Factory queuing theory optimization method based on simulation

Abstract

The invention provides a simulation-based factory queuing theory optimization method. The method comprises the steps of obtaining an order quantity, a service counter quantity, an order emergency degree grade, order waiting time and a preset initial weight ratio; inputting the number of orders, the number of service desks, the order emergency degree levels and a preset initial weight ratio into simulation software, and obtaining the average order number, the average queue length, the average stay time and the average waiting time of the orders under different order emergency degree levels based on the order emergency degree levels; according to the order emergency degree grade and the average waiting time and the average staying time corresponding to the order emergency degree grade, adjusting a preset initial weight ratio to obtain an adjusted weight ratio; and calculating according to the order emergency degree grade, the order waiting time and the adjusted weight ratio to obtain an order processing priority corresponding to the order. According to the simulation method, a factory manager can more accurately optimize the production line, the production efficiency is improved, and the operation cost is reduced.

Description

Technical Field

[0001] The present invention relates to the field of simulation technology, and specifically to an optimization method for factory queuing theory based on simulation. Background Art

[0002] With the rapid development of intelligent manufacturing and Industry 4.0, the optimization of factory production lines has become a key link to improve production efficiency and reduce costs. Although the existing technologies have made remarkable progress in aspects such as the automation and informatization transformation of production lines, there are still obvious deficiencies in solving the problem of queuing and waiting on production lines, especially in complex and changeable production environments.

[0003] Currently, for the order queuing problem in factory production, traditional queuing theory models are mainly relied on for analysis. However, these models are usually based on idealized assumptions and are difficult to accurately reflect the dynamic changes and complexities of the actual production environment. In the construction process of existing models, there are generally limitations in the understanding of the complexity of the production environment: only static level division is used to handle order priorities, lacking a differential scheduling mechanism for orders at the same level, and the weight parameters are fixed and cannot be dynamically adapted to the actual working conditions. This static modeling method directly leads to the disconnection between the optimization scheme and the actual production requirements, not only making it difficult to effectively improve the overall efficiency, but also possibly exacerbating production imbalance and inducing secondary problems such as resource misallocation and process blockage.

[0004] Therefore, it is urgent to break through the limitations of traditional modeling paradigms and construct a production scheduling optimization system with dynamic adaptability to solve the queuing and waiting problems in complex production environments and achieve a substantial leap in the efficiency of production lines. Summary of the Invention

[0005] The present invention provides an optimization method for factory queuing theory based on simulation to solve at least one of the above problems.

[0006] The present invention provides an optimization method for factory queuing theory based on simulation, and the method includes:

[0007] Obtain the order quantity, the number of service desks, the order urgency level, the order waiting time, and a preset initial weight ratio;

[0008] Input the order quantity, the number of service desks, the order urgency level, and the preset initial weight ratio into simulation software, and respectively obtain the average order number, the average queue length, the average sojourn time, and the average waiting time of orders under different order urgency levels based on the order urgency level;

[0009] Adjust the preset initial weight ratio according to the order urgency level and the corresponding average waiting time and average sojourn time to obtain an adjusted weight ratio;

[0010] Calculate according to the order urgency level, the order waiting time, and the adjusted weight ratio to obtain the order processing priority corresponding to the order.

[0011] Furthermore, queuing theory formulas are set in the simulation software, and the average order number, average queue length, average sojourn time, and average waiting time of all orders with the same order urgency level are calculated using the queuing theory formulas.

[0012] Furthermore, calculating the average order number of all orders with the same order urgency level using the queuing theory formula specifically includes:

[0013] There are s service desks, the service times of each service desk are independent of each other, and μ is the average number of services that a service desk can complete per unit time;

[0014] λ n = λ n = 0, 1, 2,...;

[0015] where n is the number of orders in the system, and λ is the average arrival rate; λ n is the average arrival rate of orders when there are n orders in the system;

[0016]

[0017] where ρ is the system service intensity, and ρ s is the system utilization rate;

[0018] If the premise for the system to be stable is that the total service capacity is greater than the average order arrival rate, then ρ s < 1;

[0019]

[0020] where μ n is the total service rate when there are n orders in the system;

[0021]

[0022] where C n is the relative probability coefficient when the system state is n;

[0023]

[0024] where P0 is the probability that there are no orders in the system, that is, the idle probability;

[0025]

[0026] where P n is the probability that the order quantity is n when the system reaches a steady state;

[0027] When n ≥ s, that is, when the number of orders in the system is greater than or equal to the number of service desks, the orders arriving later must wait. Then:

[0028]

[0029] Among them, c(s, ρ) is the probability that an order must wait when it arrives at the system;

[0030]

[0031] Or

[0032]

[0033] Among them, L q is the average number of orders queuing and waiting in the system.

[0034] Furthermore, queuing theory formulas are used to calculate the average queue length of all orders with the same order urgency level, specifically including:

[0035] Denote the average number of orders being served as Then is also the average number of service desks that are in the busy state:

[0036]

[0037] The above formula shows that the average number of service desks in the busy state does not depend on the number of service desks s. Therefore, the average queue length L s is:

[0038]

[0039] Furthermore, queuing theory formulas are used to calculate the average sojourn time of all orders with the same order urgency level, specifically including:

[0040] The average sojourn time of an order in the system is calculated using the following formula:

[0041]

[0042] Among them, w s is the average sojourn time of an order in the system.

[0043] Furthermore, queuing theory formulas are used to calculate the average waiting time of all orders with the same order urgency level, specifically including:

[0044] The average waiting time of an order in the queue is calculated using the following formula:

[0045]

[0046] Among them, w q is the average waiting time of the order in the queue.

[0047] Furthermore, the specific steps for calculating the order processing priority are as follows:

[0048] Calculate the order processing priority corresponding to the order according to the order urgency level, the order waiting time, and the adjusted weight ratio, using the following formula:

[0049] P L = B P × X1 + W × X2;

[0050] Among them, P L is the order processing priority; B p is the order urgency level; W is the waiting time;

[0051] X1 is the weight ratio 1; X2 is the weight ratio 2;

[0052] And, X1 + X2 = 100%.

[0053] Furthermore, the order urgency level is divided into three levels and nine categories;

[0054] Among them: categories 1, 2, and 3 are low; categories 4, 5, and 6 are medium; categories 7, 8, and 9 are high.

[0055] Compared with the prior art, the advantages of the present invention are as follows:

[0056] The present invention provides a simulation-based optimization method for factory queuing theory, which can obtain the average order number, average queue length, average sojourn time, and average waiting time of orders under different order urgency levels in a simulation software based on the order urgency level. According to the order urgency level and the corresponding average waiting time and average sojourn time, the preset initial weight ratio is adjusted to obtain the adjusted weight ratio, and the order processing priority corresponding to the order is calculated according to the order urgency level, the order waiting time, and the adjusted weight ratio. Through the simulation software of the present invention, factory managers can more accurately predict the production parameters of orders, thereby adjusting production strategies to improve efficiency.

[0057] The simulation method is closer to the actual production environment, enabling factory managers to more precisely optimize the production line, improve production efficiency, and reduce operating costs.

[0058] It can be seen that compared with the prior art, the present invention has outstanding substantive features and significant progress, and the beneficial effects of its implementation are also obvious. Description of the Drawings

[0059] Figure 1Schematic flowchart of an optimization method for factory queuing theory based on simulation according to the present invention. Detailed implementation manners

[0060] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0061] Figure 1 Schematic flowchart of an optimization method for factory queuing theory based on simulation according to the present invention.

[0062] As Figure 1 shown, an optimization method for factory queuing theory based on simulation provided by the present invention includes:

[0063] Obtain the order quantity, the number of service desks, the order urgency level, the order waiting time, and a preset initial weight ratio;

[0064] Input the order quantity, the number of service desks, the order urgency level, and the preset initial weight ratio into the simulation software, and respectively obtain the average order number, average queue length, average sojourn time, and average waiting time of orders under different order urgency levels based on the order urgency level;

[0065] Adjust the preset initial weight ratio according to the order urgency level and the corresponding average waiting time and average sojourn time to obtain the adjusted weight ratio;

[0066] Calculate according to the order urgency level, the order waiting time, and the adjusted weight ratio to obtain the order processing priority corresponding to the order.

[0067] The optimization method for factory queuing theory based on simulation provided by the present invention can respectively obtain the average order number, average queue length, average sojourn time, and average waiting time of orders under different order urgency levels in the simulation software based on the order urgency level. According to the order urgency level and the corresponding average waiting time and average sojourn time, the preset initial weight ratio is adjusted to obtain the adjusted weight ratio, and then calculated according to the order urgency level, the order waiting time, and the adjusted weight ratio, so as to obtain the order processing priority corresponding to the order. Through the simulation software of the present invention, factory managers can more accurately predict the production parameters of orders, thereby adjusting production strategies to improve efficiency.

[0068] In an embodiment of the present invention, obtain the order quantity, the number of service desks, the order urgency level, the order waiting time, and a preset initial weight ratio;

[0069] Input the order quantity, the number of service desks, the order urgency level, and the preset initial weight ratio into the simulation software. Based on the order urgency level, obtain the average order number, average queue length, average sojourn time, and average waiting time of the orders under different order urgency levels.

[0070] In the simulation software, there is a queuing theory formula set. Use the queuing theory formula to calculate the average order number, average queue length, average sojourn time, and average waiting time of all orders under the same order urgency level.

[0071] In the simulation software, assume that each order arrives independently, and the successive arrivals follow a Poisson process with an average arrival rate of λ. There are s service desks in the system, and the service times of each service desk are independent of each other and follow a negative exponential distribution with a parameter of μ. When an order arrives, if there is an idle service desk, the order will be immediately received and served; otherwise, the order will form a queue to wait, and the waiting time is infinite.

[0072] It should be noted that if the number of service desks is less than the number of orders, the service desks will give priority to processing orders with a higher order urgency level. The simulation software is also equipped with a display that can real-time display the average order number, average queue length, average sojourn time, and average waiting time of the orders generated at the same level.

[0073] Discussing the steady-state distribution of this queuing system, the following formula can be obtained:

[0074] λ n = λ n = 0, 1, 2,...;

[0075] where n is the number of orders in the system, and λ is the average arrival rate; λ n is the average arrival rate of the orders when there are n orders in the system;

[0076] There are s service desks in total, and the service times of each service desk are independent of each other. And μ is the average number of services that a service desk can complete per unit time;

[0077]

[0078] where ρ is the system service intensity, and ρ s is the system utilization rate; The premise for the system to be stable is that the total service capacity is greater than the average order arrival rate, that is, ρ s < 1;

[0079]

[0080] where μ n is the total service rate when there are n orders in the system;

[0081]

[0082] Among them, C n is the relative probability coefficient when the system state is n;

[0083]

[0084] Among them, P0 is the probability that there is no order in the system, that is, the idle probability;

[0085]

[0086] Among them, P n is the probability that the number of orders is n when the system reaches a steady state;

[0087] When n ≥ s, that is, when the number of orders in the system is greater than or equal to the number of service desks, the orders arriving later must wait, then:

[0088]

[0089] This formula is also called the Erlang waiting formula, where c(s, ρ) is the probability that an order must wait when it arrives at the system, and it is also the probability that all service desks are in a busy state;

[0090]

[0091] Or

[0092]

[0093] Among them, L q is the average number of orders queuing in the system.

[0094] Denote the average number of orders being served as Then is also the average number of service desks in a busy state, so there is the following:

[0095]

[0096] The above formula shows that the average number of service desks in a busy state does not depend on the number of service desks s, so the average queue length L s is:

[0097]

[0098] For the multi-service desk model, Little's formula still holds, and the average sojourn time of an order in the system is calculated using the following formula:

[0099]

[0100] Among them, w sIt is the average sojourn time of the order in the system.

[0101] The average waiting time of the order in the queue is calculated by the following formula:

[0102]

[0103] where, w q is the average waiting time of the order in the queue.

[0104] Preferably, according to the order urgency level and its corresponding average waiting time and average sojourn time, the preset initial weight ratio is adjusted to obtain the adjusted weight ratio;

[0105] According to the order urgency level, the order waiting time and the adjusted weight ratio, the order processing priority corresponding to the order is calculated.

[0106] The specific steps for calculating the order processing priority are as follows:

[0107] The order processing priority corresponding to the order is calculated according to the order urgency level, the order waiting time and the adjusted weight ratio by the following formula:

[0108] P L = B P × X1 + W × X2;

[0109] where, P L is the order processing priority; B p is the order urgency level; W is the waiting time;

[0110] X1 is the weight ratio 1; X2 is the weight ratio 2;

[0111] And, X1 + X2 = 100%.

[0112] Among them, the weight ratios corresponding to different orders can be the same or different.

[0113] Among them, the proportions of X1 and X2 are dynamically adjusted according to the calculated average waiting time, average sojourn time and order urgency level.

[0114] Preferably, the order urgency level is divided into three levels, a total of 9 categories;

[0115] Among them: categories 1, 2, and 3 are mild; categories 4, 5, and 6 are moderate; categories 7, 8, and 9 are high.

[0116] In another embodiment of the present invention, the weight ratios corresponding to the order urgency level and the waiting time for calculating the order processing priority are not fixed, but are dynamically adjusted according to the order urgency level and the waiting time of the current order, so as to ensure a more reasonable queuing arrangement for each order.

[0117] The specific method is as follows: Count the order urgency levels of the orders, and divide the order urgency levels into three levels and nine categories; among them: categories 1, 2, and 3 are low; categories 4, 5, and 6 are medium; categories 7, 8, and 9 are high.

[0118] Input the order quantity, the number of service desks, and the order urgency level into the simulation software, and respectively obtain the average order number, average queue length, average sojourn time, and average waiting time of the orders generated at the three levels.

[0119] According to the average order number, average queue length, average sojourn time, and average waiting time data of the order urgency levels at the three levels, if all four groups of data are within the preset reasonable range, calculate the order processing priority according to the initial weight ratio, and queue and produce all orders according to the order processing priority; if the four groups of data are not within the preset range, adjust the initial weight ratio, use the new weight ratio as the initial weight ratio, and then input it into the simulation software, and repeat the above steps until all four groups of data are within the preset reasonable range, calculate the order processing priority according to the finally adjusted weight ratio, and queue and produce all orders according to the order processing priority.

[0120] For example, initially set X1 and X2 to 70% and 30% respectively, input the order quantity, the number of service desks, and the order urgency level into the simulation software, and respectively obtain the average order number, average queue length, average sojourn time, and average waiting time of the orders generated at the three levels. If the average waiting time of the orders with a low order urgency level is relatively long, then correspondingly reduce the weight ratio X1 of the order urgency level and increase the weight ratio X2 of the corresponding waiting time. Then, judge whether the current weight ratio is appropriate according to the data such as the average order number, average queue length, average sojourn time, and average waiting time of the orders generated at the three levels. If the weight ratio is adjusted to: X1 = 60%, X2 = 40%, and all four groups of data of the average order number, average queue length, average sojourn time, and average waiting time are within the preset reasonable range, calculate the order processing priority according to the finally adjusted weight ratio, so as to make a more reasonable production scheduling arrangement and avoid customer loss.

[0121] In another embodiment of the present invention, the initial X1 and X2 are respectively set to 70% and 30%. When the business urgency levels of all the orders in the queuing sequence are greater than or equal to 7 and less than or equal to 9, that is, when there are more important orders and the order urgency levels are at the same level, the weight ratio X1 of the order urgency level is decreased, and the weight ratio X2 of the corresponding waiting time is increased. If the weight ratio is adjusted to X1 = 40% and X2 = 60%, and the four sets of data of the average order number, average queue length, average sojourn time, and average waiting time are all within the preset reasonable range, then the order processing priority is calculated according to the finally adjusted weight ratio, so as to make a more reasonable production scheduling arrangement and avoid overdue delivery of orders due to too long waiting time.

[0122] For the same and similar parts among the various embodiments in this specification, reference may be made to each other.

[0123] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A simulation-based optimization method for factory queuing theory, characterized in that, The method includes: Obtaining the order quantity, the number of service desks, the order urgency level, the order waiting time, and a preset initial weight ratio; Inputting the order quantity, the number of service desks, the order urgency level, and the preset initial weight ratio into simulation software, and obtaining the average order number, average queue length, average sojourn time, and average waiting time of orders under different order urgency levels respectively based on the order urgency level; Adjusting the preset initial weight ratio according to the order urgency level and the corresponding average waiting time and average sojourn time to obtain an adjusted weight ratio; Calculating the order processing priority corresponding to the order according to the order urgency level, the order waiting time, and the adjusted weight ratio.

2. The simulation-based factory queuing theory optimization method according to claim 1, characterized in that A queuing theory formula is set in the simulation software, and the average order number, average queue length, average sojourn time, and average waiting time of all orders under the same order urgency level are calculated using the queuing theory formula.

3. The simulation-based factory queuing theory optimization method according to claim 2, wherein Calculating the average order number of all orders under the same order urgency level using the queuing theory formula specifically includes: There are s service desks, the service times of each service desk are independent of each other, and μ is the average number of services that a service desk can complete per unit time; λ n = λ n = 0, 1, 2,...; where n is the number of orders in the system and λ is the average arrival rate; λ n is the average arrival rate of orders when there are n orders in the system; Among them, ρ is the system service intensity, and ρ s is the system utilization rate; If the premise for the system to be stable is that the total service capacity is greater than the average order arrival rate, then ρ s <1; where μ n is the total service rate when there are n orders in the system; Among them, C n is the relative probability coefficient when the system state is n; Among them, P0 is the probability that there is no order in the system, that is, the idle probability; where P n is the probability when the order quantity is n at the steady state of the system; When n≥s, that is, when the order quantity in the system is greater than or equal to the number of service desks, the orders arriving later must wait, then: Among them, c(s,ρ) is the probability that an order must wait when it arrives at the system; Or Among them, L q is the average number of orders waiting in line in the system.

4. The simulation-based factory queuing theory optimization method according to claim 3, characterized in that Calculating the average queue length of all orders under the same order urgency level using the queuing theory formula specifically includes: Let the average number of orders being served be Then is also the average number of service desks that are busy: The average number of service desks in the busy state does not depend on the number of service desks s, so the average queue length L s is as follows:

5. The simulation-based factory queuing theory optimization method according to claim 4, wherein Calculating the average sojourn time of all orders under the same order urgency level using the queuing theory formula specifically includes: The average sojourn time of an order in the system is calculated using the following formula: where w s is the average sojourn time of the order in the system.

6. The simulation-based factory queuing theory optimization method according to claim 5, wherein Calculating the average waiting time of all orders under the same order urgency level using the queuing theory formula specifically includes: The average waiting time of an order in the queue is calculated using the following formula: where w q is the average waiting time of the order in the queue.

7. The simulation-based factory queuing theory optimization method according to claim 1, wherein The specific steps for calculating the order processing priority are: Calculating the order processing priority corresponding to the order according to the order urgency level, the order waiting time, and the adjusted weight ratio using the following formula: P L = B P × X1 + W × X2; Among them, P L is the order processing priority; B p is the order urgency level; W is the waiting time; X1 is the weight ratio 1; X2 is the weight ratio 2; And, X1 + X2 = 100%.

8. The simulation-based factory queuing theory optimization method according to claim 1, wherein The order urgency level is divided into three levels and nine categories; Among them: categories 1, 2, and 3 are mild; categories 4, 5, and 6 are moderate; categories 7, 8, and 9 are high.

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