CN113377847A - Restaurant mixed ordering method for takeout platform - Google Patents
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- 238000000034 method Methods 0.000 title claims abstract description 16
- 239000011159 matrix material Substances 0.000 claims abstract description 19
- 238000000354 decomposition reaction Methods 0.000 claims abstract description 9
- 238000006243 chemical reaction Methods 0.000 claims abstract description 6
- 238000012163 sequencing technique Methods 0.000 claims description 27
- 230000004927 fusion Effects 0.000 claims description 9
- 230000008707 rearrangement Effects 0.000 claims description 6
- 238000012216 screening Methods 0.000 claims description 6
- 238000002156 mixing Methods 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 4
- 238000007405 data analysis Methods 0.000 claims description 3
- 230000001932 seasonal effect Effects 0.000 claims description 3
- 238000005516 engineering process Methods 0.000 abstract description 2
- 230000001502 supplementing effect Effects 0.000 abstract 1
- 230000000694 effects Effects 0.000 description 2
- 230000006870 function Effects 0.000 description 2
- 238000010801 machine learning Methods 0.000 description 2
- 241001122767 Theaceae Species 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 235000021152 breakfast Nutrition 0.000 description 1
- 235000009508 confectionery Nutrition 0.000 description 1
- 230000001186 cumulative effect Effects 0.000 description 1
- 235000006694 eating habits Nutrition 0.000 description 1
- 235000013410 fast food Nutrition 0.000 description 1
- 235000015220 hamburgers Nutrition 0.000 description 1
- 239000008267 milk Substances 0.000 description 1
- 210000004080 milk Anatomy 0.000 description 1
- 235000013336 milk Nutrition 0.000 description 1
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- 239000013589 supplement Substances 0.000 description 1
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/24—Querying
- G06F16/248—Presentation of query results
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
- G06F16/24—Querying
- G06F16/245—Query processing
- G06F16/2457—Query processing with adaptation to user needs
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q30/00—Commerce
- G06Q30/06—Buying, selling or leasing transactions
- G06Q30/0601—Electronic shopping [e-shopping]
- G06Q30/0631—Item recommendations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q30/00—Commerce
- G06Q30/06—Buying, selling or leasing transactions
- G06Q30/0601—Electronic shopping [e-shopping]
- G06Q30/0633—Lists, e.g. purchase orders, compilation or processing
- G06Q30/0635—Processing of requisition or of purchase orders
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
- G06Q50/10—Services
- G06Q50/12—Hotels or restaurants
Abstract
The invention discloses a restaurant mixed ordering method for a take-out platform, which comprehensively considers the restaurant order sales volume of the take-out platform in recent time periods, the operation cooperation with merchants, personal preference of users and other factors, and realizes the ordering recommendation of restaurants near the users based on the technologies of data statistics, singular value decomposition and the like. Firstly, maintaining and supplementing the data of all restaurants in the database: setting operation weight and marking the classification of the cuisine; secondly, recent orders are analyzed and modeled: firstly, determining restaurant order sales volume in different time periods; secondly, calculating the preference of the user in the cuisine by using an SVD matrix decomposition algorithm; then, the restaurant near the user is ranked and displayed by comprehensively considering the conditions of the restaurants, the distance from the user, the operation weight, the time-sharing order sales volume, the time for the user to browse the platform, the dish preference and other factors. The relevant data of a take-out platform is used for testing, and the improvement of the click rate and the order conversion rate is facilitated by the method.
Description
Technical Field
The invention relates to the technical field of network information, in particular to a restaurant mixed ordering method for a takeout platform.
Background
The restaurant ranking effect on the take-away platform can directly affect the user experience, the sales volume of the merchant and the platform income. In restaurant sequencing recommendation, a platform generally considers the following two aspects, one is that from the perspective of a user, by utilizing a relevant algorithm of statistics and machine learning, restaurants with higher sales volume and which are possibly liked by the user to place orders are preferentially displayed in the restaurant sequencing process, so that the user experience and the platform order volume are improved; the other is from the aspect of platform operation, the specific conditions such as whether the restaurant purchases the advertisement on the platform, the current discount strength of the restaurant, the quality of the restaurant, the depth of cooperation with the platform and the like are mainly considered, and the exposure rate of a specific merchant is improved from the aspect of operation. In practical application, if only the angle of a user is considered for sequencing, the platform loses the control force on the sequencing of the restaurant, and the business expansion and the flow guidance of the platform and a merchant are not facilitated; similarly, if only from the operation perspective, the browsing experience of the user and the order conversion rate are affected. How to comprehensively consider the above two factors in the ordering is a problem to be solved.
Disclosure of Invention
In order to solve the problems, the invention simultaneously considers the user angle and the operation angle in the ordering process, and respectively brings the restaurant order sales volume of the take-out platform in a recent time period, the operation cooperation of a merchant, the personal preference of the user and the like into the ordering consideration factors, thereby providing the restaurant ordering recommendation method based on the technologies of data statistics, Singular Value Decomposition (SVD) and the like. The method comprises the steps that firstly, an operator maintains and supplements necessary data of a restaurant table in a database, secondly, a recent order is analyzed and modeled, then, the restaurants are sorted according to the state of the restaurants, the time of a user browsing platform, the comprehensive sales volume and the operation angle, and finally, the sorting is locally adjusted according to the preference of a user for a cuisine.
In order to achieve the purpose, the invention adopts the following technical scheme:
a restaurant mixed sequencing method of a take-out platform comprises the following steps:
step 1, restaurant data processing
Marking all restaurants in a restaurant table in a takeaway platform database relates to two aspects: a weight is given to the restaurant from the operation angle and is used as the operation weight of the restaurant; marking the restaurants according to the cuisine categories to which the restaurants belong;
1.1 restaurant operation weight assignment
In actual operation, an operation department can endow a restaurant with an operation weight value according to the cooperation condition of the platform and a merchant; the smaller the operation weight value of a restaurant is, the restaurant should be displayed preferentially from the operation perspective;
1.2 restaurant cuisine markers
The cuisine category is an important characteristic of the restaurant and is an important factor to be considered when the user carries out restaurant sequencing recommendation, so that the cuisine category of the restaurant needs to be marked in advance; a restaurant has a plurality of dish labels according to dishes mainly sold by the restaurant;
step 2 order data analysis
Reading historical order data of the platform, wherein the data comprises the following fields: order ID, order time, user ID, restaurant ID, and restaurant cuisine;
2.1 time-phased sales statistics
Counting the order sales volume of each restaurant in time intervals by taking the read historical order data as a unit in hours;
2.2 calculating user cuisine preferences
Generating a hidden vector for each user and cuisine category by using a matrix decomposition algorithm, positioning the user and the cuisine on a space represented by the hidden vector, wherein the cuisine with a similar distance to the user shows that the user is more interested, so that a higher exposure rate is allocated to restaurants of the cuisine category; calculating the preference of the user for each cuisine in advance by using an SVD algorithm, and selecting three cuisine categories which are most preferred by each user for subsequent sequencing;
step 3 restaurant blending ranking
When the user uses the sorting function, the following operations are performed:
3.1 restaurant screening
The restaurant screening is divided into two steps, firstly, the real-time or input position information of the user is obtained, and only restaurants in the city where the user is located are reserved according to the position information; then, the restaurants in the off-shelf state are filtered, and only the restaurants in the business on the day are reserved;
3.2 freight calculation and sorting based on freight Interval
Calculating freight rates of the restaurants and the users, which are screened out from the 3.1, according to freight rate rules of the platform according to the positions of the users;
and setting a plurality of freight intervals from low to high, and marking the restaurants according to the freight intervals where the restaurants are located.
Sorting the restaurants from low to high according to the marked freight intervals by using the weak sequence relation;
3.3 order of operation
On the basis of sorting of the 3.2 freight intervals, sorting restaurants in different freight intervals according to operation weight values by using a weak order relation, and recording the obtained result as operation sorting; the operational ordering is considered to be a rearrangement of restaurants in each freight interval, but keeping restaurants in lower freight intervals entirely ahead of restaurants in higher freight intervals as a whole;
3.4 sales ordering
The integral point time of the user browsing platform is approximated, the restaurants in each freight interval of 3.2 are sorted again according to the corresponding integral point sales data in 2.1 by using the weak sequence relation, and the obtained results are recorded as sales sorting; sales ranking is considered another sort of rearrangement for restaurants in each freight interval, but keeping restaurants in lower freight intervals entirely ahead of restaurants in higher freight intervals as a whole;
3.5 order fusion
Mixing the sequencing results of 3.3 and 3.4, and sequencing according to the operation of odd-numbered times and the sales of even-numbered times; for the two-party sequencing of the same restaurant, selecting the ranking on the former side for display, deleting the ranking on the latter side and sequentially replacing the ranking by the restaurants on the latter side; if the odd number of times and the even number of times of a restaurant are the same, the odd number of times is used for showing. Thereby obtaining a fusion order;
3.6 rank adjustment based on class
Reading the user preference cuisine categories calculated in advance in the step 2.2, and then dividing the fusion sorting result generated in the step 3.5 by taking each continuous 20 restaurants as a sorting block; for 20 restaurants in a sequencing block, setting the top of the 20 restaurants for preferential display, and keeping the sequence of the set restaurants unchanged during the setting; and so on, the same operation is executed on all the sorting blocks; the order adjustment enables the restaurant with the dish family preferred by the user to be displayed at a position closer to the front, so that the click rate and the order conversion rate are improved;
outputting and displaying the finally adjusted sorting result;
step 4 data update
The ordering in 2.2, 3.3, 3.4 needs to be updated once per week to take into account the influence of timeliness and seasonal factors on the order.
Compared with the prior art, the invention has the following advantages:
1) the restaurant ordering method comprehensively considers factors such as restaurant order sales volume, operation cooperation of merchants, personal preference of users and the like to order restaurants of a take-out platform;
2) the restaurants with high sales volume and high operation value are displayed preferentially on the whole, so that the user experience and the platform income are improved;
3) in consideration of different eating habits of the consumers in the morning, the evening and the evening, the method of time-sharing statistics is used when the sales volume of the restaurant order is processed, and the sequencing effect is improved;
4) the SVD algorithm in machine learning is used for calculating the preference of the user to all cuisine (not all restaurants), so that the matrix sparseness problem existing in the traditional recommendation algorithm is well solved;
5) the displayed restaurant ranking list can be dynamically updated, the ranking results seen by different users due to different preferences are obviously different, and the displayed restaurant ranking list is prevented from being uniform;
6) on the basis of the restaurant ranking list after the ranking fusion, the ranking adjustment is continuously carried out according to the preference of the cuisine of the user, restaurants which the user may like are preferentially displayed, and the click rate and the order conversion rate are improved;
7) from the operation perspective, when the restaurant which is helpful for purchasing the advertisement in the early period stops purchasing the advertisement, the sales volume brought by the high exposure still can be kept at a higher rank in the sales volume sequencing, so that the exposure is prevented from dropping sharply, and the willingness of the restaurant to purchase the advertisement is improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The present invention is described in further detail below with reference to specific embodiments.
As shown in FIG. 1, the present invention
A restaurant mixed sequencing method of a take-out platform comprises the following steps:
step 1, restaurant data processing
Marking all restaurants in a restaurant table of a take-out platform database mainly relates to two aspects: a weight is given to the restaurant from the operation angle and is used as the operation weight of the restaurant; and marking the restaurants according to the cuisine categories of the restaurants.
1.1 restaurant operation weight assignment
In actual operation, the operation department may give operation weight to the restaurant according to the cooperation situation of the platform and the merchant, such as whether the restaurant purchases the advertisement on the platform, the current discount strength of the restaurant, the quality of the restaurant, the cooperation depth with the platform, and the like. The smaller the weight value of a restaurant operation indicates that the restaurant should be displayed preferentially from the operation perspective.
1.2 restaurant cuisine markers
The cuisine category is an important characteristic of the restaurant and an important factor to be considered when the user makes restaurant ranking recommendation, so that the cuisine category of the restaurant needs to be marked in advance. Generally, the following categories can be mainly considered: sweet milk tea, Yuexing, Macao, Shanghai, Chuanxiang, spicy, Japanese and Korean cuisine, breakfast snack, hamburger fast food, western dinner and the like. The excessive types of the cuisine can cause the problem of sparseness in subsequent matrix calculation, and about 10 are suggested. A restaurant may have multiple tags depending on the dishes it primarily sells.
Step 2 order data analysis
And only reading platform order data of the last two weeks in consideration of seasons and time efficiency. The following fields need to be included in the data: order ID, order time, user ID, restaurant ID, and restaurant cuisine.
2.1 time-phased sales statistics
And counting the order sales volume of all restaurants in the time periods of 30 minutes before and 30 minutes after each hour in the past two weeks by taking the read historical order data as the unit of hour. For example, the order sales at 12 noon calculates the respective cumulative sales for all restaurants in the 11:31 to 12:30 time period each day for the last two weeks. This data needs to be computed well in advance for use in sorting.
2.2 calculating user cuisine preferences
The matrix decomposition algorithm is a very classical sorting recommendation algorithm, a hidden vector is generated for each user and cuisine category, the user and the cuisine are positioned on a space represented by the hidden vector, cuisine with a close distance to the user shows that the user is more interested, and then restaurants of the cuisine can be given a higher exposure in the sorting process. Singular Value Decomposition (SVD) is a common method in matrix decomposition. The invention uses SVD algorithm to calculate the preference of the user for the dish series in advance.
Processing the read order data to generate a co-occurrence matrix M of the user ID and the restaurant cuisine, wherein the row of the co-occurrence matrix M represents the user, the column of the co-occurrence matrix M represents the cuisine, and the order placing times of the user i in the restaurant with the cuisine label of j in the past two-week history order are counted as an element MijThe value of (a). Assuming that the matrix M is an M × n matrix, it can be decomposed into M ═ U ∑ VTWhere U is an m × m orthogonal matrix, V is an n × n orthogonal matrix, and Σ is an m × n diagonal matrix. Taking larger k elements in the diagonal matrix sigma as implicit features, deleting other dimensionalities of sigma and corresponding dimensionalities in U and V, and decomposing the matrix M into M ≈ M' ═ Um×k∑k×kVk×n TAnd the matrix decomposition with the implicit quantity dimension of k is completed.
From the matrix M', the three cuisine with the largest preference value of each user are selected as the preference cuisine of the user.
Step 3 restaurant blending ranking
When the user uses the sorting function, the following operations are performed:
3.1 restaurant screening
The restaurant screening is divided into two steps, firstly, the real-time or input position information of the user is obtained, and only restaurants in the city where the user is located are reserved according to the position information. Then, the restaurants in the states of business suspension, off-shelf and the like are filtered, and only the restaurants in the business day are reserved.
3.2 freight calculation and sorting based on freight Interval
And calculating freight rates of the restaurants and the user generated by the restaurant and the user according to the freight rate rule of the platform for the restaurants screened in the 3.1 according to the position of the user.
Several freight intervals are set from low to high, such as interval a ═ a, B), interval B ═ B, C), interval C ═ C, d), and the like. The restaurant is then marked according to the freight interval in which it is located.
Weak ordering relation is a binary relation and has wide application in the ordering field. A binary relation is called a weak order relation if the following two conditions are met,
and (4) sorting the restaurants from low to high according to the marked freight intervals by using a weak ordering relation (dish ordering relation).
3.3 order of operation
On the basis of 3.2 freight interval sequencing, restaurant in different freight intervals are respectively sequenced according to operation weight values by using weak ordering relations (wait ordering relations), and the obtained results are recorded as operation sequencing. It is noted that the operational ordering can be viewed as a rearrangement of restaurants within each freight interval, but that restaurants that remain lower freight intervals overall are ordered completely before restaurants in higher freight intervals.
3.4 sales ordering
Approximate the hour of the user browsing the platform, e.g., 11:31 to 12:30 using hour 12. And (3) sorting the restaurants in each freight interval of 3.2 by using a weak ordering relation (dish ordering relation) according to the corresponding whole-point sales volume data in 2.1, and recording the obtained result as sales volume sorting. Likewise, the sales ranking can be viewed as another rearrangement of restaurants in each freight interval, but with restaurants in lower freight intervals overall kept completely ahead of restaurants in higher freight intervals.
3.5 order fusion
The sequencing results of 3.3 and 3.4 are mixed, and operation sequencing is used according to the sequencing of odd-numbered times, and sales sequencing is used for even-numbered times. For the two-party sequencing of the same restaurant, the previous position is selected for showing, and the later position is deleted and replaced by the subsequent restaurant in sequence. If the odd number of times and the even number of times of a restaurant are the same, the odd number of times is used for showing. Thereby resulting in a fusion ordering.
3.6 rank adjustment based on class
And reading the user preference menu categories calculated in advance in 2.2. The fused ranking results generated in 3.5 are then divided as a ranking block for each successive 20 restaurants. For 20 restaurants in a sorting block, the restaurant with the cuisine category consistent with the preference category of the user is set to be preferentially displayed at the top of the 20 restaurants, and the sequence of the set restaurants is kept unchanged during the setting. And so on, the same operation is performed for all the sorting blocks. The order adjustment enables the restaurant with the dish preference of the user to be displayed at a position closer to the front, and is beneficial to improving the click rate and the order conversion rate.
And outputting and displaying the finally adjusted sorting result.
Step 4 data update
Taking into account the influence of seasonal factors on the order, it is necessary to update the rankings in 2.2, 3.3, 3.4 once per week.
Claims (1)
1. A restaurant mixed ordering method for a take-out platform is characterized by comprising the following steps: the method comprises the following steps:
step 1, restaurant data processing
Marking all restaurants in a restaurant table in a takeaway platform database relates to two aspects: a weight is given to the restaurant from the operation angle and is used as the operation weight of the restaurant; marking the restaurants according to the cuisine categories to which the restaurants belong;
1.1 restaurant operation weight assignment
In actual operation, an operation department can endow a restaurant with an operation weight value according to the cooperation condition of the platform and a merchant; the smaller the operation weight value of a restaurant is, the restaurant should be displayed preferentially from the operation perspective;
1.2 restaurant cuisine markers
The cuisine category is an important characteristic of the restaurant and is an important factor to be considered when the user carries out restaurant sequencing recommendation, so that the cuisine category of the restaurant needs to be marked in advance; a restaurant has a plurality of dish labels according to dishes mainly sold by the restaurant;
step 2 order data analysis
Reading historical order data of the platform, wherein the data comprises the following fields: order ID, order time, user ID, restaurant ID, and restaurant cuisine;
2.1 time-phased sales statistics
Counting the order sales volume of each restaurant in time intervals by taking the read historical order data as a unit in hours;
2.2 calculating user cuisine preferences
Generating a hidden vector for each user and cuisine category by using a matrix decomposition algorithm, positioning the user and the cuisine on a space represented by the hidden vector, wherein the cuisine with a similar distance to the user shows that the user is more interested, so that a higher exposure rate is allocated to restaurants of the cuisine category; calculating the preference of the user for each cuisine in advance by using an SVD algorithm, and selecting three cuisine categories which are most preferred by each user for subsequent sequencing;
step 3 restaurant blending ranking
When the user uses the sorting function, the following operations are performed:
3.1 restaurant screening
The restaurant screening is divided into two steps, firstly, the real-time or input position information of the user is obtained, and only restaurants in the city where the user is located are reserved according to the position information; then, the restaurants in the off-shelf state are filtered, and only the restaurants in the business on the day are reserved;
3.2 freight calculation and sorting based on freight Interval
Calculating freight rates of the restaurants and the users, which are screened out from the 3.1, according to freight rate rules of the platform according to the positions of the users;
and setting a plurality of freight intervals from low to high, and marking the restaurants according to the freight intervals where the restaurants are located.
Sorting the restaurants from low to high according to the marked freight intervals by using the weak sequence relation;
3.3 order of operation
On the basis of sorting of the 3.2 freight intervals, sorting restaurants in different freight intervals according to operation weight values by using a weak order relation, and recording the obtained result as operation sorting; the operational ordering is considered to be a rearrangement of restaurants in each freight interval, but keeping restaurants in lower freight intervals entirely ahead of restaurants in higher freight intervals as a whole;
3.4 sales ordering
The integral point time of the user browsing platform is approximated, the restaurants in each freight interval of 3.2 are sorted again according to the corresponding integral point sales data in 2.1 by using the weak sequence relation, and the obtained results are recorded as sales sorting; sales ranking is considered another sort of rearrangement for restaurants in each freight interval, but keeping restaurants in lower freight intervals entirely ahead of restaurants in higher freight intervals as a whole;
3.5 order fusion
Mixing the sequencing results of 3.3 and 3.4, and sequencing according to the operation of odd-numbered times and the sales of even-numbered times; for the two-party sequencing of the same restaurant, selecting the ranking on the former side for display, deleting the ranking on the latter side and sequentially replacing the ranking by the restaurants on the latter side; if the odd number of times and the even number of times of a restaurant are the same, the odd number of times is used for showing. Thereby obtaining a fusion order;
3.6 rank adjustment based on class
Reading the user preference cuisine categories calculated in advance in the step 2.2, and then dividing the fusion sorting result generated in the step 3.5 by taking each continuous 20 restaurants as a sorting block; for 20 restaurants in a sequencing block, setting the top of the 20 restaurants for preferential display, and keeping the sequence of the set restaurants unchanged during the setting; and so on, the same operation is executed on all the sorting blocks; the order adjustment enables the restaurant with the dish family preferred by the user to be displayed at a position closer to the front, so that the click rate and the order conversion rate are improved;
outputting and displaying the finally adjusted sorting result;
step 4 data update
The ordering in 2.2, 3.3, 3.4 needs to be updated once per week to take into account the influence of timeliness and seasonal factors on the order.
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US20140214534A1 (en) * | 2012-10-18 | 2014-07-31 | Israel L'Heureux | Restaurant menu generation and in-restaurant promotions |
CN108648058A (en) * | 2018-05-15 | 2018-10-12 | 北京三快在线科技有限公司 | Model sequencing method and device, electronic equipment, storage medium |
CN111859188A (en) * | 2020-07-03 | 2020-10-30 | 美味不用等(上海)信息科技股份有限公司 | Restaurant recommendation method and system based on hierarchical analysis of large-scale matrix |
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Application publication date: 20210910 |
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