CN112331295A - Optimization method of hospital automatic medicine distribution system - Google Patents

Optimization method of hospital automatic medicine distribution system Download PDF

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CN112331295A
CN112331295A CN202011249305.8A CN202011249305A CN112331295A CN 112331295 A CN112331295 A CN 112331295A CN 202011249305 A CN202011249305 A CN 202011249305A CN 112331295 A CN112331295 A CN 112331295A
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CN112331295B (en
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陈婉莹
龚业明
褚佳
朱安定
张芮
赵振
罗振军
陈燊
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Shanghai Ruishenglian Information Technology Co ltd
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Abstract

An optimization method of an automatic medicine distribution system of a hospital divides the environment of the automatic medicine distribution system of the hospital into a normal demand environment and an emergency demand environment, solves a nested queuing model under the normal demand environment through a second-order approximation method, solves the nested queuing model under the emergency demand environment through a convergence approximation algorithm, analyzes the accuracy of the model through simulation verification, finds bottleneck resources of the automatic medicine distribution system, improves a medicine distribution process, and optimizes an interaction mode between a pharmacy and a medicine transportation AGV; according to the method, the nested queuing network model is constructed, each link is quantitatively analyzed, the system performance is evaluated, bottleneck resources influencing the waiting time of a patient can be conveniently searched, the medicine distribution process is improved, and the interaction mode between a pharmacy and the medicine transportation AGV is optimized.

Description

Optimization method of hospital automatic medicine distribution system
Technical Field
The invention relates to the field of management science and engineering, in particular to an optimization method of an automatic medicine distribution system of a hospital.
Background
The efficiency of drug distribution inside hospitals has a large influence on patient satisfaction, and therefore, drug distribution is considered to be one of the most important activities of hospitals. For a long time, the problem of mixed flow of people and goods always exists in a medicine distribution mode in a hospital, the medicine distribution mode mainly adopts a mode of combining a full-time delivery team, a trolley and a plurality of elevators, and the mode of mixed transportation of people flow and logistics not only increases the risks of infection and spread of diseases, but also increases the workload of medical workers. Hospitals are places where personnel flow and material flow are concentrated, once a disease high-incidence period is met, the disadvantages of the people-goods mixed flow medicine distribution mode are more prominent, and along with the development of an intelligent logistics system, an intelligent medicine distribution system with high operation efficiency and low accident rate is increasingly applied to various hospitals.
To reduce patient latency, there is a need to improve the operating efficiency of intelligent medication dispensing systems, which are mainly affected by three factors: coordination among various departments; the interaction mode between the pharmacy and the AGV for medicine transportation and the operation mode of the AGV for medicine transportation. Conventional statistical methods and mathematical models are difficult to represent the way complex systems operate, and therefore, there is a need for a new method for optimizing the operating efficiency of an intelligent medication dispensing system and reducing patient waiting times.
Disclosure of Invention
In view of the above, to solve the above deficiencies of the prior art, an object of the present invention is to provide an optimization method for an automatic drug delivery system in a hospital, which quantitatively analyzes each link and evaluates system performance by constructing a nested queuing network model, so as to facilitate searching for bottleneck resources affecting patient waiting time, improve drug delivery process, and optimize an interaction mode between a pharmacy and a drug transport AGV.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method of optimizing an automated hospital drug dispensing system, comprising the steps of:
s1, dividing the environment of the automatic medicine distribution system of the hospital into a normal demand environment and an emergency demand environment;
s2, solving the nested queuing model under the normal demand environment by a second-order approximation method: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow under a normal demand environment, establishing a corresponding queue in each flow, enabling the arrival time of a patient to obey general distribution, and solving the waiting time and the response time of each stage;
s3, solving the nested queuing model under the emergency demand environment through an aggregation approximation algorithm: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow in an emergency demand environment, wherein the arrival time of a patient obeys exponential distribution, and the waiting time and the response time of each stage are calculated;
s4, verifying the accuracy of the analysis model through simulation, finding the bottleneck resource of the automatic medicine distribution system, improving the medicine distribution process and optimizing the interaction mode between the pharmacy and the medicine transportation AGV;
s5, constructing a queuing model of department drug requests, a queuing model of pharmacy drug requests and a queuing model of drug transportation requests according to the numerical distribution of patient drug requests, the numerical distribution generated by prescriptions and the numerical distribution of drug preparations respectively;
s6, constructing a numerical relationship between the patient medicine request and the prescription according to the corresponding relationship between the patient medicine request and the prescription generation through the coefficient of variation: the coefficient of variation of the patient's drug request is
Figure BDA0002771070000000031
Coefficient of variation of prescription generationIs that
Figure BDA0002771070000000032
If a department has p patients and the number of pharmacy departments in a hospital is 1, the medicine department is used
Figure BDA0002771070000000033
S7, constructing a numerical relationship between the prescription generation and the drug transportation request through the coefficient of variation according to the corresponding relationship between the prescription generation and the drug transportation request: the coefficient of variation of the drug delivery request is
Figure BDA0002771070000000034
The number of pharmacists is m, then
Figure BDA0002771070000000035
S8, decomposing the nested queuing network model into three independent queuing models;
s9, calculating the utilization rate of each server and the expected waiting time at each server;
the server utilization rate takes the utilization rate of the ith department as an example:
Figure BDA0002771070000000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002771070000000037
is the arrival rate of the ith node, q is the number of doctors in the ith node,
Figure BDA0002771070000000038
is the average service rate;
the expected latency at each server is given by the ith node as follows:
Figure BDA0002771070000000039
in the formula, utilization ratio
Figure BDA00027710700000000310
Patient to i node arrival time interval coefficient of variation
Figure BDA00027710700000000311
Coefficient of variation of doctor's service time
Figure BDA00027710700000000312
The relationship with the number q of doctors at the ith node is as follows:
Figure BDA0002771070000000041
Figure BDA0002771070000000042
Figure BDA0002771070000000043
Figure BDA0002771070000000044
Figure BDA0002771070000000045
the expected latency at each server is:
Figure BDA0002771070000000046
s10, calculating the expected waiting number of each server, taking the ith node as an example QAiNamely:
Figure BDA0002771070000000047
through the calculation of the waiting number, the waiting time based on the litter law is obtained, and the waiting time at the ith node is as follows:
Figure BDA0002771070000000048
the response time of the ith node is:
Figure BDA0002771070000000051
further, the hospital automatic drug dispensing system is used as follows: the doctor in each department makes a prescription according to the health condition of each patient and sends the prescription to the pharmacy, and the pharmacist prepares the medicine according to the prescription, and then loads the medicine onto the medicine transportation AGV, and the AGV distributes the medicine to each department.
Further, the emergency demand environment refers to a situation that a patient has a large number of emergency visits, and when the average number of visits per hour exceeds 10, the hospital is in an emergency demand state.
Further, in step S2, the process of solving the nested queuing model in the normal demand environment by the second-order approximation method is as follows:
assuming that patient arrival time and service time follow a general distribution, departments follow a uniform distribution, and each department is modeled as a GI/G/q queue;
second, calculate the utilization rate of the ith department
Figure BDA0002771070000000052
And expected waiting time of ith department
Figure BDA0002771070000000053
The coefficient of variation of the time interval of the patient's departure time is
Figure BDA0002771070000000054
Thirdly, the probability of the patient in the ith department is piCalculating the expected waiting time of the patient in the department as 1/g
Figure BDA0002771070000000055
Fourthly, the number of pharmacists is m, and the pharmacy is modeled as a GI/G/m queue;
fifthly, calculating the utilization rate of the pharmacy
Figure BDA0002771070000000056
And expected wait time for prescription in pharmacy
Figure BDA0002771070000000061
The coefficient of variation of the time interval of the prescription departure time is
Figure BDA0002771070000000062
Sixthly, the average arrival rate of the medicine transportation model is
Figure BDA0002771070000000063
The coefficient of variation of the time interval of arrival is
Figure BDA0002771070000000064
Average service rate of
Figure BDA0002771070000000065
The coefficient of variation of the service time is
Figure BDA0002771070000000066
The above data may be calculated from statistical data, with known input parameters, modeling the drug delivery AGV using a semi-open queuing network (SOQN) with n, the drug delivery AGV will queue to service at an Infinite Server (IS) station once the AGV and drug are available;
seventhly, calculating the time for the ith department to finish the drug transportation into
Figure BDA0002771070000000067
Wherein i is 1, 2, …, g;
Figure BDA0002771070000000068
and
Figure BDA0002771070000000069
respectively representing the journey time from the pharmacy to the i department and the journey time from the i department to the pharmacy, wherein
Figure BDA00027710700000000610
XlIndicating a determined time to load/unload the medicine;
eighthly, assuming that the ith floor is a floor between the ith department and the pharmacy, the vertical distance between the pharmacy and the ith department is hi, D is the distance between the entrance and the exit of each department, v is the speed of the AGV for transporting the medicine, and the transportation time is
Figure BDA00027710700000000611
Nine, assuming that the probability of the drug delivery AGV reaching each department is the same, the expected usage time for one drug delivery AGV is
Figure BDA00027710700000000612
The patients and the prescriptions are in one-to-one correspondence, and the arrival rate of the patients in each department and the arrival rate of the prescriptions in the pharmacy are lambdaB＝gλAiWherein the number of departments is g, the number of pharmacists is m, and the variation coefficient of the time interval between the prescription and the pharmacy is
Figure BDA00027710700000000613
The AGV for transporting the medicine is filled, and the variation coefficient of the time interval of the prescription leaving the pharmacy is
Figure BDA00027710700000000614
Eleven, calculating the waiting time based on the litter law by calculating the waiting number, wherein the waiting time at the ith node is as follows:
Figure BDA0002771070000000071
the response time of the ith node is:
Figure BDA0002771070000000072
establishing a GI/G/n equivalent model to replace the medicine transportation IS-SOQN corresponding to the automatic medicine distribution system; calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure BDA0002771070000000073
And expected wait time for a medication delivery AGV
Figure BDA0002771070000000074
The coefficient of variation of the interval of AGV departure times is
Figure BDA0002771070000000075
The expected throughput time for preparing the pharmaceutical product is
Figure BDA0002771070000000076
Further, in step S3, the process of solving the nested queuing model in the emergency demand environment by the aggregation approximation method is as follows:
first, assuming that the patient's arrival obeys an exponential distribution, it is calculated using the classical method proposed by Bolch, and the average queue length for the ith department is
Figure BDA0002771070000000077
Second, calculate the probability that the patient must wait in the queue
Figure BDA0002771070000000078
Thirdly, according to the Litter theorem, the waiting time is
Figure BDA0002771070000000079
Fourthly, the average team of the pharmacy is calculated by using the classic method proposed by BolchColumn length of
Figure BDA00027710700000000710
Fifthly, calculating the probability that the arriving prescription must wait in the queue
Figure BDA00027710700000000711
Sixthly, according to the Litter theorem, the waiting time is
Figure BDA0002771070000000081
Seventhly, because the semi-open queue model comprises a plurality of servers, the aggregation approximation method proposed by Buitenhekto et al is adopted for calculation, and the steps are as follows:
converting the semi-open queuing network into a first closed-loop queuing network, representing a synchronization station J by S +1, and calculating the first closed-loop queuing network by using approximate average value analysis, wherein the throughput TH1(n) is the number of AGV in drug transportation in the system;
replacing the synchronization station M +1 with a load-dependent index server and creating a second closed-loop queuing network, for which in the S service station first closed-loop queuing network, the M +1 service station is in the second closed-loop queuing network, λ represents the arrival rate of the patient, when n>1, when the nth AGV is at the S +1 station, the service rate of the station M +1 is mu (v) ═ lambda; service rate when n is 1
Figure BDA0002771070000000082
When lambda is<At TH1(n), the system runs smoothly;
analyzing the second closed-loop queuing network by using an approximate mean value analysis method to calculate the throughput TH2(n), wherein the queue length of the S station is L when n AGVs existS(n)；
Adopting the life-kill process to describe queuing, and calculating the average length of the external queue of the AGV for transporting the medicines at the S +1 station
Figure BDA0002771070000000083
Figure BDA0002771070000000084
Calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure BDA0002771070000000085
Where n represents the total number of AGVs in the automated drug delivery system, LS+1Can be calculated by approximate mean value analysis method, and the utilization rate rho of the workstations＝TH2*μs*Ks，μsIs the mean service time, K, of the station SsIs the access rate of S, LiIs the total expected queue length at the other station,
Figure BDA0002771070000000086
the transit time is
Figure BDA0002771070000000091
Further, in step S4, performing error analysis on the analysis data and the simulation data to determine the accuracy of the model; judging bottleneck resources influencing the waiting time of a patient by using the model, and providing a method for solving the bottleneck resources so as to improve a medicine distribution process; under the normal demand environment and the emergency demand environment, the interaction mode between the pharmacy and the AGV for drug transportation is optimized by analyzing the influence of the position of the pharmacy and the quantity and speed of the AGV on the waiting time of the patient, and a cost-benefit method for reducing the waiting time of the patient is found.
The invention has the beneficial effects that:
the optimization method of the hospital automatic medicine distribution system provided by the invention fully considers the flow of the hospital and the interaction process between the AGV and the staff, the evaluation method is closer to reality, and the evaluation result is more accurate;
on one hand, compared with the throughput time of the system, the waiting time of a patient has a great influence on the satisfaction degree of a hospital, therefore, the waiting time is used as a main standard for analyzing the performance of the system, the sum of a medicine demand process, a medicine preparation process and a medicine transportation process is defined as the whole waiting time, the whole waiting time is reduced as a target, the ratio of the three waiting times of the medicine demand process, the medicine preparation process and the medicine transportation process to the whole waiting time is analyzed under random conditions, the bottleneck resource of the medicine delivery process is found to be related to the inspection time of the patient, the bottleneck problem is solved, corresponding links under different conditions need to be adjusted, the medicine distribution process is improved, and the waiting time of the patient is reduced;
on the other hand, through experiments, the influence of the pharmacy position on inpatients and outpatients is quantitatively analyzed, the main influence of the pharmacy on the outpatients and the outpatients is respectively the travel distance and the waiting time, and under the random condition, the pharmacy position can be adjusted so as to effectively reduce the waiting time; considering that the waiting time of the patient can be influenced by the speed and the number of the drug transport AGVs, the waiting time of the patient is reduced by taking corresponding measures on the drug transport AGVs under normal and emergency requirements through numerical experiments; under normal demand, since the number of vehicles is not a bottleneck under normal demand, increasing vehicle speed is a more cost effective method of reducing patient waiting time. In emergency situations, increasing the number of vehicles can significantly reduce patient time over increasing vehicle speed, since vehicle number is a second bottleneck resource.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method of optimizing an automated drug dispensing system;
FIG. 2 is an automatic drug dispensing flow diagram;
FIG. 3 is a diagram of a nested queuing network model under normal demand;
fig. 4 is a schematic diagram of a nested queuing network model under emergency demand.
Detailed Description
The following specific examples are given to further clarify, complete and detailed the technical solution of the present invention. The present embodiment is a preferred embodiment based on the technical solution of the present invention, but the scope of the present invention is not limited to the following embodiments.
A method of optimizing an automated hospital drug dispensing system, comprising the steps of:
s1, dividing the environment of the automatic medicine distribution system of the hospital into a normal demand environment and an emergency demand environment;
s2, solving the nested queuing model under the normal demand environment by a second-order approximation method: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow under a normal demand environment, establishing a corresponding queue in each flow, enabling the arrival time of a patient to obey general distribution, and solving the waiting time and the response time of each stage;
s3, solving the nested queuing model under the emergency demand environment through an aggregation approximation algorithm: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow in an emergency demand environment, wherein the arrival time of a patient obeys exponential distribution, and the waiting time and the response time of each stage are calculated;
s4, verifying the accuracy of the analysis model through simulation, finding the bottleneck resource of the automatic medicine distribution system, improving the medicine distribution process and optimizing the interaction mode between the pharmacy and the medicine transportation AGV;
s5, constructing a queuing model of department drug requests, a queuing model of pharmacy drug requests and a queuing model of drug transportation requests according to the numerical distribution of patient drug requests, the numerical distribution generated by prescriptions and the numerical distribution of drug preparations respectively;
s6, constructing a numerical relationship between the patient medicine request and the prescription according to the corresponding relationship between the patient medicine request and the prescription generation through the coefficient of variation: the coefficient of variation of the patient's drug request is
Figure BDA0002771070000000121
The coefficient of variation of the prescription generation is
Figure BDA0002771070000000122
If a department has p patients and the number of pharmacy departments in a hospital is 1, the medicine department is used
Figure BDA0002771070000000123
S7, constructing a numerical relationship between the prescription generation and the drug transportation request through the coefficient of variation according to the corresponding relationship between the prescription generation and the drug transportation request: the coefficient of variation of the drug delivery request is
Figure BDA0002771070000000124
The number of pharmacists is m, then
Figure BDA0002771070000000125
S8, decomposing the nested queuing network model into three independent queuing models;
s9, calculating the utilization rate of each server and the expected waiting time at each server;
the server utilization rate takes the utilization rate of the ith department as an example:
Figure BDA0002771070000000126
in the formula (I), the compound is shown in the specification,
Figure BDA0002771070000000127
is the arrival rate of the ith node, q is the number of doctors in the ith node,
Figure BDA0002771070000000128
is the average service rate;
the expected latency at each server is given by the ith node as follows:
Figure BDA0002771070000000129
in the formula, utilization ratio
Figure BDA00027710700000001210
Patient to i node arrival time interval coefficient of variation
Figure BDA00027710700000001211
Coefficient of variation of doctor's service time
Figure BDA00027710700000001212
The relationship with the number q of doctors at the ith node is as follows:
Figure BDA00027710700000001213
Figure BDA0002771070000000131
Figure BDA0002771070000000132
Figure BDA0002771070000000133
Figure BDA0002771070000000134
the expected latency at each server is:
Figure BDA0002771070000000135
s10, calculating the expected waiting number of each server, taking the ith node as an example QAiNamely:
Figure BDA0002771070000000136
through the calculation of the waiting number, the waiting time based on the litter law is obtained, and the waiting time at the ith node is as follows:
Figure BDA0002771070000000137
the response time of the ith node is:
Figure BDA0002771070000000138
the use process of the hospital automatic medicine distribution system is as follows: doctors in each department make prescriptions according to the health condition of each patient, the prescriptions are sent to pharmacies, pharmacists prepare medicines according to the prescriptions, then the medicines are loaded into an AGV, and the AGV distributes the medicines to each department;
the medicine demand flow comprises the following steps: most hospitals arrange the same department in the same floor for convenience of administration, assuming that the number of departments is g, doctors check the medical condition of patients every day, prepare the prescription, and then the doctors send the prescription to the pharmacy, and for inpatients, the daily ward-round process is the same, so assuming that each patient has the same service time and assuming that the service of the patient follows a first-come-first-serve policy, the number q of doctors in each department is the same;
the preparation process of the medicine comprises the following steps: the prescriptions of each department are gathered to a pharmacy, the pharmacy is required to serve not only inpatients but also outpatients, most hospitals arrange the pharmacy at one floor of a building because of a large number of outpatients, after the pharmacy receives the prescriptions, existing pharmacists check the prescriptions and prepare medicines according to the prescriptions, after the preparations are completed, the medicines are placed on a shelf to wait for a vehicle, as long as the vehicle is available, the pharmacists in the pharmacy can load the medicines onto a medicine transportation AGV for transportation, generally, one hospital only comprises one pharmacy, and the number of the pharmacists in the pharmacy is assumed to be m;
and (3) medicine transportation process: a drug delivery AGV can only send a medicine to a department at a time, drug delivery AGV transports medicine from the drugstore to the nurse station of appointed department, when drug delivery AGV arrives, the nurse will lift off the medicine from the car, drug delivery AGV's the point of stopping is the drugstore, namely, drug delivery AGV accomplishes the drug delivery back, stop at the drugstore, drug delivery AGV scheduling policy is FCFS, because some medicines are fragile, so drug delivery AGV transports the medicine between drugstore and department at the uniform velocity of slowly traveling, use appointed guide path, the mode of transportation has two: one path transports the drug from the pharmacy to the department and the other path transports the drug from the department to the pharmacy; the method can reduce the vehicle congestion in one road by using two roads for running at constant speed, and in the invention, a sharing allocation strategy is assumed, all departments share the AGV for medicine transportation, and the number of the AGV for medicine transportation in the system is assumed to be n.
Further, the emergency demand environment is a condition that a large number of patients see a doctor suddenly, and when the number of patients in each department reaches more than 10 in an hour, the hospital is in the emergency demand environment; under normal requirements, when the AGV arrives, enough nurses unload the medicines; in an emergency, more nurses need to attend to the patient, and only one nurse is responsible for unloading, so there may be time waiting for the nurse when the drug delivery AGV arrives at the department.
Further, in S2, the process of solving the nested queuing model in the normal demand environment by the second-order approximation method is as follows:
assuming that patient arrival time and service time follow a general distribution, departments follow a uniform distribution, and each department is modeled as a GI/G/q queue;
second, calculate the utilization rate of the ith department
Figure BDA0002771070000000151
And expected waiting time of ith department
Figure BDA0002771070000000152
The coefficient of variation of the time interval of the patient's departure time is
Figure BDA0002771070000000153
Thirdly, the probability of the patient in the ith department is piCalculating the expected waiting time of the patient in the department as 1/g
Figure BDA0002771070000000154
Fourthly, the number of pharmacists is m, and the pharmacy is modeled as a GI/G/m queue;
fifthly, calculating the utilization rate of the pharmacy
Figure BDA0002771070000000155
And expected wait time for prescription in pharmacy
Figure BDA0002771070000000161
The coefficient of variation of the time interval of the prescription departure time is
Figure BDA0002771070000000162
Sixthly, the average arrival rate of the medicine transportation model is
Figure BDA0002771070000000163
The coefficient of variation of the time interval of arrival is
Figure BDA0002771070000000164
Average service rate of
Figure BDA0002771070000000165
The coefficient of variation of the service time is
Figure BDA0002771070000000166
The above data may be calculated from statistical data, with known input parameters, modeling the drug delivery AGV using a semi-open queuing network (SOQN) with n, the drug delivery AGV will queue to service at an Infinite Server (IS) station once the AGV and drug are available;
seventhly, calculating the time for the ith department to finish the drug transportation into
Figure BDA0002771070000000167
Wherein i is 1, 2, …, g;
Figure BDA0002771070000000168
and
Figure BDA0002771070000000169
respectively representing the journey time from the pharmacy to the i department and the journey time from the i department to the pharmacy, wherein
Figure BDA00027710700000001610
XlIndicating a determined time to load/unload the medicine;
eighthly, assuming that the ith floor is a floor between the ith department and the pharmacy, the vertical distance between the pharmacy and the ith department is hi, D is the distance between the entrance and the exit of each department, v is the speed of the AGV for transporting the medicine, and the transportation time is
Figure BDA00027710700000001611
Nine, assuming that the probability of the drug delivery AGV reaching each department is the same, the expected usage time for one drug delivery AGV is
Figure BDA00027710700000001612
The patients and the prescriptions are in one-to-one correspondence, and the arrival rate of the patients in each department and the arrival rate of the prescriptions in the pharmacy are lambdaB＝gλAiWherein the number of departments is g, the number of pharmacists is m, and the variation coefficient of the time interval between the prescription and the pharmacy is
Figure BDA00027710700000001613
The AGV for transporting the medicine is filled, and the variation coefficient of the time interval of the prescription leaving the pharmacy is
Figure BDA00027710700000001614
Eleven, calculating the waiting time based on the litter law by calculating the waiting number, wherein the waiting time at the ith node is as follows:
Figure BDA0002771070000000171
the response time of the ith node is:
Figure BDA0002771070000000172
establishing a GI/G/n equivalent model to replace the medicine transportation IS-SOQN corresponding to the automatic medicine distribution system; calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure BDA0002771070000000173
And expected wait time for a medication delivery AGV
Figure BDA0002771070000000174
The coefficient of variation of the interval of AGV departure times is
Figure BDA0002771070000000175
The expected throughput time for preparing the pharmaceutical product is
Figure BDA0002771070000000176
Further, in step S3, the process of solving the nested queuing model in the emergency demand environment by the aggregation approximation method is as follows:
first, assuming that the patient's arrival obeys an exponential distribution, it is calculated using the classical method proposed by Bolch, and the average queue length for the ith department is
Figure BDA0002771070000000177
Second, calculate the probability that the arriving patient must wait in the queue
Figure BDA0002771070000000178
Thirdly, according to the Litter theorem, the waiting time is
Figure BDA0002771070000000179
Fourthly, the calculation is carried out by using a classical method proposed by Bolch, and the average queue length of a pharmacy is
Figure BDA00027710700000001710
Fifthly, calculating the probability that the arriving prescription must wait in the queue
Figure BDA00027710700000001711
Sixthly, according to the Litter theorem, the waiting time is
Figure BDA0002771070000000181
Seventhly, because the semi-open queue model comprises a plurality of servers, the aggregation approximation method proposed by Buitenhekto et al is adopted for calculation, and the steps are as follows:
converting the semi-open queuing network into a first closed-loop queuing network, representing a synchronization station J by S +1, and calculating the first closed-loop queuing network by using approximate average value analysis, wherein the throughput TH1(n) is the number of AGV in drug transportation in the system;
replacing the synchronization station M +1 with a load-dependent index server and creating a second closed-loop queuing network, for which λ represents the arrival rate of the patient when n is the case when the S service station is in the first closed-loop queuing network and the M +1 service station is in the second closed-loop queuing network>1, when the nth AGV is at the S +1 station, the service rate of the station M +1 is mu (v) ═ lambda; service rate when n is 1
Figure BDA0002771070000000182
When lambda is<At TH1(n), the system runs smoothly;
analyzing the second closed-loop queuing network by using an approximate mean value analysis method to calculate the throughput TH2(n), wherein the queue length of the S station is L when n AGVs existS(n)；
Adopting the life-kill process to describe queuing, and calculating the average length of the external queue of the AGV for transporting the medicines at the S +1 station
Figure BDA0002771070000000183
Figure BDA0002771070000000184
Calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure BDA0002771070000000185
Where n represents the total number of AGVs in the automated drug delivery system, LS+1Can be calculated by approximate mean value analysis method, and the utilization rate rho of the workstations＝TH2*μs*Ks，μsIs the mean service time, K, of the station SsIs the access rate of S, LiIs the total expected queue length at the other station,
Figure BDA0002771070000000186
the transit time is
Figure BDA0002771070000000191
Further, in step S4, performing error analysis on the analysis data and the simulation data to determine the accuracy of the model; judging bottleneck resources influencing the waiting time of a patient by using the model, and providing a method for solving the bottleneck resources so as to improve a medicine distribution process; under normal and emergency requirements, the interaction mode between the pharmacy and the AGV for drug delivery is optimized by analyzing the influence of the position of the pharmacy and the quantity and speed of the AGV on the waiting time of the patient, and a cost-benefit method for reducing the waiting time of the patient is found.
After the model solution is completed, a simulation model is established to verify the analysis model based on the data of the first subsidiary hospital of the university of science and technology of Henan, and the model under the normal demand and the emergency demand is tested:
establishing a queuing network obtained by a verification analysis model of a 3DFlexsim simulation model, operating 100 times of repeated preheating sections for 40 hours for each scene, eliminating any initial deviation, generating an average level of which the half width of a 95% confidence interval is less than 2% due to system starting conditions, repeating each time and operating the time for 800 hours, and calculating absolute relative errors for measuring the accuracy of the analysis model
Figure BDA0002771070000000192
RaAnd RsRespectively representing an analysis result and a simulation result;
by analysis, WR，AiRepresenting the expected waiting time, p, for each patient in the departmentR，AiShows the utilization factor, T, of each department doctorR，AiIndicates the response time of each department, WR，BRepresenting the expected wait time, p, for a prescription in the pharmacyR，BShows the availability, T, of each pharmacistR，BIndicating the response time of a prescription in the pharmacy, WR，CRepresenting the expected waiting time, p, for a prescribed shipmentR，CUtilization of AGV for transporting drugs, TR，CThe frequency of the absolute error distribution, which represents the transport response time of a prescription, yields a higher average error for drug transport under emergency demand, but is acceptable because the error rate of waiting AGVs and the response time of vehicles are below 5% at the lowest, verifying the accuracy of the model.
The patient's waiting time has a greater impact on hospital satisfaction than the throughput time of the system, so using waiting time as the primary standard for analyzing system performance, defining the sum of the drug demand process, the drug preparation process and the drug delivery process as the overall waiting time, in order to reduce the overall waiting time, a bottleneck resource for the drug delivery process needs to be found;
analyzing the total waiting time spent in each procedure under normal and emergency needs, it was found that the service in the department occupied more than 50% of the total waiting time, since the examination of each patient took on average 600 seconds, which is a long time. Under normal demand, the waiting time of pharmacy is about 20% of the waiting time of 4-5 patients per department, and 40% of the waiting time of 6 patients per department, however, the waiting time of AGV for drug transportation is always less than 10%. Therefore, the number of vehicles can meet the drug delivery under normal requirements, but when the number of patients requiring drugs in each department increases, the number of pharmacists is insufficient, and in emergency requirements, the service of the department occupies more than 50% of the whole waiting time, so that the conclusion can be drawn that the main bottleneck of the drug delivery process is the service time of the department, the number of doctors is insufficient, the service time is long, in emergency requirements, the waiting time of a pharmacy is the shortest and less than 10%, but the waiting time of the vehicles exceeds 20%, so the number of vehicles is insufficient under emergency requirements;
therefore, under normal needs and existing resource configurations, the number of AGV for drug delivery is enough to meet the needs of patients, under emergency needs, the number of pharmacists under existing resource configurations is enough, the number of doctors is the bottleneck resource in the drug delivery process, and in order to reduce the waiting time of patients, the hospital administrator should increase the number of doctors on duty in each department.
Based on the simulation verification results, the analysis model is further studied as a tool to analyze how the location of the pharmacy affects the system performance:
to eliminate the discrepancy, assuming that the number of outpatients requiring medical assistance is equal to the total number of inpatients requiring medical assistance, the outpatients should go to the pharmacy by themselves to take their medication, and the inpatients can be given their medication by a nurse; the trip path of the outpatient is the same as the vehicle trip path, and the main influence of the pharmacy on the outpatient and the inpatient is the trip distance and the waiting time respectively, so the performance of the hospital automatic medicine distribution system is evaluated by utilizing the trip distance of the outpatient and the waiting time of the inpatient;
it follows from experimental data that locating the pharmacy in the middle of the hospital building can reduce the average waiting time for hospitalized patients, since locating the pharmacy in the middle of the building can reduce the travel time of the vehicle; however, under normal requirements, the number of vehicles is sufficient, the influence of the positions of pharmacies is not obvious, under emergency requirements, due to the fact that the number of vehicles is insufficient, the waiting time of inpatients can be effectively shortened by arranging the pharmacies in the middle of a building, and for outpatients, the lower trip distance is meant for one-layer pharmacies under normal requirements and emergency requirements;
thus, in order to weigh the convenience of inpatients versus outpatients, in an emergency, a hospital administrator may place a pharmacy in the middle of a building to reduce the waiting time for inpatients who may need more frequent medical assistance; under normal demand, hospital administrators can set pharmacies on a floor, as this facilitates outpatients and the waiting time for outpatients due to floor changes is shorter.
Because of the limited staff in hospitals, it is more cost effective to improve the performance of the drug delivery AGV in order to improve the system performance. According to the established analysis model, the influence of the number of vehicles and the vehicle speed on the waiting time of the patient is researched, the vehicles used by the hospital cannot move quickly, and two vehicle speeds are changed in the experiment because some medicine bottles are fragile: speed 1(m/s) and 1.5 (m/s); the numerical value experiment shows that under an emergency demand system, the influence of the speed of the AGV is greater than that of the normal demand system, because under the emergency demand, the AGV needs to be more frequently required than under the normal demand, and the faster the speed is, the shorter the waiting time is; when the arrival rate of a patient is high, the advantage of high vehicle speed is more obvious no matter normal demand or emergency demand due to the high demand rate of the AGV; under normal demand, because the AGV quantity is not the bottleneck resource under normal demand, improving the speed of a vehicle is a more economic and effective method for reducing the waiting time of a patient, and under emergency demand, because the vehicle quantity is the second bottleneck resource, the time of the patient can be obviously reduced by increasing the vehicle quantity compared with increasing the vehicle speed.
By combining the research, the method provided by the invention can search bottleneck resources influencing the waiting time of the patient, improve the medicine distribution process and optimize the interaction mode between the pharmacy and the medicine transportation AGV.
The principal features, principles and advantages of the invention have been shown and described above. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to explain the principles of the invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the invention as expressed in the following claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. A method of optimizing an automated hospital drug dispensing system, comprising the steps of:
s1, dividing the environment of the automatic medicine distribution system of the hospital into a normal demand environment and an emergency demand environment;
s2, solving the nested queuing model under the normal demand environment by a second-order approximation method: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow under a normal demand environment, establishing a corresponding queue in each flow, enabling the arrival time of a patient to obey general distribution, and solving the waiting time and the response time of each stage;
s3, solving the nested queuing model under the emergency demand environment through an aggregation approximation algorithm: applying the model to a medicine demand flow, a medicine preparation flow and a medicine transportation flow in an emergency demand environment, wherein the arrival time of a patient obeys exponential distribution, and the waiting time and the response time of each stage are calculated;
s4, verifying the accuracy of the analysis model through simulation, finding the bottleneck resource of the automatic medicine distribution system, improving the medicine distribution process and optimizing the interaction mode between the pharmacy and the medicine transportation AGV;
s5, constructing a queuing model of department drug requests, a queuing model of pharmacy drug requests and a queuing model of drug transportation requests according to the numerical distribution of patient drug requests, the numerical distribution generated by prescriptions and the numerical distribution of drug preparations respectively;
s6 correlation between patient medication request and prescription generationThe system, through the coefficient of variation, constructs a numerical relationship between the patient's medication request and the prescription: the coefficient of variation of the patient's drug request is
Figure FDA0002771069990000011
The coefficient of variation of the prescription generation is
Figure FDA0002771069990000012
If a department has p patients and the number of pharmacy departments in a hospital is 1, the medicine department is used
Figure FDA0002771069990000013
S7, constructing a numerical relationship between the prescription generation and the drug transportation request through the coefficient of variation according to the corresponding relationship between the prescription generation and the drug transportation request: the coefficient of variation of the drug delivery request is
Figure FDA0002771069990000021
The number of pharmacists is m, then
Figure FDA0002771069990000022
S8, decomposing the nested queuing network model into three independent queuing models;
s9, calculating the utilization rate of each server and the expected waiting time at each server;
the server utilization rate takes the utilization rate of the ith department as an example:
Figure FDA0002771069990000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002771069990000024
is the arrival rate of the ith node, q is the number of doctors in the ith node,
Figure FDA0002771069990000025
is the average service rate;
the expected latency at each server is given by the ith node as follows:
Figure FDA0002771069990000026
in the formula, utilization ratio
Figure FDA0002771069990000027
Patient to i node arrival time interval coefficient of variation
Figure FDA0002771069990000028
Coefficient of variation of doctor's service time
Figure FDA0002771069990000029
The relationship with the number q of doctors at the ith node is as follows:
Figure FDA00027710699900000210
Figure FDA00027710699900000211
Figure FDA00027710699900000212
Figure FDA0002771069990000031
Figure FDA0002771069990000032
the expected latency at each server is:
Figure FDA0002771069990000033
s10, calculating the expected waiting number of each server, taking the ith node as an example QAiNamely:
Figure FDA0002771069990000034
through the calculation of the waiting number, the waiting time based on the litter law is obtained, and the waiting time at the ith node is as follows:
Figure FDA0002771069990000035
the response time of the ith node is:
Figure FDA0002771069990000036
2. the method of claim 1, wherein the hospital automated drug delivery system is used as follows: the doctor in each department makes a prescription according to the health condition of each patient and sends the prescription to the pharmacy, and the pharmacist prepares the medicine according to the prescription, and then loads the medicine onto the medicine transportation AGV, and the AGV distributes the medicine to each department.
3. The method of claim 1, wherein the emergency demand environment is a sudden and large number of visits by the patient, and the hospital is in an emergency demand state when the average number of visits per hour exceeds 10 in the department.
4. The optimizing method for automatic medicine distributing system of hospital as claimed in claim 1, wherein in step S2, the process of solving the nested queuing model under the environment of normal demand by the second order approximation method is as follows:
assuming that patient arrival time and service time follow a general distribution, departments follow a uniform distribution, and each department is modeled as a GI/G/q queue;
second, calculate the utilization rate of the ith department
Figure FDA0002771069990000041
And expected waiting time of ith department
Figure FDA0002771069990000042
The coefficient of variation of the time interval of the patient's departure time is
Figure FDA0002771069990000043
Thirdly, the probability of the patient in the ith department is piCalculating the expected waiting time of the patient in the department as 1/g
Figure FDA0002771069990000044
Fourthly, the number of pharmacists is m, and the pharmacy is modeled as a GI/G/m queue;
fifthly, calculating the utilization rate of the pharmacy
Figure FDA0002771069990000045
And expected wait time for prescription in pharmacy
Figure FDA0002771069990000046
The coefficient of variation of the time interval of the prescription departure time is
Figure FDA0002771069990000047
Sixthly, the average arrival rate of the medicine transportation model is
Figure FDA0002771069990000051
The coefficient of variation of the time interval of arrival is
Figure FDA0002771069990000052
Average service rate of
Figure FDA0002771069990000053
The coefficient of variation of the service time is
Figure FDA0002771069990000054
The above data may be calculated from statistical data, with known input parameters, modeling the drug delivery AGV using a semi-open queuing network (SOQN) with n, the drug delivery AGV will queue to service at an Infinite Server (IS) station once the AGV and drug are available;
seventhly, calculating the time for the ith department to finish the drug transportation into
Figure FDA0002771069990000055
Wherein i is 1, 2, …, g;
Figure FDA0002771069990000056
and
Figure FDA0002771069990000057
respectively representing the journey time from the pharmacy to the i department and the journey time from the i department to the pharmacy, wherein
Figure FDA0002771069990000058
XlIndicating a determined time to load/unload the medicine;
eighthly, assuming that the ith floor is a floor between the ith department and the pharmacy, the vertical distance between the pharmacy and the ith department is hi, D is the distance between the entrance and the exit of each department, v is the speed of the AGV for transporting the medicine, and the transportation time is
Figure FDA0002771069990000059
Nine, assuming that the probability of the drug delivery AGV reaching each department is the same, the expected usage time for one drug delivery AGV is
Figure FDA00027710699900000510
The patients and the prescriptions are in one-to-one correspondence, and the arrival rate of the patients in each department and the arrival rate of the prescriptions in the pharmacy are lambdaB＝gλAiWherein the number of departments is g, the number of pharmacists is m, and the variation coefficient of the time interval between the prescription and the pharmacy is
Figure FDA00027710699900000511
The AGV for transporting the medicine is filled, and the variation coefficient of the time interval of the prescription leaving the pharmacy is
Figure FDA00027710699900000512
Eleven, calculating the waiting time based on the litter law by calculating the waiting number, wherein the waiting time at the ith node is as follows:
Figure FDA00027710699900000513
the response time of the ith node is:
Figure FDA0002771069990000061
establishing a GI/G/n equivalent model to replace the medicine transportation IS-SOQN corresponding to the automatic medicine distribution system; calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure FDA0002771069990000062
And expected wait time for a medication delivery AGV
Figure FDA0002771069990000063
The coefficient of variation of the interval of AGV departure times is
Figure FDA0002771069990000064
The expected throughput time for preparing the pharmaceutical product is
Figure FDA0002771069990000065
5. The method as claimed in claim 1, wherein in step S3, the process of solving the nested queuing model in the emergency demand environment by the aggregation approximation method is as follows:
first, assuming that the patient's arrival obeys an exponential distribution, it is calculated using the classical method proposed by Bolch, and the average queue length for the ith department is
Figure FDA0002771069990000066
Second, calculate the probability that the patient must wait in the queue
Figure FDA0002771069990000067
Thirdly, according to the Litter theorem, the waiting time is
Figure FDA0002771069990000068
Fourthly, the calculation is carried out by using a classical method proposed by Bolch, and the average queue length of a pharmacy is
Figure FDA0002771069990000069
Fifthly, calculating the probability that the arriving prescription must wait in the queue
Figure FDA00027710699900000610
Sixthly, according to the Litter theorem, the waiting time is
Figure FDA00027710699900000611
Seventhly, because the semi-open queue model comprises a plurality of servers, the aggregation approximation method proposed by Buitenhekto et al is adopted for calculation, and the steps are as follows:
converting the semi-open queuing network into a first closed-loop queuing network, representing a synchronization station J by S +1, and calculating the first closed-loop queuing network by using approximate average value analysis, wherein the throughput TH1(n) is the number of AGV in drug transportation in the system;
replacing the synchronization station M +1 with a load-dependent index server and creating a second closed-loop queuing network, for which in the S service station first closed-loop queuing network, the M +1 service station is in the second closed-loop queuing network, λ represents the arrival rate of the patient, when n>1, when the nth AGV is at the S +1 station, the service rate of the station M +1 is mu (v) ═ lambda; service rate when n is 1
Figure FDA0002771069990000071
When lambda is<At TH1(n), the system runs smoothly;
analyzing the second closed-loop queuing network by using an approximate mean value analysis method to calculate the throughput TH2(n), wherein the queue length of the S station is L when n AGVs existS(n)；
Adopting the life-kill process to describe queuing, and calculating the average length of the external queue of the AGV for transporting the medicines at the S +1 station
Figure FDA0002771069990000072
Figure FDA0002771069990000073
Calculating utilization rate of AGV (automated guided vehicle) for drug transportation
Figure FDA0002771069990000074
Where n represents the total number of AGVs in the automated drug delivery system, LS+1Can be calculated by approximate mean value analysis method, and the utilization rate rho of the workstations＝TH2*μs*Ks，μsIs the average clothes of the workstation SService time, KsIs the access rate of S, LiIs the total expected queue length at the other station,
Figure FDA0002771069990000075
the transit time is
Figure FDA0002771069990000076
6. The optimizing method for automatic medicine distributing system of hospital as claimed in claim 1, wherein in step S4, the analytical data and the simulation data are subjected to error analysis to judge the accuracy of the model; judging bottleneck resources influencing the waiting time of a patient by using the model, and providing a method for solving the bottleneck resources so as to improve a medicine distribution process; under the normal demand environment and the emergency demand environment, the interaction mode between the pharmacy and the AGV for drug transportation is optimized by analyzing the influence of the position of the pharmacy and the quantity and speed of the AGV on the waiting time of the patient, and a cost-benefit method for reducing the waiting time of the patient is found.
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