Many times making a decision can be easy. When the alternatives to choose are few and do not entail great risks, the sharpness and insight of the decision maker is enough. But this is not always the case and, in the catering industry, this is no exception. As problems become more complex and the number of possible alternatives increases, the risk coefficient for taking strategic will increase. So that's where the skill of the decision maker lies: knowing how to assess where it is possible to minimize this risk.
In another article the criteria that support the taking of strategic in situations of uncertainty in which probabilities of occurrence of the different events are not associated, quite the opposite occurs for this type of situation in which the calculation of probabilities allows reducing uncertainty.
A peculiarity of this type of taking strategic is that when the situation presented has ever occurred, it will allow the administrator to determine the probabilities of occurrence from his past experience.
Unfortunately, many of the strategic they should be taken in new situations, that is, where there is no previous information, so it will be useful to indicate a probability of occurrence for each event. Personally, when one does not have the slightest idea of what may happen and given the degree of importance of the events, the author suggests, and clearly states that it is the author's suggestion, to distribute the probabilities in correspondence with the number of events. For example, if four situations occur, there would be a 0,25% probability for each event. Likewise, the administrator may do so according to his criteria for situations of greater or lesser number of events and according to the possibilities that he considers to occur.
In this sense, the fact that it is possible to use past experience to develop probabilities regarding the occurrence of each event, the strategic it is taken using probabilitybased models. Therefore, the three necessary conditions for this type of decisionmaking are: a) the existence of more than one event or state of nature for each decision b) existence of previous experience to obtain probabilities for each of the events or states of nature c) all are taken under the same conditions.
Some of the criteria used to support decisionmaking used in situations of this type are:

Expected value criterion.

Criterion of the expected loss of opportunity.
These criteria will offer information for obtaining other sources of information such as:

The expected profit with perfect information.

The expected value of perfect information.
To understand each of them and exemplify the calculation methodology to follow, suppose that: the administrator of a restaurant has included in its offer the elaboration of sweets for sale to the students of the community school during recess times, and knows that one of those that is sold daily can only order its supplier in batches of 100 units However, its warehouses admit a maximum order of 400 units. His experience indicates that the daily demand range is from 100 to 400 sweets, behaving as follows:
Demand  100  200  300  400 
Probability  0.15  0.25  0.40  0.20 
The sale price of the sweet is € 0.50 and the acquisition cost per unit is € 0.30. If the product is not sold on the day, all that is left the next day can be sold at a rate of € 0.20 per unit, so the administrator needs to determine the amount of sweets that must be ordered each day in order to obtain the maximum profit:
For the application of each of the criteria, the first step that the administrator must follow is the construction of the decision matrix, taking into account the information previously presented.
Alternative decisions  Demand 100 sweets 
Demand 200 sweets  Demand 300 sweets  Demand 400 sweets 
D1 Buy 100 sweets 
20

20

20

20

D2: Buy 200 candies 
10

40

40

40

D3: Buy 300 candies 

30

60

60

D4: Buy 400 candies 
10%

20

50

80

Odds 
0.15

0.25

0.40

0.20

If I buy 100 sweets at 0.30 and the demand is for 100 sweets and I sell them at 0.50, I get a profit of € 20.00 If I buy 200 sweets and the demand is 100, I get € 100 for 20.00, but the other 100 must sell it at 0.20 , that is, I lose 0.10 for each unit, so I would lose € 10.00. Getting really only a profit of € 10.00 (20.00  10.00)
As can be seen in the matrix, in the row corresponding to D1, although the demand increases, the profit will be the same, not happening for the row corresponding to D4, where the fact of buying more sweets than what is actually demanded will allow obtaining profits, but not the desired ones when making the purchase. In other words, the risk of the sale of that amount occurring or not, and consequently that of selling below cost, is revealed.
In the case of determining the probabilities of occurrence of each event, the highest value has been assigned to the demand for 300 sweets, given that the installation's sales indicators show that sales behave over that number.
CRITERIA FOR EXPECTED VALUE (I see)
It is one of the most used when guaranteeing the best longterm result. This criterion is like an average projected into the future. It means that by repeating the same situation, as many times as it occurs, it will be expected that the average of all the results will be the same as the one calculated. It is important to bear in mind that this criterion does not ensure that all decisions turn out to be the wisest selection, however, its stable application to different situations will lead to high quality solutions.
The procedure for calculation is as follows:
n
VEi = Σ Rij Pj
j = 1
VEi = Σ Rij Pj
j = 1
Where:
VEi: Expected value for alternative i
Pj: Probability associated with the event or state of nature j
VEi: Expected value for alternative i
Pj: Probability associated with the event or state of nature j
And in this case the rule to choose the best decision would be the maximum value for profit and the minimum for when it comes to costs.
According to the case raised, the procedure is as follows:
VE1 = 20 (0.15) + 20 (0.25) + 20 (0.40) + 20 (0.20) = € 20.00
VE2 = 10 (0.15) + 40 (0.25) + 40 (0.40) + 40 (0.20) = € 35.50
VE3 = 0 (0.15) + 30 (0.25) + 60 (0.40) + 60 (0.20) = 43.50 €
VE1 = 10 (0.15) + 20 (0.25) + 50 (0.40) + 80 (0.20) = € 39.50
This criterion recommends that the best decision is to request 300 sweets daily, which would provide a maximum expected daily profit of € 43.50
CRITERIA FOR EXPECTED VALUE OF LOSS OF OPPORTUNITY (VEoi)
In the previous criterion, the possible profits were obtained if one of the lawsuits occurred. This criterion calculates the opportunity losses when each of the alternatives occurs:
n
VEOi = Σ Oij Pj
j = 1
VEOi = Σ Oij Pj
j = 1
Where: VEOi: is the expected value of the loss of opportunity for alternative i
Following the previous example, the first step would be to build the opportunity loss matrix, that is, a state of nature should occur and decide for an alternative how much I stop selling or how much I lose.
States of Nature
Alternative decisions  Demand 100 sweets 
Demand 200 sweets  Demand 300 sweets  Demand 400 sweets 
D1 Buy 100 sweets 

20

40

60

D2: Buy 200 candies 
10


20

40

D3: Buy 300 candies 
20

10


20

D4: Buy 400 candies 
30

20

10


Odds 
0.15

0.25

0.40

0.20

The procedure followed was as follows (let's see it for two states of nature and two alternative decisions)
If I buy 100 sweets and the demand is 200, then I stop selling 100 so I lose the opportunity to earn, (€ 20.00). If I buy 200 sweets and the demand is 100, I sell 100 at their normal price and the others I must sell 0.10 below their cost, so I lose € 10.00.
Once these values are obtained, the values for each of the alternatives are determined as in the case of the expected value, obtaining the following results:
VEO1 = 0 (0.15) + 20 (0.25) + 40 (0.40) + 60 (0.20) = € 33.00
VEO2 = 10 (0.15) + 0 (0.25) + 20 (0.40) + 40 (0.20) = € 17.50
VEO3 = 20 (0.15) + 10 (0.25) + 0 (0.40) + 20 (0.20) = 9.50 €VEO4 = 30 (0.15) + 20 (0.25) + 10 (0.40) + 0 (0.20) = € 33.00
In this case, decision 3 would be adopted as it represents the one that represents the least loss of opportunity.
If you are a good observer you will perceive that the above criteria lead to the same result. The application of both will offer the same results, so simply applying one of them will obtain the desired information, although this second calculation is of notorious importance since it plays an important role in the application of the following criteria:
THE VALUE OF PERFECT INFORMATION
It happens that the criteria explained above are based on the information that the decision maker has on the occurrence of the different states of nature. However, many times it is necessary to obtain additional information for decisionmaking. This criterion facilitates the value of that information, that is, how much it is convenient to pay to obtain that additional information.
The information that says exactly what is going to happen is known as perfect information, when the state of nature that is going to occur is known exactly, so it will be much easier to determine the alternative to follow. Continuing with the proposed assumption of sweets, we will proceed as follows, applying the following mathematical expression to obtain the value of the Expected Gain from Perfect Information:
n *
GEIP = Σ Rj Pj
j = 1
GEIP = Σ Rj Pj
j = 1
Where:
GEIP: Expected profit with perfect information
*
Rj: Maximum result for the state of nature j
Pj: Probability of the state of nature j
GEIP: Expected profit with perfect information
*
Rj: Maximum result for the state of nature j
Pj: Probability of the state of nature j
The procedure followed is that of, based on the information obtained with the application of the previous methods, determining the maximum expected gain that can be obtained from knowing the perfect information.
Alternative decisions  Demand 100 sweets 
Demand 200 sweets  Demand 300 sweets  Demand 400 sweets 
D1 Buy 100 sweets 
20




D2: Buy 200 candies 

40



D3: Buy 300 candies 


60


D4: Buy 400 candies 



80

Odds 
0.15

0.25

0.40

0.20

In this case the calculation is as follows:
GEIP = 20 (0.15) + 40 (0.25) + 60 (0.40) + 80 (0.20) = € 53.00
Once this value is obtained, the Expected Value of the Perfect Information can be determined, which is nothing more than the difference between the Expected Gain of the perfect Information and the result obtained from the application of the Expected Value criterion.
In this case it looks like this:
VEIP = GEIP  VE_{}
VEIP = 53.00  43.50
VEIP = 9.50
VEIP = 53.00  43.50
VEIP = 9.50
If you are a good observer, you will notice that the result obtained coincides with that obtained from the application of the Expected Value of Opportunity Loss criterion. It is for this reason that I suggest the application of both, since it will allow you to compare whether you have correctly applied each of them, since these results must coincide.
The author wishes to thank Dr. Pilar Felipe, professor of the Department of Business Sciences of the University of Havana for the transmission of her experiences in this field, of which the example has been used, making the necessary adjustments in correspondence with the sector for the interpretation of the exposed methodology.
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