at a total cost of 5,400,000. It is clear that the 4 million budget would not be enough to meet this new minimum.

The third proposal pertains to cost fluctuations of 20% above or below the current costs set, while maintain the same goals as proposal two. Running a simulation, resulted in a potential final average cost of 5,320,949. This amount sits between a minimum average cost of 4,811,615.30 and maximum average cost of 5,913,777.60. This average cost is 79,050 below the cost calculated in the previous proposal.

A list of the art pieces that would be shown and not be shown sit below with the listed requirement of Valentino and Celeste.

Valentino possesses certain requirements for the exhibit.

• He therefore decides to include only one collage.
• He therefore wants at least one wire mesh sculpture displayed if a computer-generated drawing is displayed.
  • Alternatively, he wants at least one computer-generated drawing displayed if a wire mesh sculpture is displayed.
• He therefore decides to include:
  • at least one photo-realistic painting,
  • at least one cubist painting,
  • at least one expressionist painting,
  • at least one watercolor painting, and
  • at least one oil painting.
  • At the same time, he wants the number of paintings to be no greater than three times the number of other art forms.
• Valentino wants all his own paintings included in the exhibit.
• Helen, and he wants both of her paintings displayed.
• He therefore decides to display as many pieces from David as from Enrique and to display at least one piece from each of them.
• Valentino will therefore only accept one display piece from Rick, if any at all.

Celeste also possesses her own agenda for the exhibit.

• To support female artists, she decides to include at least one piece from a female artist for every three pieces included from a male artist.
• To advance environmentalism, she decides to include either one or both of the pieces “Aging Earth” and “Wasted Resources.”
• To advance Native American rights, she decides to include at least one piece by Stuart.
• To advance science, she decides to include at least one of the following pieces: “Beyond,” “Who Has Control,” “Where are we now?” and “Pioneers.”
• For this exhibit, the museum only has enough floor space:
  • for four sculptures
  • enough wall space for around 20 paintings, collages, and drawings.
• if “Narcissism” is displayed, “Reflection” should also be displayed since “Reflection” also suggests narcissism.

Proposal 1

The Guggenheim decides to allocate $4 million to fund the exhibit. Given the pieces available and the specific requirements from Valentino and Celeste, formulate and solve a BIP model to maximize the number of pieces displayed in the exhibit without exceeding the budget. How many pieces are displayed? Which pieces are displayed?

15 ought to be displayed while maximizing floor space while remaining with a 4 million budget.

TABLE 1: Proposal 1–Planned Display Pieces

TABLE 2: Proposal 1–Pieces Not Procured for Display

The total spent to display 15 pieces is 3950000 leaving 50000. Thus around 98.75% of the budget has been allocated and utilized.

Proposal 2

To ensure that the exhibit draws the attention of the public, Celeste decides that it must include at least 20 pieces. Formulate and solve a BIP model to minimize the cost of the exhibit while displaying at least 20 pieces and meeting the requirements set by Valentino and Celeste. How much does the exhibit cost? Which pieces should be displayed?

20 total can be displayed while minimizing with with at least 20 pieces displayed.

The cost of displaying 20 pieces will be $5400000

TABLE 3: Proposal 2–Planned Display Pieces

TABLE 4: Proposal 2–Pieces Not Procured for Display

Proposal 3

Apparently Valentino and Celeste were using an old pricing sheet when they made their exhibit decisions. They still want to maintain the same criteria, but realize the cost of each piece of art could increase or decrease by as much as 20% of the cost on the old price sheet. That is, the random price change of each piece can range between –20% and +20% independently with equal probability. How does that possibility impact the cost of Celeste’s plan in part 2?

TABLE 5: Simulation Results and Comparision

Results from simulation

	Simulation	Proposal 2	Difference	Percentage Change
mean	5320949.4	5400000	-79050	-1.464
sd	156457.3	1	1	1.000
max	5913777.6	5400000	513800	9.514
min	4811615.3	5400000	-588400	-10.900

GRAPH 1: Bar Chart of Cost Distribution

TABLE 6: Individal Cost Variance

Piece ID	Piece Name	Orginal Price	Simulation Mean	Simulation SD	Min	Max
1	Perfection	300000	300873	34945	240041	359916
2	Burden	250000	248629	28165	200183	299690
3	Emergence	125000	125588	14301	100085	149938
4	Beyond	400000	399359	46403	320144	479877
5	Who Has Control?	500000	501167	58468	400197	599749
6	Domestication	400000	399742	45513	320399	479935
7	Innocence	550000	551880	63466	440258	659244
8	Aging Earth	700000	698144	79564	560179	839747
9	Wasted Resources	575000	575266	65440	460255	689129
10	Serenity	125000	124726	14387	100229	149826
11	Calm Before the Storm	300000	301897	34035	240263	359978
12	Void	150000	150169	17101	120087	179906
13	Sun	150000	149504	17582	120092	179982
14	Storefront Window	850000	855013	96422	680233	1019636
15	Harley	750000	755934	85060	600227	899955
16	Consumerism	400000	398544	45646	320129	479767
17	Reflection	175000	175935	19961	140051	209970
18	Trojan Victory	450000	449968	52721	360130	539929
19	Ziggy	500000	501794	57890	400085	599910
20	Ziggy II	500000	497554	56762	400208	599995
21	Ziggy III	500000	500505	58339	400075	599482
22	Where are we now?	650000	654664	75544	520304	779787
23	Pioneers	650000	652251	74980	520262	779895
24	Wisdom	250000	251134	28696	200122	299808
25	Superior Powers	350000	350019	41151	280004	419887
26	Living Land	450000	449216	51542	360475	539973
27	Study of a Violin	400000	399187	46363	320015	479951
28	Study of a Fruit Bowl	400000	401504	45680	320138	479930
29	My Namesake	300000	301305	34851	240195	359921
30	Narcissism	300000	299179	33961	240155	359974
31	All That Glitters	50000	49799	5808	40018	59960
32	The Rock	50000	49806	5793	40007	59988
33	Winding Road	50000	49888	5768	40004	59921
34	1071 Fifth Ave	50000	49791	5734	40060	59959

TABLE 7: Proposal 3–Planned Display Pieces

TABLE 8: Proposal 3–Pieces Not Procured for Display