Question

1.Given is a decision payoff table.

		Future Demand
Alternatives	Low	Moderate	High
Small Facility	53	31	22
Medium Facility	29	42	32
Large Facility	-5	30	53

  
a) The best decision under uncertainty using MAXIMAX is to select  facility
  
b) The best decision under uncertainty using MAXIMIN is to select  facility
  
c) The best decision under uncertainty using LAPLACE/EQUALITY LIKELY is to select  facility

d) If the probabilities for Future Demand when it is Low = 0.35, Moderate = 0.30, and High = 0.35, the expected monetary value (EMV) for the large facility = .
  
e) If the probabilities for Future Demand when it is Low = 0.35, Moderate = 0.30, and High = 0.35, the best decision under risk is to select  facility.

2. Given is a decision payoff table and a Sub Decision Payoff Table. Use Minimax Regret as an evaluation criterion to evaluate alternatives.

		Future Demand
Alternatives	Low	Moderate	High
Small Facility	53	31	22
Medium Facility	29	42	32
Large Facility	-5	30	53

  

Alternatives	Worst Regrets
Small Facility	?
Medium Facility	?
Large Facility	?

  
a) The worst regrets for alternative Small Facility is  
  
b) The worst regrets for alternative Medium Facility is  
  
c) The worst regrets for alternative Large Facility is  
  
d) The best course of action or decision by using Minimax Regret is to select  facility

3.Given is a Decision Tree Diagram. The Payoffs 1-14 are given in the table below. Answer questions a, b, and c.

Payoff	1	2	3	4	5	6	7	8	9	10	11	12	13	14
$	6	-3	5	5	8	5	5	-1	5	4	5	2	7	5

  
a) The value at node 4 is  

b) The value at node 8 is  (in 1 decimal place)
  
c) The best course of action or decision is to select alternative  

4.

Determine the center of gravity location for the destinations and shipping quantities shown below:

Destination	x	y	Quantity
D1	8	6	650
D2	2	2	250
D3	6	9	180
D4	3	8	545

a) The Center of Gravity, x-bar =  (in 2 decimal places)

b) The Center of Gravity, y-bar =  (in 2 decimal places)

Answer 1

As per Chegg guidelines i answer first 4 parts of 1 question

Alternative	Low	Moderate	High	Maximum
Small	53	31	22	53
medium	29	42	32	42
Large	-5	30	53	53

(A):-

The best decision under uncertainty using MAXIMAX is to select Small or Large facility.

The maximax criteria gives maximum of the maximum gains found in each event.

(B):-

The best decision under uncertainty using MAXIMIN is to select Medium facility.

The minimax criteria gives minimum value among all the possible maximum gains found in each facility.

(C) :-

Alternative	Equal likelihood
Small	53*0.33 + 31*0.33 +22*0.33 = 17.49+10.23 + 7.26	34.98
medium	29*0.33 + 42*0.33 + 32*0.33 = 9.57 + 13.86 + 10.56	33.99
Large	-5*0.33 + 30*0.33 + 53*0.33 = -1.65 + 9.9 + 17.49	25.74

The best decision under uncertainty using LAPLACE/EQUALITY LIKELY is to select Small facility

(D):-

Alternative	Expected value
Small	53*0.35 + 31*0.30 + 22*0.35 = 18.55 + 9.3 + 7.7	35.55
medium	29*0.35 + 42*0.30 + 32*0.35 = 10.15 + 12.6 + 11.2	33.95
Large	-5*0.35 + 30*0.30 + 53*0.35 = -1.75 + 9 + 18.55	25.8

Expected monetary value of Large facility is 25.8 . It could be seen from the table, large facility provides the expected monetary value which is equivalent to 25.8

(E):-

If the probabilities for Future Demand when it is Low = 0.35, Moderate = 0.30, and High = 0.35, the best decision under risk is to Small facility

here because small facility expect monetory value is High 35.55 see in table above.