A course scheduling method and system for multiple subjects and multiple examination rooms

Abstract

The present invention discloses an examination scheduling method and system for multiple subjects and multiple examination rooms, including: obtaining candidate information, examination information, and examination room information, grouping candidates according to the candidate information, examination information, and examination room information to obtain candidate groups; using integer programming to allocate seats for each candidate in each candidate group according to the candidate information and examination room information to obtain seat arrangements; determining an examination session sequence arrangement algorithm for candidate groups according to the examination information and examination room information, and calculating the examination session arrangement by using the examination session sequence arrangement algorithm; and outputting the examination scheduling result. The present invention designs constraint conditions and objective functions through a mathematical model, and solves the mathematical model by using integer programming, so as to comprehensively consider the requirements of multiple subjects and time conflicts, more effectively arrange the examination time period, divide candidates into different groups for examinations, better control resource allocation and time conflicts, and improve the efficiency and flexibility of examination scheduling.

Description

Technical Field

[0001] The present invention relates to the technical field of examination management systems, and particularly to an examination scheduling method and system for multiple subjects and multiple examination rooms. Background Art

[0002] Traditional examination scheduling algorithms are based on single-subject scheduling. Examinations for different subjects need to be conducted in separate time periods, which may require a large amount of examination room resources. At the same time, sufficient invigilators and other staff are needed to ensure the conduct of the examinations. Such requirements may cause difficulties in some cases where there are limited venues or scarce resources. The needs of candidate grouping are not considered. In some cases, specific examinations may require candidates to take the examinations in different groups to ensure effective resource utilization and high-efficiency examination scheduling. However, traditional algorithms cannot meet such requirements, resulting in uneven resource allocation or low examination scheduling efficiency. Summary of the Invention

[0003] To solve the above problems, the present invention provides an examination scheduling method and system for multiple subjects and multiple examination rooms. By comprehensively considering the requirements and time conflicts of multiple subjects in multiple examination rooms for examination arrangements, the problems of uneven allocation of examination resources and low examination scheduling efficiency in existing examination scheduling algorithms are solved.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] An examination scheduling method for multiple subjects and multiple examination rooms, comprising the following steps:

[0006] S1. Obtain candidate information, examination information, and examination room information, group the candidates according to the candidate information, examination information, and examination room information to obtain candidate groups, where the candidate groups include several examinations, each examination belongs to one subject, each examination is located in one examination room, and each examination includes several different candidates;

[0007] S2. According to the candidate information and examination room information, use integer programming to allocate seats for each candidate in each candidate group to obtain seat arrangements;

[0008] S3. Determine an examination session sequence arrangement algorithm for candidate groups according to the examination information and examination room information, and use the examination session sequence arrangement algorithm to calculate the examination session arrangement. Among them, in the examination session arrangement, each examination room corresponds to only one candidate group for each session, and each candidate only takes one subject examination at the same time. The examination session arrangement includes the examination room where each candidate group is located and the examination start time;

[0009] S4. Output the examination scheduling result, where the examination scheduling result includes candidate groups, seat arrangements, and examination session arrangements.

[0010] Further, the candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, the candidate requirements, and the class to which each candidate belongs; the examination information includes the total number of examination days, the number of examination sessions per day, the total number of subjects, the duration of each examination session, the weight of each subject, and the minimum interval between examinations; the examination room information includes the location of each examination room, the maximum number of candidates that each examination room can accommodate, and the attributes of each seat in each examination room.

[0011] Further, in step S1, the grouping of candidates according to the candidate information, examination information, and examination room information is specifically implemented as follows: For each candidate i, there is an examination set The examination set C i includes all the subjects selected by candidate i, and S j is the combination of the subjects selected by the candidates who have already taken examination j; for each candidate, there is an optimal examination j * ∈C i , j * The constraint condition is: where ω k is the weight of subject k, and p ik is the attribute score of candidate i in subject k; the grouping g is obtained by solving through linear programming, and the grouping g satisfies for each candidate

[0012] Further, the constraint condition of the grouping g also includes: the objective function Q, and the specific formula of the objective function Q is where, b i · k indicates whether candidate i and candidate k belong to the same class, indicates the candidate density of examination j.

[0013] Further, the specific implementation method of step S2 includes: for each examination session j, there are the following formulas:

[0014]

[0015] where, seat i represents the seat allocation of candidate i, G j represents the seat set of examination j, R i represents the requirement set of candidate i, represents the matching degree between the candidate requirements and the seat attributes; by solving using integer programming, the candidate seat grouping H is obtained.

[0016] Further, in step S3, the examination session sequence arrangement algorithm for determining candidate grouping according to examination information and examination room information further includes: for each grouping g in candidate grouping G, each subject m, each day d, and each session j, define a binary variable χ g,m,s,d , when grouping g takes the examination of subject m in the s-th session on the d-th day, then X g,m,s,d = 1, otherwise χ g,m,s,d = 0; the constraint conditions of the examination session sequence arrangement algorithm include

[0017] Further, in step S3, the constraint conditions of the examination session sequence arrangement algorithm further include:

[0018]

[0019] Further, in step S3, the constraint conditions of the examination session sequence arrangement algorithm further include:

[0020]

[0021] Further, in step S3, the specific formula of the examination session sequence arrangement algorithm is:

[0022]

[0023] where E g represents the time when the last examination session ends, T m is the start time of the examination of subject m, and under the constraint conditions, the above formula is solved using integer programming to obtain the examination session arrangement.

[0024] Through the above technical solutions, the present invention has the following beneficial effects: The present invention designs constraint conditions and objective functions through a mathematical model, and uses integer programming to solve the mathematical model, so as to comprehensively consider the requirements and time conflicts of multiple subjects, more effectively arrange the examination time period, and divide candidates into different groups for examinations. It better controls resource allocation and time conflicts, and improves the efficiency and flexibility of examination scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a schematic diagram of the overall process of an examination scheduling method for multiple subjects and multiple examination rooms of the present invention.

[0026] Figure 2 is a schematic diagram of the structure of an examination scheduling system for multiple subjects and multiple examination rooms in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0027] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Example 1

[0030] See Figure 1 , a scheduling method for multiple subjects and multiple examination rooms, including the following steps:

[0031] S1. Obtain candidate information, examination information, and examination room information, group the candidates according to the candidate information, examination information, and examination room information to obtain candidate groups. The candidate groups include several examinations. Each examination belongs to one subject, each examination is located in one examination room, and each examination includes several different candidates;

[0032] S2. According to the candidate information and examination room information, use integer programming to allocate seats for each candidate in each candidate group to obtain seat arrangements;

[0033] S3. Determine the examination session sequence arrangement algorithm for the candidate groups according to the examination information and examination room information, and calculate the examination session arrangement using the examination session sequence arrangement algorithm. Among them, in the examination session arrangement, each examination room corresponds to only one candidate group for each session, and each candidate only takes an examination of one subject at the same time. The examination session arrangement includes the examination room where each candidate group is located and the examination start time;

[0034] S4. Output the scheduling result, and the scheduling result includes candidate groups, seat arrangements, and examination session arrangements.

[0035] In an optional embodiment, the candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, candidate requirements, and the class to which each candidate belongs; the examination information includes the total number of examination days, the number of examination sessions per day, the total number of subjects, the duration of each examination session, the weight of each subject, and the minimum interval between examinations; the examination room information includes the location of each examination room, the maximum number of candidates that each examination room can accommodate, and the attributes of each seat in each examination room.

[0036] In an optional embodiment, in step S1, the grouping of candidates according to the candidate information, examination information, and examination room information is specifically implemented as follows: for each candidate i, there is an examination set The exam set C i includes all the selected subjects of candidate i, S j is the combination of the selected subjects of the existing candidates for exam j; for each candidate, there is an optimal exam j * ∈C i , j * The constraint condition for is: where ω k is the weight of subject k, p ik is the attribute score of candidate i in subject k; the grouping g is obtained by solving through linear programming, and the grouping g satisfies for each candidate

[0037] Through the above formula and using integer programming to solve, an optimal solution for candidate grouping can be obtained. Integer programming means that the variables in the programming are restricted to integers. In linear programming problems, some optimal solutions may be fractions or decimals, but for some specific problems, it is often required that the solutions of some variables must be integers. In this solution, the number of candidates, the number of examination rooms, and the number of subjects, etc. all need to be integers, while the weights, attribute scores, etc. can be non-integers. Therefore, mixed integer programming is used for solving.

[0038] The weight of the subject is the importance of the subject and is a preset value. The attribute score of the candidate in the subject is a value pre-selected by the candidate.

[0039] In an alternative embodiment, the constraint condition of the grouping g further includes: the objective function Q, and the specific formula of the objective function Q is where, b i · k indicates whether candidate i and candidate k belong to the same class, indicates the candidate density of exam j.

[0040] In order to minimize the proportion of classmates in the same examination room, we define an objective function Q to represent the proportion of classmates and minimize it.

[0041] In an alternative embodiment, the specific implementation manner of the step S2 includes: for each exam j, there is the following formula:

[0042]

[0043] where, seat i represents the seat allocation of candidate i, G j represents the seat set of exam j, R i represents the demand set of candidate i, Indicates the matching degree between the candidate's requirements and the seat attributes; solve it using integer programming to obtain the candidate seat grouping H.

[0044] The goal of this solution is to arrange the exam schedule for each candidate grouping so that all candidates can complete all subjects of the exam in the shortest time.

[0045] In an optional embodiment, in step S3, the exam session order arrangement algorithm for determining the candidate grouping according to the exam information and the examination room information further includes: for each grouping g in the candidate grouping G, each subject m, each day d, and each session j, define a binary variable χ g,m,s,d , when grouping g takes the exam of subject m in the s-th session on the d-th day, then χ g,m,s,d = 1, otherwise χ g,m,s,d = 0; the constraint conditions of the exam session order arrangement algorithm include

[0046] We hope to minimize the time when the last candidate finishes the exam. At the same time, each examination room can only be assigned to one candidate grouping in each session. Therefore, binary variables are designed to quantify the condition of whether a candidate participates in a certain exam.

[0047] In an optional embodiment, in step S3, the constraint conditions of the exam session order arrangement algorithm further include:

[0048]

[0049] The purpose of this constraint condition is to ensure that each candidate grouping must complete all subjects of the exam.

[0050] In an optional embodiment, in step S3, the constraint conditions of the exam session order arrangement algorithm further include:

[0051]

[0052] The purpose of this constraint condition is that candidates cannot take multiple subjects at the same time.

[0053] In an optional embodiment, in step S3, the specific formula of the exam session order arrangement algorithm is:

[0054]

[0055] Among them, E g represents the time when the last exam ends, T m is the start time of the exam for subject m. Solve the above formula using integer programming under the constraint conditions and ensure that the exam is carried out according to the schedule, and candidates cannot take future exams in advance to obtain the exam session arrangement.

[0056] We use off-the-shelf integer programming solvers, such as CPLEX, Gurobi, or solvers in the COIN-OR project, and utilize branch-and-bound and pruning techniques to find the optimal solution.

[0057] Example 2

[0058] See Figure 2 , a test scheduling system for multiple subjects and multiple examination rooms, including:

[0059] A candidate grouping module, which is used to obtain candidate information, examination information, and examination room information, group candidates according to the candidate information, examination information, and examination room information to obtain candidate groups, where the candidate groups include several examinations, each examination belongs to a subject, each examination is located in an examination room, and each examination includes several different candidates;

[0060] A seat allocation module, which is used to allocate seats for each candidate in each candidate group according to the candidate information and examination room information using integer programming to obtain a seat arrangement;

[0061] An examination session arrangement module, which is used to determine an algorithm for arranging the examination session order of candidate groups according to the examination information and examination room information, and calculate the examination session arrangement using the examination session order arrangement algorithm. Among them, in the examination session arrangement, each examination room corresponds to only one candidate group per session, and each candidate only takes an examination of one subject at the same time. The examination session arrangement includes the examination room where each candidate group is located and the start time of the examination;

[0062] A result output module, which is used to output the test scheduling result, and the test scheduling result includes candidate groups, seat arrangements, and examination session arrangements.

[0063] The embodiments disclosed in this specification are only an illustration of the unilateral features of the present invention. The protection scope of the present invention is not limited to this embodiment, and any other functionally equivalent embodiments fall within the protection scope of the present invention. For those skilled in the art, various corresponding changes and deformations can be made according to the technical solutions and concepts described above, and all these changes and deformations should fall within the protection scope of the claims of the present invention.

Claims

1. A method for scheduling examinations in multiple subjects and multiple examination rooms, characterized in that: The following steps are involved: S1. Obtain candidate information, test information and test room information, wherein the candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, the candidate's needs and the class to which each candidate belongs; the test information includes the total number of test days, the number of test sessions per day, the total number of subjects, the duration of each test, the weight of each subject, and the minimum interval between tests; the test room information includes the location of each test room, the maximum number of candidates each test room can accommodate, and the attributes of each seat in each test room, and group the candidates according to the candidate information, test information and test room information to obtain candidate groups, wherein the candidate groups include several tests, each test belongs to one subject, each test is located in one test room, and each test includes several different candidates, and the specific implementation method of grouping the candidates according to the candidate information, test information and test room information includes: for each candidate i, there is a test set The test set C i Includes all the subjects selected by the candidate i, S j is the combination of subjects selected by candidates for exam j; for each candidate, there is an optimal exam j * ∈C i , j * The constraints are: j∈C i , where ω k is the weight of subject k, p ik is the attribute score of examinee i on subject k; objective function Q, the specific formula of objective function Q is: Among them, b i b x Indicates whether candidate i and candidate x belong to the same class, represents the examinee density of test j; the group g is obtained by solving the linear programming, and the group g satisfies for each examinee The constraints of the group g also include: S2. According to the information of candidates and examination room, use integer programming to assign seats to each candidate in each candidate group and obtain the seat arrangement. For each examination j, there is the following formula: Among them, seat i represents the seat allocation of candidate i, G j represents the set of seats for exam j, R i represents the demand set of candidate i, Indicates the matching degree between the examinee's needs and the seat attributes; uses integer programming to solve and obtain the examinee's seat grouping H; S3. Determine the test sequence arrangement algorithm for the examinee groups according to the test information and the test room information, and calculate the test sequence arrangement using the test sequence arrangement algorithm, wherein in the test sequence arrangement, each test room and each session corresponds to only one examinee group, and each examinee only takes an exam for one subject at the same time. The test sequence arrangement includes the test room and the test start time of each examinee group. The specific formula of the test sequence arrangement algorithm is: Among them, E g Indicates the time when the last test of group g ends, T k is the start time of the exam for subject k, d is the dth day, s is the sth session, and the above formula is solved using integer programming under the constraints to obtain the exam schedule; S4. Output the test scheduling results, which include candidate grouping, seat arrangement and test time arrangement.

2. A method for scheduling examinations in multiple subjects and multiple examination rooms according to claim 1, characterized in that: In step S3, the algorithm for determining the test order arrangement of the examinees according to the test information and the test site information further includes: defining a binary variable x g,k,s,d , when group g takes the exam for subject k at the sth session on the dth day, then χ g,k,s,d =1, otherwise χ g,k,s,d =0; the constraints of the test sequence arrangement algorithm include 3. A method for scheduling examinations in multiple subjects and multiple examination rooms according to claim 2, characterized in that: In step S3, the constraints of the test sequence arrangement algorithm also include:

4. A method for scheduling examinations in multiple subjects and multiple examination rooms according to claim 3, characterized in that: In step S3, the constraints of the test sequence arrangement algorithm also include:

5. A multi-subject and multi-examination room examination scheduling system, characterized in that: include: The candidate grouping module is used to obtain candidate information, test information and test room information, wherein the candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, the candidate's needs and the class to which each candidate belongs; the test information includes the total number of test days, the number of test sessions per day, the total number of subjects, the duration of each test, the weight of each subject, and the minimum interval between tests; the test room information includes the location of each test room, the maximum number of candidates each test room can accommodate, and the attributes of each seat in each test room. The candidates are grouped according to the candidate information, the test information and the test room information to obtain the candidate grouping, wherein the candidate grouping includes several tests, each test belongs to one subject, each test is located in one test room, and each test includes several different candidates. The specific implementation method of grouping the candidates according to the candidate information, the test information and the test room information includes: for each candidate i, there is a test set The test set C i Includes all the subjects selected by the candidate i, S j is the combination of subjects selected by candidates for exam j; for each candidate, there is an optimal exam j * ∈C i , j * The constraints are: j∈C i , where ω k is the weight of subject k, p ik is the attribute score of examinee i on subject k; objective function Q, the specific formula of objective function Q is: Among them, b i b x Indicates whether candidate i and candidate x belong to the same class, represents the examinee density of test j; the group g is obtained by solving the linear programming, and the group g satisfies for each examinee j∈C i ; The seat allocation module is used to allocate seats for each candidate in each candidate group according to the candidate information and examination room information using integer programming to obtain the seat arrangement. For each examination j, there is the following formula: Among them, seat i represents the seat allocation of candidate i, G j represents the set of seats for exam j, R i represents the demand set of candidate i, Indicates the matching degree between the examinee's needs and the seat attributes; uses integer programming to solve and obtain the examinee's seat grouping H; The test arrangement module is used to determine the test sequence arrangement algorithm of the examinee group according to the test information and the test room information, and calculate the test arrangement using the test sequence arrangement algorithm, wherein in the test arrangement, each test room and each session only corresponds to one examinee group, and each examinee only takes one subject test at the same time. The test arrangement includes the test room and the test start time of each examinee group. The specific formula of the test sequence arrangement algorithm is: Among them, E g Indicates the time when the last test of group g ends, T k is the start time of the exam for subject k, d is the dth day, s is the sth session, and the above formula is solved using integer programming under the constraints to obtain the exam schedule; The result output module is used to output the test scheduling results, which include candidate grouping, seat arrangement and test time arrangement.

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