There are developments on the software implementation of the method. If anyone is interested in creating an Expert Advisor, write.I give a description of the method.
Money management is based on the Martingale modification - Labouchere,
also known as the "deletion method". This method is not as extreme as the regular martingale.
What is the principle of transaction management?At the dawn of the casino, to play on an equal footing (for example, red - black), a method was invented to double the bet when losing. I will not go into the description in detail, but this method, despite the fact that mathematically, of course, allows you to win, has negative traits. The stakes are rising in geometric progression and sooner or later, you will either win, or you will face the lack of the necessary amount in your pocket for the next doubling of the bet, or with a limit on the maximum bet on the gaming table.
Let me remind you that the mathematical probability of winning when playing classic roulette is 49%. 1% - ZERO, this is the advantage of the casino.
The elimination method is as follows. We divide our deposit into 100 parts.
1% of the deposit is one contract.We start the game with 1 contract. We take paper and a pen, write down the rates in a column one under the other.
-1
We add 1 more contract to the lost one. The next bet is 2 contracts. For example, we won. Write in a column
-1
+2
In total, we won 1 contract. We cross out everything, we start anew. The next bet is 1 contract.Consider a more interesting series.
For example, we lost the first bet. We write down on paper
-1
We add 1 more contract to the lost one. The next bet is 2 contracts. For example, we lost. Write in a column
-1
-2
Now to the first bet in the column (-1), add the last bet (-2). Total 3 contracts. Let's say we lost. We write in a column.
-1
-2
-3
Now, to the first bet in the column (-1), we add the last bet (-3). Total 4 contracts. Let's say we lose again. Write in a column
-1
-2
-3
-4
Now, to the first bet in the column (-1), we add the last bet (-4). Total 5 contracts. Let's say we lose again. Write in a column
-1
-2
-3
-4
-5
Five losses in a row. It happens… The next bet is 6 Contracts.
For example, we won. We write in a column.
-1
-2
-3
-4
-5
+6
6 contracts that we won made up for the loss of -1 and - 5 contracts! Now, cross out -1, -5 and +6.
Left:
-2
-3
-4
Now to the first bet in the column (-2), add the last bet (-4). Total 6 contracts. The next bet is 6 Contracts. Let's say we win again. Write in a column
-2
-3
-4
+6
6 contracts that we won made up for the loss of -2 and - 4 contracts! Now, cross out -2, -4 and +6.
There are -3 contracts left. Since there is nothing else in the column, we add 1.
The next bet is 4 contracts. If we win, then we cross out everything, remain in the black in 1 contract and start the streak again.We had such a series
-1
-2
-3
-4
-5
+6
+6
+4Three profitable trades compensated for 5 losing trades.
I advise you to practice on paper, several times, until the principle reaches automatism.So pay attention! In order for the system to function and win, it is necessary to have the number of profitable transactions above 33% -40% percent!!!
If anyone is in doubt, write your own long series. You can practice at any online casino that has a test game for virtual money. Divide your deposit into 100 parts. Bet only on red or only on black. Keep in mind that such a method of playing can be considered by the casino as dishonest, and the casino computer, after some time, will begin to arrange series for you. opposite color 10-20-30 in a row, of course, we won’t talk about any 33-40 percentage ratio and you will lose.But the principle remains the same, 33% of wins compensate for 66% of losses.
Thus, applying such money management in practical Forex trading, we need trading system, which has a 50% chance of winning, and the ratio of possible profit to possible loss is greater than or equal to 1,
those. Profit factor >=1.
In order for the transport problem of linear programming to have a solution, it is necessary and sufficient that the total reserves of suppliers are equal to the total demands of consumers, i.e. the task must be with the right balance.
Theorem 38.2 Property of the system of restrictions of the transport problem
The rank of the system of vector-conditions of the transport problem is N=m+n-1 (m are suppliers, n are consumers)
Reference solution of the transport problem
A reference solution of a transport problem is any feasible solution for which the condition vectors corresponding to positive coordinates are linearly independent.
Due to the fact that the rank of the system of vector-conditions of the transport problem is equal to m + n - 1, the reference solution cannot have more than m + n-1 coordinates other than zero. The number of non-zero coordinates of a non-degenerate reference solution is equal to m + n-1, and for a degenerate reference solution it is less than m + n-1
Cyclecycle is such a sequence of cells in the table of the transport problem (i 1 , j 1),(i 1 , j 2),(i 2 , j 2),...,(i k , j 1) in which two and only two adjacent cells located in the same row or column, with the first and last cells also in the same row or column.
The cycle is depicted in the form of a table of the transport task in the form of a closed broken line. In the cycle, any cell is a corner cell, in which the polyline link rotates by 90 degrees. The simplest cycles are shown in Figure 38.1
Theorem 38.3An admissible solution of the transport problem X=(x ij) is a reference one if and only if no cycle can be formed from the occupied cells of the table.
Strikeout method
The elimination method allows you to check whether the given solution of the transport problem is a reference one.
Let the admissible solution of the transport problem, which has m + n-1 non-zero coordinates, be written in the table. For this solution to be a reference one, the condition vectors corresponding to positive coordinates, as well as basic zeros, must be linearly independent. To do this, the cells of the table occupied by the solution must be arranged so that it is impossible to form a cycle from them.
A row or column of a table with one cell occupied cannot be included in any cycle, since the cycle has two and only two cells in each row or column. Therefore, in order to first cross out either all the rows of the table containing one occupied cell, or all the columns containing one occupied cell, then return to the columns (rows) and continue deleting.
If, as a result of deletion, all rows and columns are deleted, it means that it is impossible to select a part forming a cycle from the occupied cells of the table, and the system of the corresponding condition vectors is linearly independent, and the solution is a reference one.
If, after deletion, some cells remain, then these cells form a cycle, the system of corresponding condition vectors is linearly dependent, and the solution is not a support one.
Examples of "crossed out" (reference) and "not crossed out" (non-reference solutions):
Strikeout logic:
- Delete all columns in which there is only one occupied cell (5 0 0), (0 9 0)
- Delete all lines in which there is only one occupied cell (0 15), (2 0)
- Repeat cycle (7) (1)
Methods for constructing the initial reference solution
Northwest corner method
There are a number of methods for constructing the initial reference solution, the simplest of which is the northwest corner method.
In this method, the stocks of the next supplier by the number are used to meet the requests of the next by the number of consumers until they are completely exhausted, after which the stocks of the next supplier by the number are used.
Filling in the transport task table starts from the upper left corner, which is why the northwest corner method is called.
The method consists of a number of steps of the same type, at each of which, based on the stocks of the next supplier and the requests of the next consumer, only one cell is filled in and, accordingly, one supplier or one consumer is excluded from consideration.
Example 38.1Compile a reference solution using the northwest corner method.
1. We distribute stocks of the 1st supplier.
If the stocks of the first supplier are greater than the requests of the first consumer, then we write in the cell (1,1) the sum of the request of the first consumer and go to the second consumer. If the stocks of the first supplier are less than the requests of the first consumer, then we write in the cell (1,1) the sum of the stocks of the first supplier, exclude the first supplier from consideration and go to the second supplier.
Example: since its stocks a 1 =100 are less than the requests of the first consumer b 1 =100, then in the cell (1,1) we write the transportation x 11 =100 and exclude the supplier from consideration.
We determine the remaining unsatisfied requests of the 1st consumer b 1 = 150-100=50.
2.We distribute the stocks of the 2nd supplier.
Since its stocks a 2 = 250 are more than the remaining unsatisfied requests of the 1st consumer b 1 =50, then in the cell (2,1) we write the transportation x 21 =50 and exclude the 1st consumer from consideration.
We determine the remaining stocks of the 2nd supplier a 2 = a 2 - b 1 = 250-50=200. Since the remaining stocks of the 2nd supplier are equal to the requests of the 2nd consumer, then in the cell (2,2) we write x 22 = 200 and exclude either the 2nd supplier or the 2nd consumer at our discretion. In our example, we excluded the 2nd supplier.
We calculate the remaining unsatisfied requests of the second consumer b 2 =b 2 -a 2 =200-200=0.
150 | 200 | 100 | 100 | ||
100 | 100 | |
|||
250 | 50 |
200 |
250-50=200 200-200=0 | ||
200 | |||||
150-100-50=0 |
3. We distribute stocks of the 3rd supplier.
Important! In the previous step, we had the choice to exclude the supplier or the consumer. Since we have excluded the supplier, the requests of the 2nd consumer still remain (although they are equal to zero).
We must write the remaining requests equal to zero in the cell (3,2)
This is due to the fact that if a transportation is required to be placed in the next cell of the table (i, j), and the supplier with number i or the consumer with number j has zero stocks or requests, then a transportation equal to zero (base zero) is placed in the cell, and thereafter, either the relevant supplier or consumer is excluded from consideration.
Thus, only basic zeros are entered in the table, the remaining cells with zero transportations remain empty.
To avoid errors, after constructing the initial reference solution, it is necessary to check that the number of occupied cells is equal to m + n-1 (the base zero is also considered an occupied cell), and the condition vectors corresponding to these cells are linearly independent.
Since in the previous step we excluded the second supplier from consideration, we write x 32 =0 in cell (3,2) and exclude the second consumer.
Inventory of the 3rd supplier has not changed. In cell (3,3) we write x 33 =100 and exclude the third consumer. In the cell (3,4) we write x 34 \u003d 100. In view of the fact that our task is with the right balance, the stocks of all suppliers are exhausted and the demands of all consumers are satisfied completely and simultaneously.
reference solution | ||||
150 | 200 | 100 | 100 | |
100 | 100 | |||
250 | 50 | 200 | ||
200 | 0 | 100 | 100 |
4. We check the correctness of the construction of the reference solution.
The number of occupied cells should be equal to N=m(suppliers)+m(consumers) - 1=3+4 - 1=6.
Applying the method of deletion, we make sure that the solution found is "deletable" (the basis zero is marked with an asterisk).
Consequently, the condition vectors corresponding to the occupied cells are linearly independent, and the constructed solution is indeed a reference one.
Minimum cost method
Method minimum cost is simple and allows you to build a reference solution that is close enough to the optimal one, since it uses the cost matrix of the transport problem C=(c ij).
Like the northwest corner method, it consists of a series of steps of the same type, each of which fills only one cell of the table corresponding to the minimum cost:
and only one row (provider) or one column (consumer) is excluded from consideration. The next cell corresponding to is filled in according to the same rules as in the northwest corner method. The supplier is excluded from consideration if its cargo stocks are fully used. The consumer is excluded from consideration if his requests are fully satisfied. At each step, either one supplier or one consumer is eliminated. Moreover, if the supplier has not yet been excluded, but its stocks are equal to zero, then at the step when this supplier is required to deliver the goods, a basic zero is entered in the corresponding cell of the table and only then the supplier is excluded from consideration. Likewise with the consumer.
Using the minimum cost method, construct the initial reference solution of the transport problem.
1. We write down the cost matrix separately in order to make it more convenient to choose the minimum costs.
2. Among the elements of the cost matrix, select the lowest cost C 11 =1, mark it with a circle. This cost takes place during the transportation of goods from the 1st supplier to the 1st consumer. In the appropriate cell, we write down the maximum possible volume of transportation:
x 11 \u003d min (a 1; b 1) \u003d min (60; 40) \u003d 40 those. minimum between the stocks of the 1st supplier and the requests of the 1st consumer.
2.1. We reduce the stocks of the 1st supplier by 40.
2.2. We exclude from consideration the 1st consumer, since his requests are fully satisfied. Cross out the 1st column in matrix C.
3. In the rest of the matrix C, the minimum cost is the cost C 14 =2. The maximum possible transportation that can be carried out from the 1st supplier to the 4th consumer is equal to x 14 \u003d min (a 1 "; b 4) \u003d min (20; 60) \u003d 20, where a 1 primed is the remaining inventory of the first supplier.
3.1. The stocks of the 1st supplier are exhausted, so we exclude it from consideration.
3.2. We decrease the requests of the 4th consumer by 20.
4. In the rest of the matrix C, the minimum cost is C 24 =C 32 =3. Fill in one of the two cells of the table (2.4) or (3.2). Let's write in a cell x 24 \u003d min (a 2; b 4) \u003d min (80; 40) \u003d 40 .
4.1. The requests of the 4th consumer are satisfied. We exclude it from consideration by deleting the 4th column in the matrix C.
4.2. We reduce the stocks of the 2nd supplier 80-40=40.
5. In the rest of the matrix C, the minimum cost is C 32 =3. We write in the cell (3,2) of the table transportation x 32 \u003d min (a 3; b 2) \u003d min (100; 60) \u003d 60.
5.1. We exclude from consideration the 2nd consumer. We exclude the 2nd column from the matrix C.
5.2. Let's reduce the stocks of the 3rd supplier 100-60=40
6. In the rest of the matrix C, the minimum cost C 33 =6. We write in the cell (3,3) of the table transportation x 33 \u003d min (a 3 "; b 3) \u003d min (40; 80) \u003d 40
6.1. We exclude from consideration the 3rd supplier, and from the matrix C the 3rd row.
6.2. We determine the remaining requests of the 3rd consumer 80-40=40.
7. The only element left in the matrix C is C 23 =8. We write in the cell of the table (2.3) transportation X 23 =40.
8. We check the correctness of the construction of the reference solution.
The number of occupied cells in the table is N=m+n - 1=3+4 -1.
Using the elimination method, we check the linear independence of the condition vectors corresponding to the positive coordinates of the solution. The order of deletion is shown in the X matrix:
Conclusion: The solution by the minimum cost method (table 38.3) is "crossed out" and, therefore, pivotal.
There are two ways to correct erroneous entries: proofreading and redacting. The method of proofreading is that the incorrect entry is crossed out and the correct one is written above it. The correction is certified by the signature of the person responsible for keeping records. This method is used if the error is discovered shortly after it was made and its correction will not cause changes in the totals. If the error was reflected in the final data, then its correction by proofreading would cause many strikethroughs and corrective entries. To avoid this, the red storno method is used, which consists in repeating the incorrect entry in red ink. Then make the correct entry in normal color ink. Red color means that the entry is incorrect and must be subtracted when calculating.
About how articles are transferred from the Journal to the General Ledger, why two articles in the Main Ledger are formed from one article in the Journal, also about the method of crossing out articles in the Journal, and finally, about two numbers in the Main Ledger that are marked in the margins of the Journal, and why this is done.
ALSO ABOUT THE METHOD OF STRIKING OUT
Errors made are corrected in the registers by crossing out in red ink, provided that errors are identified before the results are put down. The correct amount is indicated above the crossed out amount in black ink. In the event that an error is found in the order journal after the totals are entered in it, but before they are entered into the General Ledger, the correction is carried out in the free lines or columns provided after the totals. Adjustment of turnover is made out by a specially compiled accounting statement. Its data is entered into the General Ledger separately. After the results of journal-orders are recorded in the General Ledger, corrections in them are not allowed.
Information about the actual availability of property is recorded in the inventory lists and acts in at least 2 copies. In inventories, it is not allowed to leave blank lines, and on the last pages, blank lines are crossed out. Blots and erasures are not allowed, and corrections of errors are made in all copies of the inventories by crossing out the wrong entries and putting down the correct ones over the crossed out ones. Corrections must be agreed and signed by all members of the inventory commission and materially responsible persons. On each page of the inventories, the number of serial numbers of material assets and the total amount in material indicators recorded on this page are indicated in words, regardless of the units in which these values are shown in pieces, kilograms, meters, etc. On last page In the inventory, a note is made about checking prices, taxing and calculating the totals signed by the members of the inventory commission. The inventories are signed by all members of the inventory commission and, moreover, the financially responsible persons at the end of the inventory give a receipt confirming the inspection of the property by the commission in their presence and the absence of any claims against the members of the commission.
Blots, erasures, etc. are not allowed in documents. Errors in documents should be corrected by crossing out the incorrect text or amount and writing the correct text or amount over the crossed out ones.
In the sections Information about work, Information about awards, Information about rewards of the work book (insert), it is not allowed to cross out previously made inaccurate or incorrect entries.
In the Details of Incentives section, it is not allowed to strike through previously entered inaccurate or incorrect entries. If it is necessary to change the record, the corresponding serial number date of making the entry, the Entry for No. such and such is invalid and the correct entry is made.
Corrections in the text, strikethroughs
Crossing out the endorsement violates their continuous series, and
Strikethrough is regarded as a one-way deal aimed at
Correction of errors should be made in all copies of the inventories by crossing out the wrong entries and putting down the correct entries over the crossed out entries. Corrections must be agreed and signed by all members of the inventory commission and financially responsible persons.
Depending on the prevailing specifics of transportation for various types of cargo and certain directions, a number of forms or proformas of standard charters (charter parties) are used, usually developed by associations of shipowners and charterers, individual large firms or concerns, associations of charterers-senders or recipients of goods. In some cases, standard charter forms apply, but with additions and modifications specific to the individual shipper or consignee. Even before the ship is submitted for loading, and in any case before the cargo is accepted on board, it is very important to study the charter and not only determine the standard proforma with its specific features, but also to analyze the specific terms of this contract of carriage. Particular attention should be paid to postscripts, insertions, strikethroughs, additions made to the standard charter pro forma, since these deviations from the usual printed text often contain very significant conditions.
Enlargement of the scale of prices (crossing out zeros).
Secret voting at meetings of the faculty council and the academic council of the university provides for filling out a ballot, which indicates the surname, name, patronymic of the applicant, position, department. The decision is made by crossing out or leaving the name of the applicant. All applicants for a specific position are included in one ballot. The decision of the academic council of the university or the faculty council can be appealed to the rector of the university only in case of violation of the existing situation. The rector has the right to appoint a second consideration of the issue at a meeting of the academic council of the university or faculty council.
Entries in the inventories must be made accurately, without blots, erasures and corrections. Bug fixes. should be carried out by crossing out the erroneous entries so that the strikethrough can be read, and making the correct entries. Corrections in the names of goods and products, their quantities, prices must be agreed and confirmed by the signatures of all members of the commission. The correction of an error must be stipulated by the inscription Corrected to believe with the date and certified by the signature of the person who made the correction (accountant). The word proof from the Latin orre tio means correction and is used in cases where the error is of a private nature, i.e. made in one document or register and discovered before the entries and counting of turnovers on the accounts for a given month are completed.
The corrective way to correct errors is to cross out the wrong text or amount and write the correct text or amount over the crossed out one. Strikethrough is done with one line so that you can read the strikethrough. In this case, it is necessary to cross out the entire amount, even if an error is made in only one digit. The correction of the error must be specified and confirmed approved in the document - by the signatures of the persons who signed the document in the accounting registers
Representatives over powerful programs in the class of preparation of text documents provide the possibility of color highlighting, various effects (strikethrough, hidden text). An automatic kerning and spacing operation for character pairs can be provided. Kerning refers to the adjustment of the spacing between certain pairs of characters with large font sizes, when there is an increase in the inter-letter spacing due to the peculiarities of writing the character. Discharge - the operation of increasing the inter-letter space to improve the appearance of a line of text and align the right borders of lines.
Task number 4. Increase in the number of transactions:
What calls to action can be? Example: “Call now”, “Find out more on our website”, “Find out more by calling…”.
P.S. If you just read this article and have not implemented any of the specified methods increase, then you have wasted your time.
If you are going to implement in your organization 2-3 ways you like to increase sales, then you are in for good results.
If you decide to use each of the methods described here, then the problem of inventory will cease to exist for you. And you will forget that once this question was so relevant for you.
P.P.S. What is a profitable plant? This is an enterprise that is aware of what place its products occupy in the market and sells them competently! Sales work is the same lead generation. Sales funnel analysis, online marketing. All the same!
The elimination method allows you to check whether the given solution of the transport problem is a reference one.
Let the admissible solution of the transport problem, which has m + n-1 non-zero coordinate, be written in the table. For this solution to be a reference one, the condition vectors corresponding to positive coordinates must be linearly independent. To do this, the cells of the table occupied by the solution must be arranged so that it is impossible to form a cycle out of them.
A row or column of a table with one occupied cell cannot be included in any cycle, since the cycle has two and only two cells in each row or column. Therefore, you can first delete either all rows of the table containing one occupied cell, or all columns containing one occupied cell, then return to the columns (rows) and continue their deletion. If, as a result of deletion, all rows and columns are deleted, then it is impossible to select a part forming a cycle from the occupied cells of the table, and the system of the corresponding condition vectors is linearly independent, and the solution is a support one. If, after the deletions, some cells remain, then these cells form a cycle, the system of the corresponding condition vectors is linearly dependent, and the solution is not a support one.
Below are examples of “deleted” (reference) and “non-deleted” (non-reference) solutions:
;
“crossed out” “non-crossed out”
6. Methods for constructing the initial reference solution. Northwest corner method.
There are a number of methods for constructing the initial reference solution, the simplest of which is the northwest corner method. In this method, the stocks of the next supplier are used to meet the requests of the next consumers until they are completely exhausted, after which the stocks of the next supplier by number are used.
Filling in the table of the transport task starts from the upper left corner and consists of a number of steps of the same type. At each step, based on the stocks of the next supplier and the requests of the next consumer, only one cell is filled in and, accordingly, one supplier or consumer is excluded from consideration. This is done in this way:
It is customary to enter zero shipments in the table only when they fall into the cell (i, j) to be filled in. If the next cell of the table (i, j) requires transportation, and the i-th supplier or j-th consumer has zero stocks or requests, then a transportation equal to zero (base zero) is placed in the cell, and after that, as usual, the relevant supplier or consumer is excluded from consideration. Thus, only basic zeros are entered in the table, the remaining cells with zero transportations remain empty.
To avoid errors, after constructing the initial reference solution, it is necessary to check that the number of occupied cells is equal to m + n-1 and the condition vectors corresponding to these cells are linearly independent.
Theorem 4. The solution of the transport problem constructed by the northwest corner method is the reference one.
Proof. The number of table cells occupied by the reference solution should be equal to N=m+n-1. at each step of building a solution using the northwest corner method, one cell is filled in and one row (supplier) or one column (consumer) of the problem table is excluded from consideration. After m+n-2 steps, m+n-2 cells will be occupied in the table. At the same time, one row and one column will remain uncrossed out, while there is only one unoccupied cell. When this last cell is filled, the number of occupied cells will be m+n-2+1=m+n-1.
Let us verify that the vectors corresponding to the cells occupied by the reference solution are linearly independent. Let's use the elimination method. All occupied cells can be crossed out if you do this in the order in which they were filled.
It must be kept in mind that the northwest corner method does not take into account the cost of transportation, so the reference solution built by this method may be far from optimal.