Quantitative methods in the Restoration?
A question… ¿At how many moments in our lives have we had to take a decision? An answer… In many. Decisions that have been sustained by common sense, the rational and the intuitive. Perhaps, many have been wrong and the consequence of it has had to be paid, but its social involvement is limited.
In the same way it happens in the businessare taken quite often strategic, but this time, with a level of economic and social involvement that can have serious consequences for the environment in which the organization itself and the personnel that depend on it operate.
Un
restaurant is a company that is based on the same principles of
administration and the general organization than the others, and in which decisions are also made:
change the menu, increase or decrease prices, change suppliers, hire a chef or a maitre d ', expand, reduce, buy, sell, advertise, reduce staff, vary hoursFinally, countless of them must be supported by the information available to be able to bring them to a successful end; always bearing in mind that decision is not the same as choosing or selecting, although based on prior knowledge of the range of options and the evaluation of possible results, if you are going to assume them.
In this context, several authors have addressed the topic, mainly focused on the production system, developing methodologies that facilitate decisionmaking through the application of mathematical instruments.
In the author's opinion, qualitative methods should not be ruled out. They offer relevant information, which combined with those obtained by the quantitative ones make it easier, as long as they are correctly interpreted, to make decisions on the matter than the demand.
In the
field of services, and very particularly in those related to food and beverage services, the interpretation of criteria that clients refer to on the basis of quality, such as temperature, decoration, delivery time, quantity, etc. and that are obtained from the application of satisfaction surveys, something that we commonly do in the
restaurant, together with those derived from the application of the quantitative methods that report on
preferences from the analysis that can be done through menu engineering, the levels of difference and indifference of the clients in relation to the offer, the costmargin analysis, service cycles, prices, etc. They allow you to identify where the problem is and make decisions.
The fact of making a decision based on the application of quantitative methods requires the identification of the problem in question, which perhaps can be expressed in the qualitative methods, as explained above, and consequently, the administrator of
restaurant You must evaluate the possible alternatives and the consequences of the application of each of them.
A simple example, it could be that when tabulating the surveys of the month it is obtained as a result that customers think that they like fish, but not the one offered in the facility, therefore, when doing the menu engineering study, the their popularity declines. In this case the qualitative methods offer one information and the quantitative ones another, so it is necessary to merge them to make a decision, since the problem is evident; customers want fish, but not the one offered by the house, raising the following questions: What fish do we buy? From whom? And how many varieties of fishbased dishes can be introduced on the menu?
The various authors who have addressed the topic agree that there are five elements that must be present in a situation that requires a decision: 1) the existence of a set of alternative decisions, 2) the environment in which the problem arises, 3) the results of the use of a certain alternative, 4) the existence of a decision maker and 5) the knowledge that one has about the behavior of the states of nature, the first three being essential for the decision. Likewise, they refer to the existence of four environments in which the problem may arise: certainty, risk, uncertainty and conflict.
It is the author's intention to address in this article, although it does not rule out the possibility of doing it later with the rest of the methods, the decision criteria that can be applied in uncertain conditions. In this environment, multiple consequences can be identified for each alternative, but the probability of occurrence of each one is not known. The final decision is based on subjective criteria of the decisionmaker and qualitative rather than quantitative methods are applied, some of which, the best known, are set out below:
Let's see it with an example applied to Gain, but in the same way they can be applied to
costs. In the latter, it would be taken into account that the highest profit is always sought at the lowest cost. Each of the criteria will be exemplified from the following assumption.
Directive
Restaurant "Equis" must decide its sales strategy for the next season taking into account, for this, the type of fish to be used and the sales behavior. The possible fish to be used will be designated by 1, 2 and 3, while the possible behaviors of the sales states can be classified as 4, 5 and 6, summarizing the profit estimates that can be obtained in the following decision matrix:

Sales Estimate 
Decisions 
4 (Normal) 
5 (Excellent) 
6 (Good) 
Fish 1 
350€ 
390€ 
300€ 
Fish 2 
250€ 
300€ 
350€ 
Fish 3 
200 € 
550€ 
450€ 
Pessimistic or Wald's (maximin): This criterion is seeking to follow that action that guarantees obtaining the maximum of the minimums of the different results that may be generated from each of the estimates made when using each of the proposed products; that is, avoid the worst result.
Type of Fish

Worst Result

Fish 1

300

Fish 2

250

Fish 3

200

In this case, fish 1 would be selected, with which a minimum profit of € 300 would be obtained. If he
restaurant Selecting this alternative could obtain greater results as observed in the row of values corresponding to this product.
Optimist (maximax): This criterion, unlike the previous one, only takes into account the best possible result of each action (the maximum of the maximums), thinking that it will not lose the opportunity to obtain the highest possible value (highest profit or lowest cost), but it does not take into account account for the losses that may result from not having the product that generates this result and therefore it is necessary to use another.
Type of Fish

Best Result

Fish 1

390

Fish 2

350

Fish 3

550

In this case, this criterion states that the best result would be obtained from using fish 3, however, if the row is analyzed in its entirety, using this product the company could generate losses of up to € 200.
Laplace: also known as "of equal probability" or of "insufficient reason." This criterion takes into account all the values and consists of assigning probabilities of occurrence of using any of the products. The method consists of obtaining the average value for each product.
Type of Fish

Average Result

Fish 1

(350 + 390 + 300) / 3 = 346.6

Fish 2

(250+300+350)/3 = 300

Fish 3

(200+550+450)/3 = 266.6

In this case the best alternative is Fish 1, which generates the best average result
Savage: It is a pessimistic criterion and is also known by the "loss of opportunity" because its creator to replace the Pessimistic criterion introduces the criterion of loss of opportunity or repentance and assumes that for a given state of nature, there is always one or more alternatives that produces a better result less than the opportunity, considering that if you choose a product that provides a result less than the "best" then a loss of opportunity occurs.
In this case, it is common to make a matrix, known as “Loss of opportunity”, where for each consequence the best result for each product (profit) and the least for cost (cost) would be selected and the system of how much would be stopped would be applied. get an alternative occur for a consequence
Technically it would be as follows from proceeding as shown below.
For example, for consequence 4, the best result is selected by subtracting each of the estimates made for each product:
Consequence 4: Best Result 250
Consequence 5: Best Result 450
Consequence 6: Best Result 350
It would remain:

4 
5 
6 
1 
350  350 = 0 
550  390 = 160 
450  300 = 150 
2 
350  250 = 100 
550  300 = 250 
450  350 = 100 
3 
350  (200) = 550 
550  550 = 0 
450  450 = 0 
Once the opportunity loss values have been obtained, the best results are selected for each type of fish and the least is selected from them. This means that if fish 1 is selected, only a loss of opportunity of € 160 would occur.
Type of Fish

Higher Result

Fish 1

160

Fish 2

250

Fish 3

550

Hurwicz: it is equivalent to the weighted sum of the extreme results of both lines of action. Since no one is always optimistic or always pessimistic, Hurwicz's criterion establishes an intermediate path between maximin and maximax and part of combining weights of optimism and pessimism. The author considers the use of an optimism coefficient denoted by α that can take any value between 0 and 1. The coefficient α is chosen based on subjective reasons, that is, the more dangerous the situation, the more we want to make sure of it. the lower our risk inclination will be and therefore the smaller the value we will place on α. In this case, the author recommends not using values of 0.5, which would make interpretation difficult.
In this case we proceed as follows: first a value is assigned for the optimism coefficient, which the author suggests is between 0.6 and 0.9, remaining as follows for a coefficient of 0.7.

Optimistic value


Pessimistic value

Result

Fish 1

0.7 (390)

+

0.3 (300)

363

Fish 2

0.7 (350)

+

0.3 (250)

320

Fish 3

0.7 (550)

+

0.3 (200)

325

Selected the highest value, which in this case would be fish 1
In summary, each of these criteria is represented mathematically as follows:
Decision forms
For each alternative decision, the matrix data is read horizontally and analyzed vertically.
Criterion 
Gain 
Cost 
Pessimistic or Wald 
Of the minimum profit the highest result. 
From the maximum cost the less result. 
Optimistic 
From the highest profit the best result. 
The lowest cost, the lowest result. 
Laplace 
The average result is determined (adding each of the values that make up the alternative decision and dividing by the number of nature states and selecting the highest. 
The average result is determined (adding each of the values that make up the alternative decision and dividing by the number of nature states and selecting the least. 
Savage 
Opportunity loss matrix is developed. When it comes to profit, the highest value is chosen from each of the states of nature and the lowest is for cost, and the rest is subtracted (vertically) and the maximum value is selected from each alternative decision and then the minimum. 
Hurwicz 
It is required to define a value for the optimism coefficient. (between 06 and 1) and the values obtained in the optimistic criterion are multiplied by each one and added to the multiple of the difference between 1 and the optimism coefficient. 
It is required to define a value for the optimism coefficient. (between 01 and 0.4) and the values obtained in the pessimistic criterion are multiplied by each one and added to the multiple of the difference between 1 and the optimism coefficient. 

The author recommends in this last criterion not to establish values for the coefficient of 0.5. 
Once each of the results has been obtained, a table can be drawn up that reflects the results obtained in each of the criteria and select the most convenient decision, according to the analysis made by the decisionmaker, who is the one with the last word.
Criterion 
Pessimistic 
Optimistic 
Laplace 
Savage 
Hurwicz 
Decision 
Fish
1

Fish
3

Fish
1

Fish
1

Fish
1

Deciding is not easy, it requires sharpness on the part of whoever has to do it, relying on methods that facilitate or reveal information for it is a strategy that I recommend at all times. With technological advancement and the development of computing these can be brought to spreadsheets that perform operations much faster.
What is exposed here is only part of the great variety of quantitative techniques of
management that they are applicable to the business world and that they can be used in the restaurant business. In future articles, if the reader allows it, we will discuss others that will surely be useful.
Finally, 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.