Examination scheduling method and system for multiple subjects and multiple examination rooms

Abstract

Disclosed in the present invention are an examination scheduling method and system for multiple subjects and multiple examination rooms, comprising: acquiring examinee information, examination information and examination room information, and grouping examinees on the basis of the examinee information, the examination information and the examination room information to obtain examinee groups; on the basis of the examinee information and the examination room information, using integer programming to assign seats for each examinee in each examinee group, so as to obtain a seating arrangement; determining an examination session sequence arrangement algorithm for the examinee groups on the basis of the examination information and the examination room information, and using the examination session sequence arrangement algorithm to perform calculation to obtain an examination session sequence arrangement; and outputting an examination scheduling result. The present invention designs constraint conditions and an objective function by means of a mathematical model, and utilizes integer programming to solve the mathematical model, so as to comprehensively consider the requirements and time conflicts of multiple subjects, more effectively arrange examination time periods, and divide examinees into different groups for examination, thereby better controlling resource allocation and time conflicts, and improving the efficiency and flexibility of examination scheduling.

Description

Multi-subject multi-exam room arrangement method and system TECHNICAL FIELD

[0001] The present application relates to the technical field of examination management systems, and in particular to a multi-subject multi-exam room arrangement method and system. BACKGROUND

[0002] Traditional exam arrangement algorithms are based on single-subject exam arrangement, and different subject exams need to be conducted in different time periods, which may require a large number of exam room resources. At the same time, enough invigilators and other staff are needed to ensure the conduct of the exam. Such a requirement may cause difficulties in some situations where the venue is limited or resources are scarce. The needs of examinee grouping are not considered. In some cases, a particular exam may require examinees to take the exam according to different groupings to ensure efficient resource utilization and high efficiency of exam arrangement. However, the traditional algorithm cannot meet this requirement, resulting in uneven distribution of exam resources or low efficiency of exam arrangement. SUMMARY

[0003] To solve the above problems, the present application provides a multi-subject multi-exam room arrangement method and system, which arranges the exam by comprehensively considering the needs and time conflicts of multiple subjects in multiple exam rooms, solving the problems of uneven distribution of exam resources and low efficiency of exam arrangement of the existing exam arrangement algorithm.

[0004] To achieve the above purpose, the present application provides the following technical solutions:

[0005] A multi-subject multi-exam room arrangement method, comprising the following steps:

[0006] S1. Obtain examinee information, exam information and exam room information, group the examinees according to the examinee information, exam information and exam room information, and obtain examinee groups, wherein the examinee groups include a plurality of exams, each exam belongs to a subject, each exam is located in an exam room, and each exam includes a plurality of different examinees;

[0007] S2. According to the examinee information and the exam room information, use integer programming to allocate seats for each examinee in each examinee group, and obtain a seat arrangement;

[0008] S3. Determine an exam sequence arrangement algorithm for the examinee groups according to the exam information and the exam room information, and calculate the exam sequence arrangement using the exam sequence arrangement algorithm, wherein in the exam sequence arrangement, each exam room corresponds to only one examinee group for each session, each examinee participates in only one subject exam at the same time, and the exam sequence arrangement includes the exam room and the start time of each examinee group;

[0009] S4. Output the exam arrangement result, which includes the examinee groups, the seat arrangement and the exam sequence arrangement.

[0010] Further, the examinee information includes the number of examinees, the selected subjects of each examinee, the attributes of each examinee on each selected subject, the examinee demand and the class to which each examinee belongs; the examination information includes the total number of days of examination, the examination sessions per day, the total number of subjects, the duration of each examination, the weight of each subject, and the minimum interval between examinations; and the examination room information includes the location of each examination room, the maximum number of examinees accommodated by each examination room, and the attributes of each seat in each examination room.

[0011] Further, in step S1, the grouping of examinees according to the examinee information, the examination information and the examination room information is implemented in the following manner: for each examinee i, there is an examination set , which includes all the selected subjects of examinee i, is the combination of selected subjects of examinees of examination j; for each examinee, there is an optimal examination , , with the constraint condition: , where is the weight of subject k, is the attribute score of examinee i on subject k; the grouping g is obtained by linear programming, which satisfies for each examinee.

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

[0013] Further, the specific implementation of step S2 includes the following formula for each examination j:

[0014] ,

[0015] where, indicates the seat allocation of examinee i, indicates the seat set of examination j, indicates the demand set of examinee i, indicates the matching degree between examinee demand and seat attributes; the examinee seat grouping H is obtained by integer programming.

[0016] Furthermore, in step S3, the algorithm for determining the exam session order of candidate groups based on exam information and exam room information further includes: defining a binary variable for each group g in candidate group G, each subject m, each day d, and each session j. When group g takes the exam for subject m in session s on day d, then ,otherwise The constraints of the examination order arrangement algorithm include: .

[0017] Furthermore, in step S3, the constraints of the examination order arrangement algorithm also include:

[0018] .

[0019] Furthermore, in step S3, the constraints of the examination order arrangement algorithm also include:

[0020] .

[0021] Furthermore, in step S3, the specific formula for the examination order arrangement algorithm is as follows:

[0022] ,

[0023] in, Indicates the end time of the last exam. Let m be the start time of the exam. Under constraints, use integer programming to solve the above formula to obtain the exam schedule.

[0024] Through the above technical solution, the present invention has the following beneficial effects: The present invention designs constraints and objective functions using a mathematical model, and solves the mathematical model using integer programming to comprehensively consider the needs and time conflicts of multiple subjects, more effectively arranging examination time slots and dividing candidates into different groups for examination. This better controls resource allocation and time conflicts, improving the efficiency and flexibility of examination scheduling. Attached Figure Description

[0025] Figure 1 is a schematic diagram of the overall process of a multi-subject, multi-examination-room scheduling method according to the present invention.

[0026] Figure 2 is a schematic diagram of a multi-subject, multi-examination-room scheduling system according to an embodiment of the present invention. Detailed Implementation

[0027] With reference to the drawings, the technical solutions in the embodiments of the present application will be clearly and completely described in order to make the above and other objectives, characteristics and advantages of the present application more apparent. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of the present application.

[0028] In order to make the above and other objectives, characteristics and advantages of the present application more apparent, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0029] Embodiment 1

[0030] Referring to FIG. 1, a multi-subject multi-exam room scheduling method includes the following steps:

[0031] S1. Obtain examinee information, examination information and exam room information, group the examinees according to the examinee information, the examination information and the exam room information to obtain examinee groups, wherein the examinee groups include a plurality of examinations, each examination belongs to a subject, each examination is located in an exam room, and each examination includes a plurality of different examinees;

[0032] S2. Assign seats to each examinee in each examinee group according to the examinee information and the exam room information using integer programming to obtain a seat arrangement;

[0033] S3. Determine an examination sequence arrangement algorithm for the examinee groups according to the examination information and the exam room information, and calculate the examination sequence arrangement using the examination sequence arrangement algorithm, wherein in the examination sequence arrangement, each exam room corresponds to only one examinee group for each examination, each examinee participates in only one examination of a subject at the same time, and the examination sequence arrangement includes the exam room and the start time of each examination of each examinee group;

[0034] S4. Output the examination scheduling result, wherein the examination scheduling result includes the examinee groups, the seat arrangement and the examination sequence arrangement.

[0035] In an optional embodiment, the examinee information includes the number of examinees, the selected subjects of each examinee, the attributes of each examinee in each selected subject, the examinee requirements and the class to which each examinee belongs; the examination information includes the total number of examinations, the examination sessions per day, the total number of subjects, the duration of each examination, the weight of each subject, and the minimum interval between examinations; and the exam room information includes the location of each exam room, the maximum number of examinees accommodated by each exam room, and the attributes of each seat in each exam room.

[0036] In an optional embodiment, in step S1, grouping the examinees according to the examinee information, the examination information and the exam room information includes the following specific implementation: for each examinee i, there is an examination set , the examination set including all selected subjects of examinee i, a combination of selected subjects of examinees who have taken examination j; for each examinee, there is an optimal examination , The constraint condition is: wherein is the weight of subject k, is the attribute score of examinee i on subject k; the grouping g is obtained by solving linear programming, which satisfies for each examinee.

[0037] By the above formula, and by solving using integer programming, an optimal solution of examinee grouping can be obtained. Integer programming refers to the limitation of variables in programming to integers. In linear programming problems, some optimal solutions can be fractions or decimals, but for some specific problems, it is often required that the solutions of some variables must be integers. In this scheme, the number of examinees, the number of examination rooms, and the number of subjects all need to be integers, while the weights and attribute scores can be non-integers, so mixed integer programming is used for solving.

[0038] The weight of the subject is the importance of the subject, which is a pre-set numerical value. The attribute score of the examinee on the subject is the pre-selected numerical value of the examinee.

[0039] In an optional embodiment, the constraint condition of the grouping g further includes a target function Q, and the specific formula of the target function Q is wherein, indicates whether examinee i and examinee k belong to the same class, indicates the examinee density of examination j.

[0040] In order to minimize the proportion of classmates in the same examination room, a target function Q is defined to represent the proportion of classmates, and the target function Q is minimized.

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

[0042] ,

[0043] wherein, indicates the seat allocation of examinee i, indicates the seat set of examination j, indicates the demand set of examinee i, indicates the matching degree between examinee demand and seat attribute; by solving using integer programming, the examinee seat grouping H is obtained.

[0044] The goal of the present solution is to arrange the examination schedule for each examinee group so that all examinees complete all subjects in the shortest time.

[0045] In an optional embodiment, in step S3, the examination sequence arrangement algorithm for determining the examinee group according to the examination information and the examination room information further comprises: for each group g in the examinee group G, each subject m, each day d, and each session j, defining a binary variable , when the group g participates in the examination of the subject m in the s-th session on the d-th day, then , otherwise ; the constraint condition of the examination sequence arrangement algorithm comprises .

[0046] We want to minimize the time when the last examinee finishes the examination, and each examination room can only be assigned to one examinee group for each session, so we design a binary variable to quantify the condition of whether an examinee participates in an examination.

[0047] In an optional embodiment, in step S3, the constraint condition of the examination sequence arrangement algorithm further comprises:

[0048] .

[0049] The purpose of this constraint condition is to make each examinee group complete the examination of all subjects.

[0050] In an optional embodiment, in step S3, the constraint condition of the examination sequence arrangement algorithm further comprises:

[0051] .

[0052] The purpose of this constraint condition is to prevent an examinee from participating in multiple subjects at the same time.

[0053] In an optional embodiment, in step S3, the specific formula of the examination sequence arrangement algorithm is:

[0054] ,

[0055] wherein, represents the time when the last examination ends, is the start time of the examination of the subject m, and the above formula is solved by integer programming under the constraint condition to ensure that the examination is conducted according to the schedule and the examinee cannot participate in future examinations in advance, and the examination sequence arrangement is obtained.

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

[0057] Embodiment 2

[0058] Referring to FIG. 2, a multi-subject multi-exam room scheduling system includes:

[0059] A candidate grouping module is configured to obtain candidate information, examination information, and examination room information, group the candidates according to the candidate information, the examination information, and the examination room information, and obtain candidate groups, wherein each candidate group includes examinations of one subject, each examination is located in one examination room, and each examination includes different candidates.

[0060] A seat allocation module is configured to allocate seats for each candidate in each candidate group according to the candidate information and the examination room information using integer programming, and obtain seat arrangements.

[0061] An examination sequence arrangement module is configured to determine an examination sequence arrangement algorithm for the candidate groups according to the examination information and the examination room information, and obtain the examination sequence arrangement using the examination sequence arrangement algorithm, wherein each examination room in the examination sequence arrangement corresponds to only one candidate group, each candidate participates in only one subject examination at the same time, and the examination sequence arrangement includes the examination room and the start time of each examination of each candidate group.

[0062] A result output module is configured to output a scheduling result, wherein the scheduling result includes the candidate groups, the seat arrangements, and the examination sequence arrangement.

[0063] The embodiments disclosed in the specification are only an example of one-sided features of the present application, and the protection scope of the present application is not limited to this embodiment. Any other functionally equivalent embodiments fall within the protection scope of the present application. For those skilled in the art, other various corresponding changes and modifications can be made according to the above-described technical solutions and concepts, and all these changes and modifications should belong to the protection scope of the claims of the present application.

Claims

1. A method for scheduling examinations in multiple subjects and multiple examination rooms, characterized in that, Includes the following steps: S1. Obtain candidate information, examination information, and examination room information. The candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, candidate needs, 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. Candidates are grouped according to the candidate information, examination information, and examination room information to obtain candidate groups. Each candidate group includes several examination sessions, each examination session belongs to one subject, each examination session is located in one examination room, and each examination session includes several different candidates. The specific implementation of grouping candidates according to the candidate information, examination information, and examination room information includes: for each candidate i, there exists an examination set... The set of exams Including all subjects selected by candidate i, Let the capacity be the j-th exam. For candidate i's course selection combination, Let j be the combination of subjects selected by candidates; for each candidate, there exists an optimal combination of subjects. ， The constraints are: ,in The weight of subject k, For candidate i, the attribute score on subject k; based on The constraints are solved by linear programming. Solving for the group g yields a group that satisfies the following condition for each examinee: ； The constraints on the grouping g also include: an objective function Q, the specific formula of which is: Where i represents candidate i, and x represents candidate x. This indicates whether candidate i and candidate x belong to the same class. If candidate i and candidate x belong to the same class, then... =1, when candidate i and candidate x do not belong to the same class. =0， This represents the density of test takers in test j. S2. Based on the candidate information and examination room information, use integer programming to allocate seats for each candidate in each candidate group, resulting in the seating arrangement. For each examination j, there exists a candidate seating grouping formula: ， in, This indicates the seat assignment for candidate i. Let the set of seats for exam j be represented. Let i represent the set of requirements for candidate i. This indicates the degree of matching between test takers' needs and seat attributes. This indicates the seating attribute of exam j. Let represent the k-th desired seat for candidate i; solve the candidate seat grouping formula using integer programming to obtain the candidate seat grouping H; S3. Determine the exam session order algorithm for candidate groups based on exam information and exam room information, and calculate the exam session arrangement using the exam session order algorithm. In the exam session arrangement, each exam room corresponds to only one candidate group per session, and each candidate takes only one subject exam at a time. The exam session arrangement includes the exam room and exam start time for each candidate group. The specific formula for the exam session order algorithm is as follows: ,in, Indicates the end time of the last exam. Let m be the start time of the exam, d be the day d, and s be the sth exam session on day d. Solve the above formula using integer programming under constraints to obtain the exam session arrangement. S4. Output the exam scheduling results, which include candidate grouping, seating arrangement, and exam session arrangement.

2. The examination scheduling method for multiple subjects and multiple examination rooms according to claim 1, characterized in that, In step S3, the algorithm for determining the exam order of candidate groups based on exam information and exam room information further includes: for each group g in candidate group H, each subject m, and d representing the s-th exam on day d, a binary variable is defined. When group g takes the exam for subject m in session s on day d, then ,otherwise The constraints of the examination order arrangement algorithm include: Where M is the total number of subjects.

3. The examination scheduling method for multiple subjects and multiple examination rooms according to claim 2, characterized in that, In step S3, the constraints of the examination order arrangement algorithm also include: ， Where S represents the total number of exam sessions per day, and D represents the total number of exam days.

4. The examination scheduling method for multiple subjects and multiple examination rooms according to claim 3, characterized in that, In step S3, the constraints of the examination order arrangement algorithm also include: ， Where M represents the total number of subjects.

5. A multi-subject, multi-examination-room scheduling system, characterized in that, include: The candidate grouping module is used to acquire candidate information, examination information, and examination room information. The candidate information includes the number of candidates, the subjects selected by each candidate, the attributes of each candidate in each selected subject, candidate needs, 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. Candidates are grouped according to the candidate information, examination information, and examination room information to obtain candidate groups. Each candidate group includes several examination sessions, each examination session belongs to one subject, each examination session is located in one examination room, and each examination session includes several different candidates. The specific implementation of grouping candidates according to the candidate information, examination information, and examination room information includes: for each candidate i, there exists an examination set... The set of exams Including all subjects selected by candidate i, Let the capacity be the j-th exam. For candidate i's course selection combination, Let j be the combination of subjects selected by candidates; for each candidate, there exists an optimal combination of subjects. ， The constraints are: ,in The weight of subject k, For candidate i, the attribute score on subject k; based on The constraints are solved using linear programming to obtain group g, which satisfies the following conditions for each candidate. The constraints on the grouping g also include: an objective function Q, the specific formula of which is as follows: Where i represents candidate i, and x represents candidate x. This indicates whether candidate i and candidate x belong to the same class. If candidate i and candidate x belong to the same class, then... =1, when candidate i and candidate x do not belong to the same class. =0， Let represent the candidate density for exam j; the seat allocation module is used to allocate seats for each candidate in each candidate group using integer programming based on candidate information and exam room information, resulting in a seating arrangement. For each exam j, there exists a candidate seat grouping formula: ， in, This indicates the seat assignment for candidate i. Let the set of seats for exam j be represented. Let i represent the set of requirements for candidate i. This indicates the degree of matching between test takers' needs and seat attributes. This indicates the seating attribute of exam j. Let represent the k-th desired seat for candidate i; solve the candidate seat grouping formula using integer programming to obtain the candidate seat grouping H; The exam session arrangement module is used to determine the exam session order algorithm for student groups based on exam information and exam room information, and to calculate the exam session arrangement using the exam session order arrangement algorithm. In this arrangement, each exam room corresponds to only one student group per session, and each student takes only one subject exam at a time. The exam session arrangement includes the exam room and exam start time for each student group. The specific formula for the exam session order arrangement algorithm is as follows: ,in, Indicates the end time of the last exam. Let m be the start time of the exam, d be the day d, and s be the sth exam session on day d. Solve the above formula using integer programming under constraints to obtain the exam session arrangement. The results output module is used to output the exam scheduling results, which include candidate grouping, seating arrangement, and exam session arrangement.

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