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Phase 2 - Solve problems by applying the algorithms of the Unit 1

Sofia Martinez 26 septiembre 2019

Universidad Nacional Abierta y a Distancia Escuela de Ciencias Básicas, Tecnología e Ingeniería Competencias comunicativas

Exercise 1. Decision trees, EVPI and EVMI

Teratex, a textile company that has a productive experience in the foreign market of 25 years, must decide if it manufactures a new product in its main plant, or if on the contrary the purchase from an external supplier. The profits depend on the demand of the product. The table shows projected profits, in millions of dollars.

Table 1. Decision process for the commercialization of the product States of nature Decision alternative

Manufacture Subcontract Buy Probabilities Ʃ = 1

Demand lowutility

Demand low average - utility

321 335 318 0,35

352 353 361 0,35

Demand High utility 367 381 375 0,3

According to the corresponding information in Table 1 and the Predicted Value of Perfect Information (EVPI) theory, the Expected Value of Sample Information (EVMI) and Decision Trees, respond: a. Use EVPI to determine if the company should try to get a better estimate of the demand. b. A test market study of potential product demand is expected to report a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are: P(F/low) = 0,35

P(D/low) = 0,65

P(F/low average) = 0,41

P(D/ low average) = 0,59

P(F/high) = 0,32

P(D/high) = 0,68

a. What is the expected value of market research information? b. What is the efficiency of the information?

Solución a.

Use EVPI to determine if the company should try to get a better estimate of the demand.

BAJA (0,35)

FABRICAR

321

112

MEDIA NODO BAJA(0,35) 2

352

123

MEDIA ALTA (0,3)

367

110

BAJA (0,35)

335

117

MEDIA BAJA (0,35)

353

124

MEDIA ALTA (0,3)

381

114

BAJA (0,35)

318

111

MEDIA BAJA (0,35)

361

126

MEDIA ALTA (0,3)

375

113

NODO SUBCONTRATAR NODO 1 3

COMPRAR

NODO 4

345

355

350

Nodo 2 Nodo 3 Nodo 4 Nodo 1

345 355 350 355

La decisión recomendada por el método del valor esperado es fabricar con un pago de 355 millones de dolares. EVPI = EVwPI – EVwoPI EVwPI = (0.35x335) + (0,35x361)+(0,3x381) = 357,9 EVwoPI = 355 EVPI = 357,9 – 355 = 2, 9 = 3

b. A test market study of potential product demand is expected to report a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are: P(F/low) = 0,35

P(D/low) = 0,65

P(F/low average) = 0,41

P(D/ low average) = 0,59

P(F/high) = 0,32

P(D/high) = 0,68

Teorema de Bayes

P(A₁) = 0,35 , P(A₂) = 0,35

P(A₃) = 0,3

FAVORABLE Estados de la naturaleza

Probabilidades previas

Probabilidades condicionales P(F)

Probabilidades conjuntas

Probabilidades posteriores

ALTA MEDIA BAJA

0,35 0,35 0,3

0,35 0,41 0,32

0,1225 0,1435 0,096

0,33839779 0,39640884 0,26519337

P(F)

0,362

FAVORABLE Estados de la naturaleza

Probabilidades previas

Probabilidades condicionales P(F)

Probabilidades conjuntas

Probabilidades posteriores

ALTA MEDIA BAJA

0,35 0,35 0,3

0,65 0,59 0,68

0,2275 0,2065 0,204

0,356583072 0,323667712 0,319749216

P(F)

0,638

FABRICAR

FAVORABLE (O,362)

NODE 2

SUBCONTRATA R

COMPRAR

NODO 4

NOD0 5

NODO 6

NODE 1 FABRICAR

DESFAVORABL E (0,638)

NODE 3

SUBCONTRATA R

COMPRAR

NODO 7

NODO 8

NODO 9

BAJA

0,34

321

MEDIA BAJA

0,40

352

MEDIA ALTA

0,27

367

BAJA

0,34

335

MEDIA BAJA

0,4

353

MEDIAALTA

0,27

381

BAJA

0,34

318

MEDIA BAJA

0,4

361

MEDIAALTA

0,27

375

BAJA

0,36

321

MEDIA BAJA

0,32

352

MEDIAALTA

0,32

367

BAJA

0,36

335

MEDIA BAJA

0,32

353

MEDIAALTA

0,32

381

BAJA

0,36

318

MEDIA BAJA

0,32

361

MEDIAALTA

0,32

375

VE (Nodo 4) = 349,03 VE (Nodo 5) = 357,97 VE (Nodo 6) = 353,77 VE (Nodo 7) = 345,64 VE (Nodo 8) = 355,48 VE (Nodo 9) = 350 Favorable (Nodo 2) = Max ( Nodo4, Nodo5, Nodo6) = 367,97 Desfavorable (Nodo 3) = Max ( Nodo7, Nodo8, Nodo9) = 355,48

349,03

357,97

353,77

345,64

355,48

350

a.

What is the expected value of market research information?

VE (Nodo1) = (0,362*367,97) + (0,638*355,48) = 360,001 b.

What is the efficiency of the information?

Valor de la información perfecta: VEIM = VecIM – VesIM = 360,001 - 355 = 5,001 E = (VEIM/VEIP) x 100 = (5,001 / 3 ) x 100 = 166,7 %

Exercise 2. Decision trees, EVPI and EVMI ElectroCom, a company that manufactures electronic components for the introduction in its product catalog, must decide whether to manufacture a new product in its main plant, subcontract it with company supervision or if it buys it from an external supplier. The profits depend on the demand of the product. The table shows projected profits, in millions of dollars.

According to the corresponding information in Table 2 and the Predicted Value of Perfect Information (EVPI) theory, the Expected Value of Sample Information (EVMI) and Decision Trees, respond: a. Use EVPI to determine if the company should try to get a better estimate of the demand. b. A test market study of potential product demand is expected to report a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are:

P(F/low) = 0,15

P(D/low) = 0,85

P(F/low average) = 0,45

P(D/ low average) = 0,55

P(F/high medium) = 0,3

P(D/ high medium) = 0,7

P(F/high) = 0,5

P(D/high) = 0,5

c. What is the expected value of market research information? d. What is the efficiency of the information?