CN105894241A - Inverted-triangle-based mixed shift arrangement system and method for flexible service system - Google Patents

Abstract

The invention discloses an inverted-triangle-based mixed shift arrangement system and method for a flexible service system. The system comprises a user and staff management module, a historical same-period data management module, an algorithm parameter management module, a shift arrangement time management module, a unit time definition management module, a window number generation module, a newly established shit arrangement module, and a shift arrangement management module. In addition, the invention also provides an inverted-triangle-based mixed shift arrangement method for a flexible service system. According to the shift arrangement system, a shift arrangement table can be obtained based on prediction and thus a shift arrangement result is generated. The system can carry out window working staff registration restriction and monitoring and data analyses on various states, thereby realizing the management function of the window working staff effectively. The window working staff can ask for leave or carry out shift changing directly on the system; and after successful application, the system can adjust a shift arrangement plan and inquire various statistic data of the window working staff, so that the basis can be provided for science shift arrangement.

Description

The mixing Workforce Management of elastic service system based on inverted triangle and method

Technical field

The present invention relates to a kind of mixing Workforce Management and the method for elastic service system based on inverted triangle.

Background technology

In existing window services, the time management of staff uses more traditional mode: opening how many windows, how open window, completely by manually arranging, sets up staff's shift report.Due to economic fast development, the project of window services day by day increases, and quantity of service quickly increases, service request is the highest, and the open quantity of existing service Room window and window banging personnel are relatively fixed.If the method open window quantity not taking science adjusts staff's configuration, only rely on service Room window banging personnel are limited at present service ability and job performance, the service Room is in flow of the people peak period, the waiting time of client certainly will increase, efficiency of service will be given a discount, and customer satisfaction with services also will decrease；And servicing the Room at flow of the people low-valley interval, window services resource seems again idle with waste.From the analysis of management and service demand angle, the key problem servicing the Room urgently to be resolved hurrily is, for customer demand, carries out rational window and arranges and suitable personnel depaly.

Although occurring in that some scheduling methods at present, such as Patent No. 200810167327.2, entitled a kind of Workforce Management and the Chinese patent of method, but the actual demand of window services industry can not be met.

Summary of the invention

The purpose of the present invention is contemplated to solve the problems referred to above, the mixing Workforce Management of based on inverted triangle the elastic service system in the case of providing a kind of window banging personnel inadequate and method, can prediction window number, and obtain the result of arranging an order according to class and grade having strict demand, improve the enthusiasm of window banging personnel, improve the satisfaction of client.

To achieve these goals, the present invention adopts the following technical scheme that the mixing scheduling method of a kind of elastic services based on inverted triangle, comprising the steps: the window number open according to the history business datum same period prediction subsequent work time period, the minimum window number that the subsequent work time period opens is drawn by equation below:

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents client's number that average each window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is as follows:

Step 1: order

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2.

According to window banging personnel's scheduling data of revised prediction window number data genaration each time period, window banging personnel's scheduling data is drawn by following object function；

Wherein, T represents plan phase total natural law of arranging an order according to class and grade, n represents the sum of window banging personnel, is a unit of time by 15 minutes, and a workaday window banging time is divided into 27 periods, the morning, 8:30 to 8:45 was designated as the 1st period, 8:45 to 9:00 was designated as the 2nd period, and by that analogy, 12:00 to 14:00 was designated as the 15th period, 14:00 to 14:15 was designated as the 16th period, was designated as the 27th period to 16:45 to 17:00 by that analogy；c_jkMeeting the minimum window number needed for the customer demand for service jth sky k moment in representing the plan phase of arranging an order according to class and grade, queueing theory calculates each hour and needs open window number, therefore c_j1=c_j2=c_j3=c_j4, other by that analogy, therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jkAccording to substantial amounts of questionnaire survey and psychological test, SPSS is utilized to be analyzed obtaining to above-mentioned data: window banging personnel can efficiently have the service average time of quality to be 1 hour, window banging personnel must go to backstage decompression and loosen after working continuously 45 minutes or 1 hour, obviously, as shift scheduling model, should be able to infer that every window banging personnel's every workday is respectively at window and the time period of background work, decision variable x from the value of decision variable_ijkRepresent and certain window banging personnel every day in the duty of window banging period, work as x_ijkWhen value is 1, represent the i-th people in jth sky kth time period at window banging, work as x_ijkWhen value is 0, represent the i-th people in jth sky kth time period not at window banging, i=1 ..., m.Decision variable x_ijk, i=m+1, ..., n, represent the part-time window banging personnel day duty in the working hour of certain window banging, each window banging personnel only require in two time periods of window banging every day, the morning, 8:30 to 12:00 was first time period, noon, 12:00 to 14:00 was the second time period, afternoon, 14:00 to 17:00 was the 3rd time period, assume that window banging personnel only have m, remaining n-m window banging personnel is part-time staff, part-time window banging personnel do not arrange on duty noon, minimum for optimization aim in total working time the shortest and outfit the personnel storehouse of queuing time and all windows meeting client, draw above-mentioned object function；

Constraints:

2(1-x_{ij , k})x_{ij , k+1}≤x_{ij , k+2}+x_{ij , k+3},

Above formula ensures that the staff of full-time window works 3 time periods the most continuously once work；

Above formula ensures that full-time window banging personnel work 4 time periods the most continuously once work；

Above formula ensures full-time window banging personnel's morning or afternoon once two unit of time of having a rest, ensuing all the morning or afternoon to not be used in window banging.

Above formula ensures any one sky in window banging person works's day, the i.e. morning, noon, afternoon, only two time periods of work or a time period, and the darg time is less than 8 hours；

If above formula ensures that window banging personnel are on duty for certain day noon, then he (she) 12 front half an hours not in window services, so guarantee noon on duty before have the time to have lunch and have time on duty at noon；

If above formula ensures that full-time window banging personnel are on duty for noon, then afternoon he (she) not at window banging；

Above formula ensures that full-time window banging personnel's morning or afternoon can not only work 1 time period before leaving offices, i.e. 15 minutes；

Above formula ensures that full-time window banging personnel can only work 2 time periods before leaving offices in the morning or afternoon, i.e. 30 minutes:

Above formula ensures that jth sky random time section k is operated at full capacity；

Above formula ensure jth sky have noon and only window banging personnel on duty；

Realize the another kind of scheduling model of window banging personnel " inverted triangle " below；

DefinitionDefinition indicative function:

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

Definition

SetIn element andEqual number is designated as n₂, to arbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Time of having a rest compensate the window banging personnel to second group as far as possible and complete, draw:

If working as n₁＜ 4 and c_j13=d_j1Time,

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

Work as n₁When=6,

Other situations are by that analogy, through limited number of time recursion, have selected the working pattern of window banging person works's day full-time for m, and the working time duration of the working time every day time length ratio of remaining n-m part-time window window banging personnel above-mentioned m window banging personnel every day is short；

Above formula ensures that full-time window banging personnel net cycle time length within a cycle is less than 1 hour.

Preferably: the history business datum same period includes business item, time of drawing a bill, waiting time, deadline, accepts window and window banging personnel.

Preferably: client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

On the other hand, the mixing Workforce Management of a kind of elastic services based on inverted triangle, including:

History contemporaneous data management module, for the record of historical data and management:

Window number generation module, according to the window number that the history business datum same period prediction subsequent work time period is open, the minimum window number that the subsequent work time period opens is drawn by equation below:

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents client's number that average each window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is as follows:

Step 1: order

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2.

Newly-built module of arranging an order according to class and grade, according to window banging personnel's scheduling data of revised prediction window number data genaration each time period, window banging personnel's scheduling data is drawn by following object function；

Wherein, T represents plan phase total natural law of arranging an order according to class and grade, n represents the sum of window banging personnel, is a unit of time by 15 minutes, and a workaday window banging time is divided into 27 periods, the morning, 8:30 to 8:45 was designated as the 1st period, 8:45 to 9:00 was designated as the 2nd period, and by that analogy, 12:00 to 14:00 was designated as the 15th period, 14:00 to 14:15 was designated as the 16th period, was designated as the 27th period to 16:45 to 17:00 by that analogy；c_jkMeeting the minimum window number needed for the customer demand for service jth sky k moment in representing the plan phase of arranging an order according to class and grade, queueing theory calculates each hour and needs open window number, therefore c_j1=c_j2=c_j3=c_j4, other by that analogy, therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jkAccording to substantial amounts of questionnaire survey and psychological test, SPSS is utilized to be analyzed obtaining to above-mentioned data: window banging personnel can efficiently have the service average time of quality to be 1 hour, window banging personnel must go to backstage decompression and loosen after working continuously 45 minutes or 1 hour, obviously, as shift scheduling model, should be able to infer that every window banging personnel's every workday is respectively at window and the time period of background work, decision variable x from the value of decision variable_ijk, represent the full-time window banging personnel day duty in the working hour of certain window banging, i=1 ..., m.Decision variable x_ijk, i=m+1, ..., n, represent the part-time window banging personnel day duty in the working hour of certain window banging, each window banging personnel only require in two time periods of window banging every day, the morning, 8:30 to 12:00 was first time period, noon, 12:00 to 14:00 was the second time period, afternoon, 14:00 to 17:00 was the 3rd time period, when window banging personnel day are engraved in window banging in the some time, value is 1, it is otherwise 0, assume that window banging personnel only have m, remaining n-m window banging personnel is part-time staff, part-time window banging personnel do not arrange on duty noon, minimum for optimization aim in total working time the shortest and outfit the personnel storehouse of queuing time and all windows meeting client, draw above-mentioned object function；

Constraints:

2(1-x_{ij , k})x_{ij , k+1}≤x_{ij , k+2}+x_{ij , k+3},

Above formula ensures that full-time window banging personnel work 3 time periods the most continuously once work；

Above formula ensures that full-time window banging personnel work 4 time periods the most continuously once work；

Above formula ensures full-time window banging personnel's morning or afternoon once two unit of time of having a rest, ensuing all the morning or afternoon to not be used in window banging；

Above formula ensures any one sky in window banging person works's day, the i.e. morning, noon, afternoon, only two time periods of work or a time period, and the darg time is less than 8 hours；

If above formula ensures that full-time window banging personnel are on duty for certain day noon, then he (she) 12 front half an hours not in window services, so guarantee noon on duty before have the time to have lunch and have time on duty at noon；

If above formula ensures that full-time window banging personnel are on duty for noon, then afternoon he (she) not at window banging；

Above formula ensures that full-time window banging personnel's morning or afternoon can not only work 1 time period before leaving offices；

Above formula ensures that full-time window banging personnel can only work 2 time periods before leaving offices in the morning or afternoon；

Above formula ensures that any sky random time section k is operated at full capacity；

Above formula ensure jth sky have noon and only full-time window banging personnel on duty；

Realize the scheduling model of window banging personnel " inverted triangle " below；

DefinitionDefinition indicative function:

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

Definition

SetIn element andEqual number is designated as n₂, to arbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Time of having a rest compensate the window banging personnel to second group as far as possible and complete, draw:

If working as n₁＜ 4 and c_j13=d_j1Time,

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

Work as n₁When=6,

Other situations are by that analogy, through limited number of time recursion, have selected the working pattern of window banging person works's day full-time for m, and the working time duration of the working time every day time length ratio of remaining n-m part-time window banging personnel above-mentioned m window banging personnel every day is short；

Above formula ensures that full-time window banging personnel net cycle time length within a cycle is less than 1 hour.

Preferably: in history contemporaneous data management module, the history business datum same period includes business item, time of drawing a bill, waiting time, deadline, accepts window and window banging personnel.

Preferably: in window number generation module, client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

Preferably: include user and staff's benefits module, for record window staff's personal information, window banging personnel's personal information includes name, job number and telephone number.

Preferably: include that algorithm parameter manages module, for the various parameters needed for prediction window number and algorithm of arranging an order according to class and grade being carried out typing and dynamically management, hop count and maximum motor-driven staff number every day when requiring including the maximum disparity between traffic handling time, business weight, queue length, client's latency tolerant upper limit, employee's High-effective Service duration, period maximal workload and minimum workload, participate in arranging an order according to class and grade shared by quantity of cadres, noon.

Preferably: segment management module when including arranging an order according to class and grade, classify every day when prediction window number concrete start and end time of period carries out typing and management.

Preferably: including unit interval definition management module, when automatic scheduling, the concrete start and end time of 27 unit time period carries out typing and management.

Preferably: include management module of arranging an order according to class and grade, query statistic, data backup, reduction, system user and rights management are measured for the realization person works that arranges an order according to class and grade.

Elastic services system refers to that staff can neatly, independently select the contents such as concrete time or the place of work on the premise of the task completing regulation or fixing working time length, to replace the system in unified, fixing commuter time.The implementation of this working system, for establishing good window services external, strengthening the humanistic care to window banging personnel, promote window services efficiency, of far-reaching significance.

1. improve window banging efficiency, reduce client's transacting business time.The total management system in the service Room not only records each item data of the transacting business of client, the most also window banging personnel is carried out performance appraisal." work efficiency " is to weigh the leading indicator of job performance, and improve work efficiency it is crucial that rationally shortens every business handles duration.And the key factor affecting efficiency is staff's Physiological Psychology stability state, service ability and service level.Implement elastic services system, core work time and non-core working time can be distinguished, guarantee that window banging personnel obtain enough rests and vocational study in the non-core working time, the energy having abundance in the time period that core work time i.e. business is the busiest keeps optimum state, devote oneself to work, thus improve job performance.Implement elastic services system, can be according to client's flow and the measuring and calculating of portfolio, open suitable service window, staff provides service with optimal working condition simultaneously, and client can obtain good service, it is possible to reduce waiting time and transacting business time.

2. alleviate window banging personnel's pressure, meet Batch Processing needs.Window banging makes pressure source from many-side because of its particularity.One is that post is fixed, the most constant including job site, working time.Two is that content is single, the business operation relative mechanical of process, repetition.Three is that service standard is unified, discipline execution is strict, including window mental outlook, operating process, service quality etc..All day, window banging personnel were in spirit high pressure conditions for a long time in the face of client, once caused anxiety, the negative emotions such as be sick of, easily affect work efficiency, reduce service level, and serious will damage customer relationship.Therefore, set up comprehensive mental pressure dredge decompression mechanism without benefits.Setting up elastic services system, window banging personnel will have reasonable time acceptable learning and dredge, reduce pressure and have a rest, and conscientiously alleviate long-term physical weariness, spiritual high pressure conditions.Carry out elastic services system, also allow for window banging personnel can planned, have the time to carry out customer profile arrangement on backstage, amended record client-related information, associated materials are transferred to administration section, effectively meet background work needs.

3. promote post learning and communication, promote professional qualities.The window management degree of becoming more meticulous improves constantly, and the unicity of the stationarity in window post and job content largely affects the lifting of ' professional.Under elastic services system, window personnel can utilize the elastic services time to carry out window service study, can carry out business communication with other posies personnel, carry out mutually study, allow more window management " specialized personnel " change to " versatile person ".

Compared with prior art, there is advantages that Workforce Management proposed by the invention can not only obtain shift report by prediction thus generates and arrange an order according to class and grade result.Can be by window banging personnel being logged in the monitoring and data analysis limited with various states, it is effectively realized the management function to window banging personnel, window banging personnel can ask for leave the most on this system, adjust class, system adjustable entire row shift plan and window banging demographic data after applying for successfully, arrange an order according to class and grade offer foundation for science.

Accompanying drawing explanation

Fig. 1 is the mixing Workforce Management corn module schematic diagram of elastic services based on inverted triangle in embodiment.

Fig. 2 is the mixing Workforce Management basic data of elastic services based on inverted triangle in embodiment and secondary module diagram.

Fig. 3 is the mixing Workforce Management flow chart of elastic services based on inverted triangle in embodiment.

Detailed description of the invention

The present invention arranges an order according to class and grade at systematic analysis restriction window on the basis of factor, and application queueing theory and nonlinear integer programming establish mixing Workforce Management and the method for the service a kind of elastic services based on inverted triangle in hall.Especially for the insufficient situation of window banging personnel.

Embodiment one: see Fig. 1 to Fig. 3, a kind of mixing scheduling method of elastic services based on inverted triangle, comprising the steps: the window number open according to the history business datum same period prediction subsequent work time period, the minimum window number that the subsequent work time period opens is drawn by equation below:

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents client's number that average each window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is as follows:

Step 1: order

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2；

According to window banging personnel's scheduling data of revised prediction window number data genaration each time period, window banging personnel's scheduling data is drawn by object function；

In the case of window banging is undermanned, every skylight opening scheduling model is lined up " inverted triangle ", and (window banging personnel are once work, except noon, the time of having a rest of window banging personnel is only a unit of time, this definition is harsher, having a lot of situation nothing to solve, therefore condition is somewhat relaxed.), i.e. before window banging personnel operate at full capacity as far as possible, the work of window banging personnel every day below is the fewest, client flow peak when, part-time staff can be engaged, the most i.e. ensure the service quality of window, also reduce the cost of serving of window.

The function realized has, and window banging personnel work 45 minutes or 1 hour continuously, can have a rest 15 minutes；The service Room arranges a staff on duty and staff on duty at noon to not be used in window services at 11:30 to 12:00 noon, but needs in morning hours service；The staff of each window services is only serviced two periods in a working day (morning, noon, afternoon)；Staff's education of window banging can be presetted in the cycle of one month, go on business or have a holiday and do not affect his total time in window services the whole cycle；All staff in window services are few (error is 1 hour) in the time difference of the inherent window services of 1 cycle (1 month).

Realizing above-mentioned functions by following mathematical model, relevant parameter is defined as follows: T represents the plan phase total natural law (typically with 1 month as cycle) of arranging an order according to class and grade；N represents the sum of window banging personnel.It was a unit of time by 15 minutes, one workaday window banging time is divided into 27 periods, the morning, 8:30 to 8:45 was designated as the 1st period, 8:45 to 9:00 was designated as the 2nd period, by that analogy, 12:00 to 14:00 was designated as the 15th period, and 14:00 to 14:15 was designated as the 16th period, was designated as the 27th period to 16:45 to 17:00 by that analogy.c_jk(queueing theory calculates each hour and needs open window number, therefore c minimum window number needed for meeting the customer demand for service jth sky k moment in representing the plan phase of arranging an order according to class and grade_j1=c_j2=c_j3=c_j4, other by that analogy), therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jk.According to substantial amounts of questionnaire survey and psychological test, utilizing SPSS to be analyzed obtaining to above-mentioned data: window banging personnel can efficiently have the service average time of quality to be 1 hour, window banging personnel must go to backstage decompression and loosen after working continuously 45 minutes or 1 hour.Obviously, as shift scheduling model, should be able to infer that every window banging personnel's every workday is respectively at window and the time period of background work, decision variable x from the value of decision variable_ijkRepresent and certain window banging personnel every day in the duty of window banging period, work as x_ijkWhen value is 1, represent the i-th people in jth sky kth time period at window banging, work as x_ijkWhen value is 0, represent the i-th people in jth sky kth time period not at window banging, i=1 ..., m.Decision variable x_ijk, i=m+1 ..., n, represent the part-time window banging personnel day duty in the working hour of certain window banging.Each window banging personnel only require every day two time periods of window banging (morning 8:30 to 12:00, noon 12:00 to 14:00, afternoon 14:00 to 17:00).Assuming that window banging personnel only have m, remaining n-m window banging personnel is part-time staff, and part-time window banging personnel do not arrange on duty noon.Minimum for optimization aim in total working time (unit is 15 minutes) the shortest and outfit the personnel storehouse of queuing time and all windows meeting client, then object function is:

Description according to window shifts arrangement and analysis, and combine the definition of decision variable, the constraints of model mainly has:

2(1-x_{ij , k})x_{ij , k+1}≤x_{ij , k+2}+x_{ij , k+3},

Above formula ensure that the staff of window works 3 time periods (45 minutes) the most continuously once work；

Above formula ensure that window banging personnel work 4 time periods (60 minutes) the most continuously once work；

Above formula ensure that and full-time window banging personnel's morning or afternoon once two unit of time of having a rest, ensuing all the morning or afternoon not be used in window banging.

Above formula ensure that only two time periods of work of any one sky (morning, noon, afternoon) in window banging person works's day or a time period (the darg time is less than 8 hours)；

If above formula ensure that window banging personnel, certain day noon is on duty, then he (she) 12 front half an hours not in window services, so ensure that noon has the time to have lunch and has time on duty at noon before on duty；Because window banging personnel on duty at noon have only to select the morning or work in afternoon, through substantial amounts of investigation, substantial amounts of window banging department wishes to link up on duty on duty for noon and morning, so convenient looking after staff on duty at noon and take off afternoon or go on business and arrange files on backstage, following formula can ensure that the morning is on duty and noon on duty connects.

If above formula ensure window banging personnel on duty for noon, then afternoon he (she) not at window banging；

Above formula ensure that 1 time period (15 minutes) that can not only work before leaving offices in window banging personnel's morning or afternoon；

Above formula ensure that window banging personnel before leaving offices can 2 time periods (30 minutes) of work in the morning or afternoon；

Above formula ensure that jth sky random time section k (by historical data, utilize the theory of statistics and queueing theory ensure client's waiting time do not surpass 15 minutes estimate window number) operate at full capacity；

Above formula ensure that jth sky have noon and only window banging personnel on duty.

Realize the another kind of scheduling model of window banging personnel " inverted triangle " below.

DefinitionDefinition indicative function:

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

Definition

SetIn element andEqual number is designated as n₂.To arbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Time of having a rest compensate the window banging personnel to second group as far as possible and complete, Wo Menyou

If working as n₁＜ 4 and c_j13=d_j1Time,

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

Work as n₁When=6,

Other situations are by that analogy, through limited number of time recursion, have selected m window banging personnel (full-time staff) workaday working pattern, and the working time duration of the working time every day time length ratio of remaining n-m window banging personnel (part-time window banging personnel) above-mentioned m window banging personnel every day is short.

Above formula ensure that the full-time staff of window within a cycle net cycle time length less than 1 hour (embodying fair principle).

The history business datum same period includes business item, time of drawing a bill, waiting time, deadline, accepts window and working window cadre.

Client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

(window banging personnel are once work in the present invention, every skylight opening scheduling model to be lined up " inverted triangle ", except noon, the time of having a rest of window banging personnel is only a unit of time), window banging personnel the most above operate at full capacity as far as possible, the work of window banging personnel every day below is the fewest, client flow peak when, can engage part-time staff, the most i.e. ensure the service quality of window, also reduce the cost of serving of window.

Embodiment two: the mixing Workforce Management of a kind of elastic services based on inverted triangle, mainly includes history contemporaneous data management module, window number generation module and newly-built module etc. of arranging an order according to class and grade.

History contemporaneous data management module is for the record of historical data and management:

The window number that window number generation module opened according to the history business datum same period prediction subsequent work time period.

Extract service Room window every historical data (client arrive the service Room time, etc. the time to be serviced and finish thing and leave time and the average time of window banging personnel's transacting business in the service Room), applied time series analysis, the following a period of time unit time inner segment client of prediction arrives the flow of the people in the service Room, utilizes the Theoretical Calculation of queueing theory to go out window and offers quantity.Meeting client's waiting time less than on the premise of 15 minutes (parameter), client is set to variable waiting time.Working time section can make seasonal adjustment according to local working requirement.Client needs to be set as parameter waiting time, can be modified according to the practical situation of user.Open window number is set as parameter, and user can the practical situation of basis be adjusted.A large amount of historical datas of the flow of the people that client arrives service Room day part are divided into two classes, a class to be dull seasons, and another kind of is the busy season.Further according to the attribute of window services industry, being divided into two classes, the such as beginning of the month, the end of month to be divided into busy the data that client in month arrives service Room flow of the people, section remaining time (intermediate period) of month is idle.Calculating each period client in dull season (busy and idle time) again and arrive the average total number of persons in the service Room and each period client in busy season (busy and idle time) arrives the average total number of persons in the service Room, such as day part refers to 8:30-9:30,9:30-10:30 etc..Each period client of recycling dull season (busy and idle time) arrives the ARMA model (ARMA) in the average total number of persons binding time sequence analysis in the service Room and dopes each period client in dull season (busy and idle time) and arrive the number in the service Room；Each period client using the busy season (busy and idle time) arrives the average total number of persons in the service Room and combines ARMA model in season (SARMA) and dope each period client in busy season (busy and idle time) and arrive the number in the service Room.The service of window meets separate quantum condition entropy, the average customer number serviced in the parameter μ representation unit time of quantum condition entropy, we arrive a large amount of historical datas in the service Room and test client, discovery client arrives the rule in the service Room and substantially obeys Poisson distribution, under the hypothesis that the average latency that client can tolerate is 15 minutes (can be set to parameter), the M/M/c model (formula (1) the most hereinafter) that therefore we can utilize queueing theory classical calculates the window number that each period rationally opens.

The minimum window number that the subsequent work time period opens is drawn by equation below:

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents client's number that average each window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is following (owing to c is positive integer and is difficult to be obtained by analysis mode, therefore calculating through the following steps):

Step 1: order(stable state can be reached for queuing process to consider)

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2.

Business averagely handles time acquisition: when importing new historical data in system, system automatically carries out new business and averagely handles the calculating of time.

Prediction window generates, when user selects to arrange an order according to class and grade beginnings, after the end time, can be according to historical data generation prediction window, and based on start and end time, duration, it is thus achieved that prediction window quantity.

Newly-built module window banging personnel's scheduling data (utilizing 0-1 nonlinear programming to realize automatic elastic to arrange an order according to class and grade) according to revised prediction window number data genaration each time period of arranging an order according to class and grade, window banging personnel's scheduling data is drawn by object function；

In the case of window banging is undermanned, every skylight opening scheduling model is lined up " inverted triangle ", and (window banging personnel are once work, except noon, the time of having a rest of window banging personnel is only a unit of time, this definition is harsher, having a lot of situation nothing to solve, therefore condition is somewhat relaxed.), i.e. before window banging personnel operate at full capacity as far as possible, the work of window banging personnel every day below is the fewest, client flow peak when, part-time staff can be engaged, the most i.e. ensure the service quality of window, also reduce the cost of serving of window.

The function realized has, and window banging personnel work 45 minutes or 1 hour continuously, can have a rest 15 minutes；The service Room arranges a staff on duty and staff on duty at noon to not be used in window services at 11:30 to 12:00 noon, but needs in morning hours service；The staff of each window services is only serviced two periods in a working day (morning, noon, afternoon)；Staff's education of window banging can be presetted in the cycle of one month, go on business or have a holiday and do not affect his total time in window services the whole cycle；All staff in window services are few (error is 1 hour) in the time difference of the inherent window services of 1 cycle (1 month).

Realizing above-mentioned functions by following mathematical model, relevant parameter is defined as follows: T represents the plan phase total natural law (typically with 1 month as cycle) of arranging an order according to class and grade；N represents the sum of window banging personnel.It was a unit of time by 15 minutes, one workaday window banging time is divided into 27 periods, the morning, 8:30 to 8:45 was designated as the 1st period, 8:45 to 9:00 was designated as the 2nd period, by that analogy, 12:00 to 14:00 was designated as the 15th period, and 14:00 to 14:15 was designated as the 16th period, was designated as the 27th period to 16:45 to 17:00 by that analogy；c_jk(queueing theory calculates each hour and needs open window number, therefore c minimum window number needed for meeting the customer demand for service jth sky k moment in representing the plan phase of arranging an order according to class and grade_j1=c_j2=c_j3=c_j4, other by that analogy), therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jk.According to substantial amounts of questionnaire survey and psychological test, utilizing SPSS to be analyzed obtaining to above-mentioned data: window banging personnel can efficiently have the service average time of quality to be 1 hour, window banging personnel must go to backstage decompression and loosen after working continuously 45 minutes or 1 hour.Obviously, as shift scheduling model, should be able to infer that every window banging personnel's every workday is respectively at window and the time period of background work, decision variable x from the value of decision variable_ijk, represent the full-time window banging personnel day duty in the working hour of certain window banging, i=1 ..., m.Decision variable x_ijk, i=m+1 ..., n, represent the part-time window banging personnel day duty in the working hour of certain window banging.Each window banging personnel only require at two time periods of window banging (morning 8:30 to 12:00 every day, noon 12:00 to 14:00, afternoon 14:00 to 17:00), when window banging personnel day are engraved in window banging in the some time, value is 1, is otherwise 0.X the most at that time_ijk=1 represents that the i-th window banging personnel are engraved in certain window banging when jth sky k.Assuming that window banging personnel only have m, remaining n-m window banging personnel is part-time staff, and part-time window banging personnel do not arrange on duty noon.Minimum for optimization aim in total working time (unit is 15 minutes) the shortest and outfit the personnel storehouse of queuing time and all windows meeting client, then object function is:

Description according to window shifts arrangement and analysis, and combine the definition of decision variable, the constraints of model mainly has:

2(1-x_{ij , k})x_{ij , k+1}≤x_{ij , k+2}+x_{ij , k+3},

Above formula ensure that full-time window banging personnel work 3 time periods (45 minutes) the most continuously once work；

Above formula ensure that full-time window banging personnel work 4 time periods (60 minutes) the most continuously once work；

Above formula ensure that and full-time window banging personnel's morning or afternoon once two unit of time of having a rest, ensuing all the morning or afternoon not be used in window banging.

Above formula ensure that only two time periods of work of any one sky (morning, noon, afternoon) in window banging person works's day or a time period (the darg time is less than 8 hours)；

If above formula ensure that window banging personnel, certain day noon is on duty, then he (she) 12 front half an hours not in window services, so ensure that noon has the time to have lunch and has time on duty at noon before on duty；Because window banging personnel on duty at noon have only to select the morning or work in afternoon, through substantial amounts of investigation, substantial amounts of window banging department wishes to link up on duty on duty for noon and morning, so convenient looking after staff on duty at noon and take off afternoon or go on business and arrange files on backstage, following formula can ensure that the morning is on duty and noon on duty connects.

If above formula ensures that full-time window banging personnel are on duty for noon, then afternoon he (she) not at window banging；

Above formula ensure that full-time window banging personnel's morning or afternoon can not only work 1 time period before leaving offices；

Above formula ensure that full-time window banging personnel can only work 2 time periods before leaving offices in the morning or afternoon；

Above formula ensure that jth sky random time section k (by historical data, utilize the theory of statistics and queueing theory ensure client's waiting time do not surpass 15 minutes estimate window number) operate at full capacity；

Above formula ensure that jth sky have noon and only full-time window banging personnel on duty.

Realize the supplementary scheduling model of window banging personnel " inverted triangle " below.

DefinitionDefinition indicative function:

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

Definition

SetIn element andEqual number is designated as n₂.To arbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Time of having a rest compensate the window banging personnel to second group as far as possible and complete, Wo Menyou

If working as n₁＜ 4 and c_j13=d_j1Time,

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

Work as n₁When=6,

Other situations are by that analogy, through limited number of time recursion, have selected the working pattern of window banging person works's day full-time for m, and the working time duration of the working time every day above-mentioned m of time length ratio of remaining n-m part-time window banging personnel full-time window banging personnel every day is short；

Above formula ensure that full-time window banging personnel difference of net cycle time within a cycle is less than 1 hour.

In history contemporaneous data management module, the history business datum same period includes business item, time of drawing a bill, waiting time, deadline, accepts window and window banging personnel.

In window number generation module, client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

User and staff's benefits module, for record window staff's personal information, window banging personnel's personal information includes name, job number and telephone number.

Algorithm parameter management module, for the various parameters needed for prediction window number and algorithm of arranging an order according to class and grade being carried out typing and dynamically management, hop count and maximum motor-driven staff number every day when requiring including the maximum disparity between traffic handling time, business weight, queue length, client's latency tolerant upper limit, employee's High-effective Service duration, period maximal workload and minimum workload, participate in arranging an order according to class and grade shared by quantity of cadres, noon.

Segment management module when arranging an order according to class and grade, the concrete start and end time of period of classifying every day when prediction window number carries out typing and management.

Unit interval definition management module, when automatic scheduling, the concrete start and end time of 27 unit time period carries out typing and management.

Arrange an order according to class and grade management module, measure query statistic, data backup, reduction, system user and rights management for the realization person works that arranges an order according to class and grade.

The example of model solves

Obviously, above-mentioned model is a nonlinear integer programming model, and integer programming is a NPC problem, it is impossible to ensure to try to achieve optimal solution in polynomial time, it is true that we utilize Lingo program calculation the most not obtain optimal solution or near-optimal solution in one week.We select c language that variable is carried out dimension-reduction treatment, and through substantial amounts of data test, result shows to be no more than on common computer to calculate optimal solution in two minutes.

After we carry out statistical disposition to the historical data of Yunhe County of bureau of local taxation, Lishui, Zhejiang Province, obtain predicting in January, 2016 following data.

The cadre that pays taxes of window averagely handles a business 5.6 minutes, and taxpayer waits and being less than average time 15 minutes, goes out, by the M/M/C model pre-estimating of queueing theory, the window number that January, day part weekly was opened.

The 0-1 nonlinear programming model set up by us, calculates the elastic shift report on duty of the cadre that pays taxes.

Employee's net cycle time

1	2	3	4	5	6	7	8	9
									196	197	197	197	196	197	100	60	20

Numeral 1, represent the window banging personnel state at window banging, numeral 0, represent window banging personnel array data on backstage or do other thing, employee 1,2,3,4,5,6 is full-time window banging personnel, window banging personnel 7,8,9 are part-time window banging personnel, and in one cycle of full-time window banging personnel, (two weeks) are basically identical in the time of window banging.Visible by example, the present invention proposes the solution of elastic services and more manually arranges an order according to class and grade and have the advantage that

1. the constraints of this example window personnel flexible scheduling is more than 2000, and decision variable, more than 2000, is arranged an order according to class and grade if manual, solved optimal solution extremely difficult.

2. can effectively control the custom queueing waiting time by scientific algorithm with arranging an order according to class and grade.

3. elastic service shift scheduling model can dynamically change the number adjusting window working according to demand, ensures that good service reduces the cost of unit simultaneously by the window banging that engagement is part-time.

Illustrate as a example by Local Tax Bureau of Lishui Yunhe County now.After elastic service system is carried out, taxpayer, a linear window are paid taxes work cadre, and window management layer three aspect achieves win-win.Service person-time, business handling amount increase on year-on-year basis.Tax handling service hall, the phenomenons such as personnel are empty are greatly reduced, work efficiency, averagely handle the time, taxpayer's satisfaction has lifting.

After elastic service pilot processed, taxpayer is no longer than 15 minutes waiting time, and the satisfaction of service is improved by taxpayer.Tax handling service hall staff window banging duration is greatly shortened, and shortens to from the 18.5 ten thousand of the same period last year hours more than 80,000 hour, and the actual ratio accepting business hours and total window line duration brings up to 44.45% from 22.67%, and other data see table.

Note: the last week :-21 days on the 17th November；One week after :-28 days on the 24th November.

The foregoing is only the preferred embodiment of the present invention, protection scope of the present invention is not limited in above-mentioned embodiment, and every technical scheme belonging to the principle of the invention belongs to protection scope of the present invention.For a person skilled in the art, the some improvement carried out on the premise of without departing from the principle of the present invention, these improvement also should be regarded as protection scope of the present invention.

Claims (10)

1. the mixing scheduling method of an elastic services based on inverted triangle, it is characterised in that include Following steps:

According to the window number that the history business datum same period prediction subsequent work time period is open, subsequent work time The minimum window number of Duan Kaifang is drawn by equation below:

$\begin{array}{c}{W}_q=\frac{L_q}{\mathrm{\λ}}=\frac{{\left(c\mathrm{\ρ}\right)}^c\mathrm{\ρ}}{c!{(1-\mathrm{\ρ})}^2}{P}_0=\\ \frac{{\left(c\mathrm{\ρ}\right)}^c\mathrm{\ρ}}{c!{(1-\mathrm{\ρ})}^2}{\[\underset{k=0}{\overset{c-1}{\Σ}}\frac{{\left(c\mathrm{\ρ}\right)}^k}{k!}+\frac{{\left(c\mathrm{\ρ}\right)}^c}{c!(1-\mathrm{\ρ})}\]}^{-1}.\end{array}---\left(1\right)$

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents average every Client's number that one window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is as follows:

Step 1: order

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required Minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2；

According to window banging personnel's scheduling data of revised prediction window number data genaration each time period, Window banging personnel's scheduling data is drawn by following object function；

$\left\{\begin{array}{c}{\mathrm{minz}}_1=\underset{i=1}{\overset{n}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{ijk}+7\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}{x}_{ij15}+\underset{i=m+1}{\overset{n-m}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{ijk};\\ {\mathrm{minz}}_2=n.\end{array}\right.$

Wherein, T represented plan phase total natural law of arranging an order according to class and grade, and n represents the sum of window banging personnel, by 15 minutes Be a unit of time, a workaday window banging time be divided into 27 periods, the morning 8:30 extremely 8:45 was designated as the 1st period, and 8:45 to 9:00 was designated as the 2nd period, and by that analogy, 12:00 to 14:00 remembers Being the 15th period, 14:00 to 14:15 was designated as the 16th period, was designated as to 16:45 to 17:00 by that analogy 27th period；c_jkThe minimum window needed for the customer demand for service jth sky k moment is met in representing the plan phase of arranging an order according to class and grade Mouth number, queueing theory calculates each hour and needs open window number, therefore c_j1=c_j2=c_j3=c_j4, other by that analogy, Therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jk, according to substantial amounts of Questionnaire survey and psychological test, utilize SPSS to be analyzed obtaining to above-mentioned data: window banging personnel can The service average time efficiently having quality is 1 hour, and window banging personnel work 45 minutes or 1 hour continuously After must go to backstage decompression loosen, it is clear that as shift scheduling model, every should be able to be inferred from the value of decision variable Window banging personnel's every workday is respectively at window and the time period of background work, decision variable x_ijkRepresent certain Individual window banging personnel work as x in the duty of window banging period every day_ijkWhen value is 1, represent the i-th people In jth sky kth time period at window banging, work as x_ijkWhen value is 0, represent that the i-th people is in jth sky kth time period Not at window banging, i=1 ..., m.Decision variable x_ijk, i=m+1 ..., n, represent part-time window banging personnel Certain day duty in the working hour of certain window banging, each window banging personnel only require every day Two time periods of window banging, the morning, 8:30 to 12:00 was first time period, noon 12:00 to 14:00 Being the second time period, afternoon, 14:00 to 17:00 was the 3rd time period, it is assumed that window banging personnel only have m, Remaining n-m window banging personnel is part-time staff, and part-time window banging personnel do not arrange on duty noon, Meet client minimum for excellent in the total working time personnel storehouse that is the shortest and that be equipped with of queuing time and all windows Change target, draw above-mentioned object function；

Constraints:

2(1-x_{Ij, k})x_{Ij, k+1}≤x_{Ij, k+2}+x_{Ij, k+3},

$\∀i\∈\{1,2,...,m\},k=1,2,...,11,16,...24,$

$2x_{ij1}\≤x_{ij2}+x_{ij3},\∀j,i\∈\{1,2,...,m\},$

Above formula ensures that the staff of full-time window works 3 time periods the most continuously once work,

$\underset{d=k}{\overset{k+4}{\Σ}}{x}_{ijd}\≤4,\∀i\∈\{1,2,...,m\},k=1,2,...,10,16,...,23,$

Above formula ensures that full-time window banging personnel work 4 time periods (60 minutes) the most continuously once work；

$x_{ijk}(1-x_{ij,k+1})(1-x_{ij,k+2})\≤\underset{n=k+3}{\overset{14}{\Π}}(1-x_{ijn}),\∀i\∈\{1,2,...,m\},j,k=1,2,...,11;$

$x_{ijk}(1-x_{ij,k+1})(1-x_{ij,k+2})\≤\underset{n=k+3}{\overset{24}{\Π}}(1-x_{ijn}),\∀i\∈\{1,2,...,m\},j,k=16,...,24;$

Above formula ensure full-time window banging personnel's morning or afternoon once two unit of time of having a rest, next All the morning or not be used in window banging afternoon；

$1\≤\[\underset{k=1}{\overset{14}{\Π}}(1-x_{ijk})+(1-x_{ij15})+\underset{k=16}{\overset{27}{\Π}}(1-x_{ijk})\]\≤2,\∀i,j,$

Any one sky in window banging person works's day that above formula guarantee is full-time, i.e. the morning, noon, afternoon, only Working two time periods or a time period, the darg time is less than 8 hours；

$\frac{1}{2}(x_{ij13}+x_{ij14})\≤1-x_{ij15},\∀i\∈\{1,2,...,m\},j,$

If above formula ensure window banging personnel on duty for certain day noon, then he (she) 12 front half an hours not at window There is the time to have lunch before service, so guarantee noon are on duty and have time on duty at noon；

$x_{ij15}\left(\underset{k=16}{\overset{27}{\Σ}}{x}_{ijk}\right)=0,\∀j,i\∈\{1,2,...,m\},$

If above formula ensures that full-time window banging personnel are on duty for noon, then afternoon he (she) not at window banging；

$x_{ij14}\≤x_{ij13},x_{ij27}\≤x_{ij26},\∀i\∈\{1,2,...,m\},$

Above formula ensures that full-time window banging personnel's morning or afternoon can not only work 1 time period (15 points before leaving offices Clock)；

$(1-x_{ij12})x_{ij13}\≤x_{ij14},(1-x_{ij25})x_{ij26}\≤x_{ij27}\∀i\∈\{1,2,...,m\},$

Above formula ensures that full-time window banging personnel can only work 2 time periods, i.e. before leaving offices in the morning or afternoon 30 minutes；

$\underset{i=1}{\overset{n}{\Σ}}{x}_{ijk}\≥c_{jk},\∀k=j,1,...,14,16,...,27,,$

Above formula ensures that jth sky random time section k is operated at full capacity；

$\underset{i=1}{\overset{m}{\Σ}}{x}_{ij14}=1,\∀j,$

Above formula ensure jth sky have noon and only full-time window banging personnel on duty；

The another kind of scheduling model that realize window banging personnel " inverted triangle " is presented herein below；

DefinitionDefinition indicative function:

$n_1\stackrel{\mathrm{\Δ}}{=}{I}_{\{d_{j1}=c_{j1}\}}+I_{\{d_{j1}=c_{j5}\}}+I_{\{d_{j1}=c_{j9}\}}+I_{\{d_{j1}=c_{j13}\}}+I_{\{d_{j1}=c_{j16}\}}+I_{\{d_{j1}=c_{j20}\}}+I_{\{d_{j1}=c_{j24}\}},$

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{1}jk}\≥21,...,\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}}jk}\≥21,\∀j,$

Definition

SetIn element andEqual number is designated as n₂, to arbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Time of having a rest to the greatest extent Amount compensates the window banging personnel to second group and completes, and draws:

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥min\{21-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{21-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

If working as n₁＜ 4 and c_j13=d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥\min \{23-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{23-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥\min \{20-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{20-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥\min \{22-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{22-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

Work as n₁When=6,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥3or4,\∀j.$

Other situations by that analogy, through limited number of time recursion, have selected m window full-time staff's working day Working pattern, and the working time every day time length ratio of the part-time window banging personnel of remaining n-m window The working time duration of above-mentioned m window banging personnel every day is short；

$\left|\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{ljk}+7\underset{j=1}{\overset{T}{\Σ}}{x}_{lj15}-\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{sjk}-7\underset{j=1}{\overset{T}{\Σ}}{x}_{sj15}\right|\≤4,\∀l,s\∈\{1,2,\mathrm{...},m\},$

Above formula ensure the full-time staff of full-time window within a cycle net cycle time length less than 1 Hour.

The mixing scheduling method of elastic services based on inverted triangle the most according to claim 1, It is characterized in that: the history business datum same period includes business item, time of drawing a bill, waiting time, the time of completing Between, accept window and window banging personnel.

The mixing scheduling method of elastic services based on inverted triangle the most according to claim 1, It is characterized in that: client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

4. the mixing Workforce Management of an elastic services based on inverted triangle, it is characterised in that including:

History contemporaneous data management module, for the record of historical data and management:

Window number generation module, according to the window that the history business datum same period prediction subsequent work time period is open Number, the minimum window number that the subsequent work time period opens is drawn by equation below:

$\begin{array}{c}{W}_q=\frac{L_q}{\mathrm{\λ}}=\frac{{\left(c\mathrm{\ρ}\right)}^c\mathrm{\ρ}}{c!{(1-\mathrm{\ρ})}^2}{P}_0=\\ \frac{{\left(c\mathrm{\ρ}\right)}^c\mathrm{\ρ}}{c!{(1-\mathrm{\ρ})}^2}{\[\underset{k=0}{\overset{c-1}{\Σ}}\frac{{\left(c\mathrm{\ρ}\right)}^k}{k!}+\frac{{\left(c\mathrm{\ρ}\right)}^c}{c!(1-\mathrm{\ρ})}\]}^{-1}.\end{array}---\left(1\right)$

Wherein, W_qRepresent client's average latency；C is open minimum window number needed for representing the service Room；Represent service intensity；λ represents the average client's number arriving the service Room per hour；μ represents average every Client's number that one window can service per hour；

t₀Representing the average latency upper limit that client can tolerate, for formula (1), calculation procedure is as follows:

Step 1: order

Step 2: calculate W according to formula (1)_qIf, W_q≤t₀, then terminating algorithm, c now is required Minimum window number；If W_q＞ t₀Then go to step 3；

Step 3: make c=c+1, goes to step 2；

Newly-built module of arranging an order according to class and grade, according to the window banging of revised prediction window number data genaration each time period Personnel's scheduling data, window banging personnel's scheduling data is drawn by following object function；

$\left\{\begin{array}{c}{\mathrm{minz}}_1=\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{ijk}+7\underset{i=1}{\overset{m}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}{x}_{ij15}+\underset{i=m+1}{\overset{n-m}{\Σ}}\underset{j=1}{\overset{T}{\Σ}}\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{ijk};\\ {\mathrm{minz}}_2=n.\end{array}\right.$

Wherein, T represented plan phase total natural law of arranging an order according to class and grade, and n represents the sum of window banging personnel, by 15 minutes Be a unit of time, a workaday window banging time be divided into 27 periods, the morning 8:30 extremely 8:45 was designated as the 1st period, and 8:45 to 9:00 was designated as the 2nd period, and by that analogy, 12:00 to 14:00 remembers Being the 15th period, 14:00 to 14:15 was designated as the 16th period, was designated as to 16:45 to 17:00 by that analogy 27th period；c_jkThe minimum window needed for the customer demand for service jth sky k moment is met in representing the plan phase of arranging an order according to class and grade Mouth number, queueing theory calculates each hour and needs open window number, therefore c_j1=c_j2=c_j3=c_j4, other by that analogy, Therefore window number c open needed for only need to calculating k=1,5,9,13,16,20,24_jk, according to substantial amounts of Questionnaire survey and psychological test, utilize SPSS to be analyzed obtaining to above-mentioned data: window banging personnel can The service average time efficiently having quality is 1 hour, and window banging personnel work 45 minutes or 1 hour continuously After must go to backstage decompression loosen, it is clear that as shift scheduling model, every should be able to be inferred from the value of decision variable Window banging personnel's every workday is respectively at window and the time period of background work, decision variable x_ijkRepresent certain Individual window banging personnel work as x in the duty of window banging period every day_ijkWhen value is 1, represent the i-th people In jth sky kth time period at window banging, work as x_ijkWhen value is 0, represent that the i-th people is in jth sky kth time period Not at window banging, i=1 ..., m.Decision variable x_ijk, i=m+1 ..., n, represent part-time window banging personnel Certain day duty in the working hour of certain window banging, each window banging personnel only require every day Two time periods of window banging, the morning, 8:30 to 12:00 was first time period, noon 12:00 to 14:00 Being the second time period, afternoon, 14:00 to 17:00 was the 3rd time period, it is assumed that window banging personnel only have m, Remaining n-m window banging personnel is part-time staff, and part-time window banging personnel do not arrange on duty noon, Meet client minimum for excellent in the total working time personnel storehouse that is the shortest and that be equipped with of queuing time and all windows Change target, draw above-mentioned object function；

Constraints:

2(1-x_{Ij, k})x_{Ij, k+1}≤x_{Ij, k+2}+x_{Ij, k+3},

$\∀i\∈\{1,2,...,m\},k=1,2,...,11,16,...24,$

$2x_{ij1}\≤x_{ij2}+x_{ij3},\∀j,i\∈\{1,2,...,m\}.$

Above formula ensures that full-time window banging personnel work 3 time periods the most continuously once work, i.e. 45 Minute；

$\underset{d=k}{\overset{k+4}{\Σ}}{x}_{ijd}\≤4,\∀i\∈\{1,2,...,m\},k=1,2,...,10,16,...23,$

Above formula ensures that full-time window banging personnel work 4 time periods (60 minutes) the most continuously once work；

$x_{ijk}(1-x_{ij,k+1})(1-x_{ij,k+2})\≤\underset{n=k+3}{\overset{14}{\Π}}(1-x_{ijn}),\∀i\∈\{1,2,...,m\},j,k=1,2,...,11;$

$x_{ijk}(1-x_{ij,k+1})(1-x_{ij,k+2})\≤\underset{n=k+3}{\overset{24}{\Π}}(1-x_{ijn}),\∀i\∈\{1,2,...,m\},j,k=16,...,24;$

Above formula ensure full-time window banging personnel's morning or afternoon once two unit of time of having a rest, next All the morning or not be used in window banging afternoon；

$1\≤\[\underset{k=1}{\overset{14}{\Π}}(1-x_{ijk})+(1-x_{ij15})+\underset{k=16}{\overset{27}{\Π}}(1-x_{ijk})\]\≤2,\∀i,j,$

Above formula ensures any one sky in window banging person works's day, the i.e. morning, noon, afternoon, only work two Individual time period or a time period, the darg time is less than 8 hours；

$\frac{1}{2}(x_{ij13}+x_{ij14})\≤1-x_{ij15},\∀i\∈\{1,2,...,m\},j,$

If above formula ensures that full-time window banging personnel are on duty for certain day noon, then he (she) 12 front half an hours not In window services, so ensure that noon has the time to have lunch and has time on duty at noon before on duty；

$x_{ij15}\left(\underset{k=16}{\overset{27}{\Σ}}{x}_{ijk}\right)=0,\∀j,i\∈\{1,2,...,m\},$

If above formula ensures that full-time window banging personnel are on duty for noon, then afternoon he (she) not at window banging；

$x_{ij14}\≤x_{ij13},x_{ij27}\≤x_{ij26}\∀i\∈\{1,2,\mathrm{...},m\},j,$

Guarantee window banging personnel's morning or afternoon that above formula is full-time can not only work 1 time period before leaving offices, and i.e. 15 Minute；

$(1-x_{ij12})x_{ij13}\≤x_{ij14},(1-x_{ij25})x_{ij26}\≤x_{ij27}\∀i\∈\{1,2,\mathrm{...},m\},j,$

Above formula ensures that full-time window banging personnel can only work 2 time periods, i.e. before leaving offices in the morning or afternoon 30 minutes；

$\underset{i=1}{\overset{n}{\Σ}}{x}_{ijk}\≥c_{jk},\∀k=1,\mathrm{...},14,16,\mathrm{...},27,j,,$

Above formula ensures that jth sky random time section k is operated at full capacity；

$\underset{i=1}{\overset{m}{\Σ}}{x}_{ij14}=1,\∀j,$

Above formula ensure jth sky have noon and only full-time window banging personnel on duty.

Realize the another kind of scheduling model of window banging personnel " inverted triangle " below；

DefinitionDefinition indicative function:

$n_1\stackrel{\mathrm{\Δ}}{=}{I}_{\{d_{j1}=c_{j1}\}}+I_{\{d_{j1}=c_{j5}\}}+I_{\{d_{j1}=c_{j9}\}}+I_{\{d_{j1}=c_{j13}\}}+I_{\{d_{j1}=c_{j16}\}}+I_{\{d_{j1}=c_{j20}\}}+I_{\{d_{j1}=c_{j24}\}},$

Set 1,2 ... m} represents the staff at window full-time job, to arbitrarily

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{1}jk}\≥21,...,\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}}jk}\≥21,\∀j;$

Definition

SetIn element andEqual number is designated as n₂, right ArbitrarilyWork as n₁＜ 4 and c_j13≠d_j1Time,Rest Time compensates the window banging personnel to second group as far as possible and completes, and draws:

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥\min \{21-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{21-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

If working as n₁＜ 4 and c_j13=d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥\min \{23-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{23-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j.$

As 4≤n₁≤ 5 and c_j13≠d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥min\{20-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥\min \{20-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

If as 4≤n₁≤ 5 and c_j13=d_j1Time,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥min\{22-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},...,$

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j2}}jk}\≥min\{22-3n_1+\[\frac{5n_1}{d_{j2}-d_{j1}}\],21\},\∀j;$

Work as n₁When=6,

$\underset{k=1,k\≠15}{\overset{27}{\Σ}}{x}_{i_{d_{j1}+1}jk}\≥3or4,\∀j.$

Other situations by that analogy, through limited number of time recursion, have selected m full-time window banging people employee Make the working pattern of day, and the working time every day time length ratio of remaining n-m part-time window banging personnel The working time duration of above-mentioned m window banging personnel every day is short；

$\left|\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{ljk}+7\underset{j=1}{\overset{T}{\Σ}}{x}_{lj15}-\underset{j=1}{\overset{T}{\Σ}}\underset{k=1}{\overset{27}{\Σ}}{x}_{sjk}-7\underset{j=1}{\overset{T}{\Σ}}{x}_{sj15}\right|\≤4,\∀l,s\∈\{1,2,\mathrm{...},m\},$

Above formula ensures that full-time window banging personnel net cycle time length within a cycle is less than 1 hour.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: in history contemporaneous data management module, the history business datum same period includes business item, goes out Ticket time, waiting time, deadline, accept window and window banging personnel.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: in window number generation module, client average latency W_qLess than 15 minutes, i.e. W_q≤ 0.25 hour.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: also include user and staff's benefits module, for record window staff's personal information, Window banging personnel's personal information includes name, job number and telephone number.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: also include that algorithm parameter manages module, needed for prediction window number and algorithm of arranging an order according to class and grade Various parameters carry out typing and dynamically management, including traffic handling time, business weight, queue length, visitor Between the family latency tolerant upper limit, employee's High-effective Service duration, period maximal workload and minimum workload Maximum disparity require, participate in arrange an order according to class and grade time shared by quantity of cadres, noon hop count and maximum motor-driven employee every day Number.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: segment management module when also including arranging an order according to class and grade, classification period to every day when prediction window number Concrete start and end time carry out typing and management.

The mixing Workforce Management of elastic services based on inverted triangle the most according to claim 4, It is characterized in that: also include unit interval definition management module, 27 unit time period when automatic scheduling Concrete start and end time carries out typing and management.