CN112598284B - Dynamic allocation method of limited resources for pension system - Google Patents
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Abstract
The invention relates to a dynamic allocation method of limited resources for a pension system, which considers the problems of dynamically allocating pension with different service quality and old people with different health conditions. The invention firstly divides the nursing homes providing different service qualities in the nursing system into a sponsored nursing home and a community nursing home, and divides the aged with different health levels into the aged with high priority and the aged with low priority, then carries out mathematical sampling on related concepts, and provides a dynamic allocation method for the nursing service system from the mathematical perspective. The method not only overcomes the defects of the prior first-come first-served distribution strategy and the complete distribution strategy commonly used in the pension system, but also greatly reduces the service cost and improves the social benefit.
Description
Technical Field
The invention relates to the service field of pension systems, in particular to a dynamic allocation problem of multiple types of limited resources and multiple types of random demands.
Background
In recent years, due to the increasing trend of aging population, care for aged people is becoming more and more important in social welfare, wherein the care for aged people is a key resource in care for aged people. However, in reality, the limited resources of the nursing homes are far from meeting the increasing needs of the elderly. In Beijing, the office nursing home bed released in the whole city in one year is only enough to meet the requirements of the old in one week. At a certain place, each old person needs to be queued for 25.5 months on average to be admitted to the office nursing home. Unfortunately, a large number of elderly people are lost each year due to the inability to reach timely service.
Aiming at the problem of scarce pension resources, in reality, the government actively encourages lightly defective old people to select community pension and pension, meanwhile, the office pension classifies the old people into different priority service classes according to the health condition of the old people, the old people with high priority enjoy the authority of being preferentially serviced, and the old people with low priority can appropriately wait in the pension system. In practice, pension systems often use two service strategies, one of which is a first come first served strategy, which schedules the elderly for admission to the pension according to the chronological order in which they apply for the pension. However, this service method brings in reality a serious problem of mismatch between the bed and the old's needs: when a sponsored backyard is occupied by too many low priority elderly people, a large number of high priority elderly people must be queued up or moved to the community backyard. It is apparent that such low quality community nursing homes do not fully meet the needs of high priority elderly people. Another is a full distribution strategy, which reserves all office backdrop beds for high priority elderly people and arranges all low priority elderly people into community backdrop. Unfortunately, when the number of high priority elderly people is small, a large number of institutional care beds are idle.
In order to make up for the deficiency of service strategies in a real-life care system, a limited care hospital bed and old people in different health states are reasonably matched, and a brand-new allocation service strategy is designed.
Disclosure of Invention
The technical solution of the invention is as follows: the method overcomes the defects of the service technology in the existing pension system, provides a dynamic allocation optimization strategy, improves the service level in the pension system, and greatly reduces the service cost.
The technical solution of the invention is as follows: a dynamic allocation method of limited resources for a pension system is realized by the following steps as shown in fig. 1:
step S1, classifying the sponsored senior citizens and the community sponsored by the government in the senior citizens system into different service grades according to the professional degree and the cost of the service; meanwhile, the old applying for the nursing home is divided into high-priority old and low-priority old according to income, health condition and presence or absence of children, and a limited resource dynamic allocation model is established;
step S2, calculating the optimal distribution level of beds at the end of each period (days, months, years and the like according to the actual situation) of the office nursing homes in the pension system and the quantity level of the aged served by the community nursing homes at each period based on a limited resource dynamic distribution model;
step S3, designing an optimal service strategy in each period in the pension system according to the optimal distribution level of the final bed of each period of the office pension and the quantity level of the aged served by the community pension in the step S2;
and S4, designing a dynamic implementation algorithm to rapidly calculate the reservation level of beds in each period of the office nursing home, the quantity level of the optimal service aged in each period of the community nursing home and the optimal service cost in the whole nursing system based on the optimal service strategy in the step S3.
In the step S1, a dynamic allocation model of limited resources is established as follows:
for the 1, …, T phase,
in the limited resource dynamic allocation model, the relation between the t+1 th period in the pension system and the number of rest beds in the office pension in the t period and the number of queued old people in the system is a dynamic transfer equation, and the relation is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the total service cost of the pension system in the t period; />
Is the expected service cost of the t+1-th to T-th pension systems; />
Is the expected minimum service cost of the pension system from the T-th period to the T-th period; y is t Is a decision variable and represents the number of beds left in the office nursing home at the end of the t period; v t Is a decision variable representing the "net remaining bed volume" of the office rest of the end of the t-th period, where v t ＝y t - "total number of non-served elderly people in the end-of-t-period pension system";
is a state vector in a pension system, where z i,t Representing the number of beds remaining after the t-th period end office nursing home fully serves class 1 to i old people as high-priority old people; z 0 The number of beds of the old in the early office of each period is represented, the old with low priority is divided into n classes according to waiting time in a queuing system, and the i-th class refers to one class;
indicating the number of high-priority and low-priority elderly people applying for pension services at the beginning of the t-th period;
the method is characterized in that the method is the initial i of the t period, i=1, …, and the n+1 old people apply for queuing quantity of old people in a public care nursing home in a pension system; u (u) i Is the cost of waiting for the class i old in each period; u (U) i Is the service cost of the i-th old assigned to the community nursing home; m is the number of office nursing homes; m+1 refers to community nursing homes; c (C) j J=1, …, m represents the number of beds of the j-th home office at the beginning of the planning period;h j representing the unit bed holding cost of the j-th office of the pension; u represents high priority elderly people; g represents low priority elderly; delta i ＝u i -u i+1 ，i＝1,…,n；△ i ＝U i -U i+1 ,i＝1,…,n；/>
Is a constant representing the total number of beds for office nursing homes j through m.
Step S2 is to calculate the number of remaining beds at the end of each period of the office nursing home and the number of service old people in each period of the community nursing home as follows:
for a sponsored nursing home, the optimal number of beds remaining in the nursing home at the end of each period is
Wherein (1)>
Is the optimal allocation level of the bed of the office nursing home in the t period; based on the optimal allocation level, the old people queuing situation and the bed surplus at random are given in the old people primary care system in each period, and the office old people care can give a uniquely determined optimal decision scheme;
for community nursing homes, the optimal number of served elderly people in each period of community nursing homes is as follows:
Step S3, designing an optimal service strategy in each period in the pension system;
for office nursing homes, if at each stageThe total number of beds available for distribution at the senior citizen's home at the beginning of the period exceeds the distribution level
Then the old with high priority is firstly arranged to be admitted to the office care, then the old with low priority is arranged to be admitted to the office care according to the rule of first arrival first serving, and the bed available for allocation of the office care is reduced to be equal to the optimal allocation level +.>
For community nursing homes, at the end of each period, if the number of aged queued in the office nursing homes exceeds
Then firstly allocating the old with low priority to the community nursing home according to the rule of first-to-last service, and then allocating the old with high priority to the community nursing home so that the total number of the old queued in the nursing home system is equal to +.>
The step S4 calculates the optimal service cost of each period in the pension system and the specific iterative process of the design implementation algorithm as follows: for the whole planning period t=t+1, T-1, …,1,
first, calculating the minimum service cost in the T+1 stage pension system
As an initial input to the algorithm;
second, based on the T+1 stage calculation result, calculating the optimal ration level of the number of the old people in the T-stage community nursing home
Third, optimal ration level based on the number of elderly people in the community care facility
As a result of the calculation, the optimal allocation level of the number of beds in the T-stage office nursing home is calculated +.>
Fourth, according to the optimal ration level of each period of the office and community nursing homes
Calculating the minimum service cost in the T-stage pension system>
Fifth step, the minimum service cost in the T-stage pension system
As the initial input of the algorithm, repeating the second, third and fourth steps until the minimum service cost in the stage 1 pension system is calculated>
Outputting the ration level of the bed of the office nursing home in each period +.>
Feed level of aged in community nursing home +.>
And optimal cost of service per phase +.>
Compared with the prior art, the invention has the advantages that: the invention solves the problem that the number of beds in the pension system is not matched with the number of old people by introducing a dynamic planning model based on the actual condition of the actual pension system. The reservation level of beds in each period of the office nursing home in the optimal pension system and the quantity level of the old served in each period of the community nursing home are obtained, the optimal service scheme in the pension system is provided, and finally an optimal service scheme implementation algorithm is designed, so that the optimal service cost in each period of the pension system is rapidly calculated. Therefore, the service level in the pension system is improved, the service cost of the pension system is reduced, and the social benefit is improved.
Drawings
Fig. 1 is a flow chart of a method for optimizing dynamic allocation of limited resources in a pension system according to the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
The pension system is typically comprised of government-sponsored office pension and private community pension. For the elderly, government-sponsored institutional care homes are better in service professionals and economy than privately-sponsored community care homes. Accordingly, the present invention first classifies the nursing home into different grades according to the quality of service of the nursing home. Meanwhile, the old people are classified into high priority and low priority according to the health state, income, presence or absence of children and the like of the old people, the old people with high priority have priority service weight, and the old people with low priority can be queued in the system.
And then, based on a real service scene, establishing a limited resource dynamic allocation model and calculating the bed level which should be reserved at the end of each period of the sponsored house and the number level of the old people which should be served by the community sponsored house in each period.
And finally, providing an optimal service strategy in each period in the pension system and designing a dynamic allocation optimization algorithm to quickly calculate the optimal service cost in the pension system in each period.
The invention will be further described in connection with an example which does not constitute any limitation of the invention in order to make it easier to understand the invention.
Assume that the average number of high priority elderly people applying for an aged care system at each stage is D U =5, average number of low priority elderly is D G =15 (one day per day). Assuming that 10 office nursing homes are provided, each office nursing home has 20 beds, low priorityThe elderly in the service system must be served after a maximum of 6 waiting periods, the whole planning period being t=12. Other cost parameters are set as follows: cost of ownership h for each office j =3-0.2 (j-1), j=1, … 10; the unit waiting cost of the old not served is as follows: u (u) i =4-0.3i, i=0, …, n+1; the unit service costs assigned to the community nursing home are: u (U) i =0.2 (i+n) (n-i+1) +4-0.3n. The reservation level of the bed of the office nursing home in each period acquired in the step S2
And the number level of old people served by community nursing home per period +.>
And the optimal service scheme of the pension system in each period obtained in the step S3, by executing the optimal allocation algorithm in the pension system designed in the step S4, the following results can be obtained:
table 1: dynamic allocation optimization strategy for limited resources
QU represents the number of old people not served after the office nursing home service; QW represents the number of non-served elderly people after service in office and community nursing homes.
As can be seen from Table 1, all elderly people arriving at the system can be served completely in the first 8 th-day office
No elderly people are assigned to community nursing homes. However, from stage 9, the bed of the office nursing home cannot satisfy all the old newly arrived at the service system. For example, in the ninth phase, the rest of the office nursing home had 27 beds, 14 of which were usedThe pavements must be reserved for the old who may reach high priority in the service system in the future, and after the service of the office nursing home, the rest 13 old must be allocated to the community nursing home. Thus, the number of elderly people served in the community nursing home at phase 9 is 9.
Finally, in order to more intuitively demonstrate the reduced cost of service and increased social benefits of the present invention in a pension system, in this embodiment, the instance is selected from a local pension system. The service conditions adopted by a regional care system are as follows:
the aged care system in a certain place firstly classifies the applied aged people into three priority service classes of heavy defects, medium defects and light defects (the heavy defects are similar to the high priority, the medium defects and the light defects are similar to the low priority) according to the health condition, income, presence or absence of the aged people and the like of the aged people, and each class of aged people is distributed into a specific aged care hospital according to the rule of first-come first-served service. If a bed of a certain type of nursing home is allocated, the old people must be queued in the corresponding service queue. The data indicates that there are serious service consequences for both the prior-to-first-serve and full-allocation strategies. Thus, the present invention uses the data from the care of the earth system to prove the value of the present invention. On average, there are 90 beds per nursing home, and the average number of severely defective elderly in the nursing system is 15 people and the number of slightly defective elderly is 30 people per day. The present example selects the relative average cost of service throughout the planning period as a measure:
table 2 relative average cost of service
Note that:
the proportion of the severely defective elderly in the nursing home relative to the slightly defective elderly in the application of each period is shown.
As can be seen from table 2, the dynamic provisioning optimization strategy proposed by the present invention performs better than the first-come-first-served strategy and the full provisioning strategy in real-world applications. Greatly reduces the service cost and improves the social welfare.
While the foregoing is directed to embodiments of the present invention, and the scope of the claims should be limited thereto, it should be appreciated that modifications and variations may be made by those skilled in the art without departing from the principles of the present invention, and that various values may be set for the period duration of the present invention, depending on the service needs in a real-life care system, as well as the scope of the present invention.
Claims (3)
1. A method for dynamic allocation of limited resources for an pension system, comprising the steps of:
step S1, classifying the sponsored senior citizens and the community sponsored by the government in the senior citizens system into different service grades according to the professional degree and the cost of the service; meanwhile, the old applying for the nursing home is divided into high-priority old and low-priority old according to income, health condition and presence or absence of children, and a limited resource dynamic allocation model is established;
step S2, calculating the optimal distribution level of the end-of-period bed of each period of the office nursing home and the quantity level of the service aged of the community nursing home in the pension system based on a limited resource dynamic distribution model;
step S3, designing an optimal service strategy in each period in the pension system according to the optimal distribution level of the final bed of each period of the office pension and the quantity level of the aged served by the community pension in the step S2;
step S4, based on the optimal service strategy in the step S3, designing a dynamic implementation algorithm to rapidly calculate the reservation level of beds in each period of the office nursing home, the quantity level of the optimal service aged in each period of the community nursing home and the optimal service cost in the whole nursing system;
in the step S1, a dynamic allocation model of limited resources is established as follows:
for the 1, …, T phase,
for the period T +1,
in the limited resource dynamic allocation model, the relation between the t+1 th period in the pension system and the number of rest beds in the office pension in the t period and the number of queued old people in the system is a dynamic transfer equation, and the relation is as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the total service cost of the pension system in the t period; />
Is the expected service cost of the t+1-th to T-th pension systems; />
Is the firstExpected minimum service cost of the T-stage to T-stage pension system; y is t Is a decision variable and represents the number of beds left in the office nursing home at the end of the t period; v t Is a decision variable representing the "net remaining bed volume" of the office rest of the end of the t-th period, where v t ＝y t - "total number of non-served elderly people in the end-of-t-period pension system"; />
Is a state vector in a pension system, where z i,t Representing the number of beds remaining after the t-th period end office nursing home fully serves class 1 to i old people as high-priority old people; the old people with low priority are divided into n classes according to waiting time in the queuing system, and the i class refers to one class; />
Indicating the number of high-priority and low-priority elderly people applying for pension services at the beginning of the t-th period; u (u) i Is the cost of waiting for the class i old in each period; u (U) i Is the service cost of the i-th old assigned to the community nursing home; m is the number of office nursing homes; />
Representing the number of the jth home office nursing home beds at the beginning of the planning period; h is a j Representing the unit bed holding cost of the j-th office of the pension; u represents high priority elderly people; g represents low priority elderly; delta i ＝u i -u i+1 ，i＝1,…,n；Δ i ＝U i -U i+1 ,i＝1,…,n；/>
Is a constant representing the total number of beds for office nursing homes j through m;
step S3, designing an optimal service strategy in each period in the pension system;
for office care homes, if the total number of beds available for distribution at the beginning of each period exceeds the distribution level
Then the old with high priority is firstly arranged to be admitted to the office care, then the old with low priority is arranged to be admitted to the office care according to the rule of first arrival first serving, and the bed available for allocation of the office care is reduced to be equal to the optimal allocation level +.>
For community nursing homes, at the end of each period, if the number of aged queued in the office nursing homes exceeds
Then firstly allocating the old with low priority to the community nursing home according to the rule of first-to-last service, and then allocating the old with high priority to the community nursing home so that the total number of the old queued in the nursing home system is equal to +.>
Wherein y is t * Optimal number of beds remaining for the final phase of the sponsored house +.>
Is the optimal ration level for the number of elderly people in the community care of phase t.
2. A method for dynamic allocation of limited resources for a pension system according to claim 1, characterized in that: step S2 is to calculate the number of remaining beds at the end of each period of the office nursing home and the number of service old people in each period of the community nursing home as follows:
for a sponsored nursing home, the optimal number of beds remaining in the nursing home at the end of each period is
Wherein (1)>
Is the t-th period maleOptimal distribution level of the nursing home bed; based on the optimal allocation level, the old people queuing situation and the bed surplus at random are given in the old people primary care system in each period, and the office old people care can give a uniquely determined optimal decision scheme;
for community nursing homes, the optimal number of served elderly people in each period of community nursing homes is as follows:
3. A method for dynamic allocation of limited resources for a pension system according to claim 1, characterized in that: the step S4 calculates the optimal service cost of each period in the pension system and the specific iterative process of the design implementation algorithm as follows:
for the whole planning period t=t+1, T-1, …,1,
first, calculating the minimum service cost in the T+1 stage pension system
As an initial input to the algorithm;
second, based on the T+1 stage calculation result, calculating the optimal ration level of the number of the old people in the T-stage community nursing home
Third, optimal ration level based on the number of elderly people in the community care facility
Calculating the result, calculating the T-stage office of the agedOptimal ration level of number of beds +.>
Fourth, according to the optimal ration level of each period of the office and community nursing homes
Calculating the minimum service cost in the T-stage pension system>
Fifth step, the minimum service cost in the T-stage pension system
As the initial input of the algorithm, repeating the second, third and fourth steps until the minimum service cost in the stage 1 pension system is calculated>
Outputting the ration level of the bed of the office nursing home in each period +.>
Feed level of aged in community nursing home +.>
And optimal cost of service per phase +.>
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