CN118313602A - An optimization method for placing orders on a multi-variety production line considering priority processing of urgent parts - Google Patents

Abstract

The invention discloses a multi-variety production line order placement optimization method considering emergency part priority processing, which comprises the following steps: s1, calculating the utilization rate of a product of a processing type k of a workstation m; s2, modeling each workstation and obtaining the expected waiting time as E (W); s3, calculating the total waiting time of the type k product on the workstation m in the period p; s4, calculating the time required for putting the type k product into the first procedure in the period p until the procedure is completed; s5, calculating the output quantity of the type k products in the planning period p; s6, calculating the work-in-process quantity of the product type k in the system at the end of the planning period p, the inventory quantity of the product type k in the system at the end of the planning period p, and the delayed delivery quantity of the product type k in the system at the end of the planning period p: s7, calculating cost; and S8, traversing corresponding cost results under different arrival rates lambda and selecting an optimal solution. The invention can find the optimal delivery scheme of the order delivery problem.

Description

An optimization method for placing orders on a multi-variety production line considering priority processing of urgent parts

Technical Field

The present invention relates to the technical field of multi-variety production lines, and in particular to a method for optimizing order placement of multi-variety production lines by taking into account priority processing of urgent parts.

Background technique

In order to adapt to the diversified production and processing needs of products, that is, to enable the production line system to realize mixed production and processing of various types of products on the production line, multi-variety production lines came into being.

For a multi-bottle production line system, it is provided with multiple workstations, each of which includes at least one production and processing equipment. Different types of products are processed at different workstations or with different equipment according to their different process paths.

For multi-variety production lines, when urgent parts arrive at some workstations, the products processed at these workstations are prioritized. Urgent parts have high priority, and the products originally produced in the production line have low priority.

Considering the priority processing of urgent parts, it is particularly important to optimize the order placement of multi-variety production lines.

Summary of the invention

The purpose of the present invention is to provide a method for optimizing the placement of orders for a multi-variety production line taking into account the priority processing of urgent parts. The method for optimizing the placement of orders for a multi-variety production line taking into account the priority processing of urgent parts can calculate the minimized sum of work-in-process cost, inventory cost and delayed delivery cost under the consideration of the arrival of urgent parts at the workstation, and select the optimal solution by traversing the minimized sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, so as to find the optimal placement plan for the multi-variety production line order placement problem.

To achieve the above object, the present invention is implemented through the following technical solutions.

A multi-variety production line order placement optimization method considering priority processing of urgent parts includes the following steps, specifically:

Step S1: Calculate the utilization rate ρ _k,m,p of products of type k processed at workstation m under a specific arrival rate λ:

λ _0,m (k,p) represents the raw material arrival rate of product type k at workstation m in period p, λ _n,m (k,p) represents the semi-finished product re-entry arrival rate of product type k at workstation m in period p, and μ _m represents the service rate of workstation m;

M _k,l represents the workstation corresponding to the lth process of product type k, and the arrival rate of raw materials corresponding to product type k at workstation m in period p is λ _0,m (k,p) = x _k,p ·[M _k,1 = m];

The arrival rate of semi-finished products corresponding to product type k at workstation m in period p

Where k represents the product type, p represents the planning period, m represents the workstation type, K represents the number of product types processed by the multi-variety production line, L _k represents the number of processes for product type k, l represents the process number, l∈{1,2,…,L _k }; x _k,p represents the amount of raw materials put into product type k in the planning period p, and x _k,p is a decision variable;

Step S2: Since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, the priority processing rule of urgent parts is considered and the GI/G/1 queuing model is used to model each workstation, and the expectation of the waiting time in the queuing system is obtained as E(W);

Step S3: Calculate the total waiting time Z _k,m,p of products of type k at workstation m within period p under a specific arrival rate λ:

The total waiting time Z _k,m,p of a product of type k at workstation m in period p consists of the following three parts: the time τ _k,m,p from the arrival of the product to the appearance of at least one idle resource at workstation m, the processing time σ _k,m,p of all urgent parts in the waiting queue before the product, and the processing time δ _k,m,p of the newly arrived urgent parts of the product during the waiting process;

Z _k,m,p =τ _k,m,p +σ _k,m,p +δ _k,m,p ;

σ _k,m,p =T _m ·E(W)·λ _out,m,p ;

δ _k,m,p =T _m ·Z _k,m,p ·λ _out,m,p ;

Where, μ _m = 1/T _m , λ _out,m,p represents the arrival rate of urgent parts to be processed at workstation m within period p, The squared coefficient of variation corresponding to the general distribution of the arrival interval of the product at workstation m is represented by: The squared coefficient of variation corresponding to the general distribution of the service time of workstation m;

Step S4, calculate the time f(k,p,l) required for a product of type k to be put into the lth process in cycle p until the process is completed, and the total processing cycle time F(k,p, _Lk ) of the product of type k under a specific arrival rate λ:

Process l of type k product is processed by workstation m, denoted as M _k,l = m; for any process l∈{1,…,L _k } of type k product, the product stay time at the corresponding workstation M _k,l is given by the processing time and waiting time Composition, therefore

Among them, processing time is known;

Step S5, based on the time f(k,p,l) required for the product of type k to be put into the lth process in period p until the process is completed, and the total processing cycle time F(k,p,L _k ) of the product of type k, calculate the output quantity y _k,p of the product type k in the planned period p under the specific arrival rate λ;

Step S6: Calculate the work-in-progress quantity wk _,p of product type k in the system at the end of planning period p, the inventory quantity hk _,p of product type k in the system at the end of planning period p, and the delayed delivery quantity bk _,p of product type k in the system at the end of planning period p under a specific arrival rate λ:

Where D _k,p represents the demand for product type k in planning period p. In a multi-variety production line, D _k,p is known.

Step S7: Calculate the sum of the work-in-process cost, inventory cost and delayed delivery cost minimized under a specific arrival rate λ. Minimizing the sum of the work-in-process cost, inventory cost and delayed delivery cost is the objective function, which is expressed as:

Among them, W _k represents the unit work-in-process cost corresponding to product type k, H _k represents the unit inventory cost corresponding to product type k, and B _k represents the unit delayed delivery cost corresponding to product type k;

Step S8: traverse the minimum sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, compare the total cost results and select the optimal solution.

Among them, in this multi-variety production line, the product process path, processable equipment and processing time are known and determined.

Among them, in this multi-variety production line, each workstation contains at least one device, and processing is carried out on a first-come, first-served basis. One device can only process one product at a time.

The beneficial effects of the present invention are as follows: the method for optimizing the order placement of a multi-variety production line considering the priority processing of urgent parts described in the present invention comprises the following steps: step S1, calculating the utilization rate ρ _k,m,p of the product of type k processed by workstation m under a specific arrival rate λ; step S2, considering the priority processing rule of urgent parts, since the arrival process and service time of the queuing system in the multi-product production line obey the general distribution, that is, using the GI/G/1 queuing model to model each workstation, and obtaining the expectation of the waiting time on the queuing system as E(W); step S3, calculating the total waiting time Z _k,m,p of the product of type k on workstation m in period p under the specific arrival rate λ; step S4, calculating the time f(k,p,l) required for the product of type k to be placed in the lth process in period p under the specific arrival rate λ until the process is completed, and the total processing cycle time F(k,p,L _k) of the product of type k ); step S5, based on the time f(k,p,l) required for the product of type k to be put into the lth process in cycle p and the total processing cycle time F(k,p, _Lk ) of the product of type k, calculate the output quantity yk _,p of product type k in the planning cycle p under a specific arrival rate λ; step S6, calculate the work-in-process quantity wk,p of product type k in the system at the end of the planning cycle p, the inventory quantity hk _,p of product type k in the system at the end of the planning cycle p, and the delayed delivery quantity bk _{, p} of product type k in the system at the end of the planning cycle p under a specific arrival rate λ: step S7, calculate the minimum sum of work-in-process cost, inventory cost and delayed delivery cost under a specific arrival rate λ; step S8, traverse the minimum sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, and select the optimal solution by comparing the total cost results. Through the above steps, the present invention can calculate the minimized sum of work-in-process cost, inventory cost and delayed delivery cost while considering the arrival of urgent parts at the workstation, and select the optimal solution by traversing the minimized sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, so as to find the optimal delivery plan for the multi-variety production line order delivery problem.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is further described below with the aid of the accompanying drawings. However, the embodiments in the accompanying drawings do not constitute any limitation to the present invention.

Figure 1 is a schematic diagram of the production order placement for a multi-variety production line.

Figure 2 is a schematic diagram of the relationship between input and output of the lth process for products of type k.

Figure 3 is a schematic diagram of the relationship between the release and output of products in the pth cycle.

Detailed ways

The present invention is described below in conjunction with specific implementation methods.

An optimization method for placing orders on a multi-variety production line considering priority processing of urgent parts. In the multi-variety production line, the product process path, processable equipment and processing time are known and determined, and each workstation contains at least one equipment, which is processed according to the first-come-first-served rule. One equipment can only process one product at a time. The production order placement process of the multi-variety production line is shown in Figure 1.

Specifically, the multi-variety production line order placement optimization method considering the priority processing of urgent parts includes the following steps, specifically:

Step S1: Calculate the utilization rate ρ _k,m,p of products of type k processed at workstation m under a specific arrival rate λ:

λ _0,m (k,p) represents the raw material arrival rate of product type k at workstation m in period p, λ _n,m (k,p) represents the semi-finished product re-entry arrival rate of product type k at workstation m in period p, and μ _m represents the service rate of workstation m;

M _k,l represents the workstation corresponding to the lth process of product type k, and the arrival rate of raw materials corresponding to product type k at workstation m in period p is λ _0,m (k,p) = x _k,p ·[M _k,1 = m];

The arrival rate of semi-finished products corresponding to product type k at workstation m in period p

Where k represents the product type, p represents the planning period, m represents the workstation type, K represents the number of product types processed by the multi-variety production line, L _k represents the number of processes for product type k, l represents the process number, l∈{1,2,…,L _k }; x _k,p represents the amount of raw materials put into product type k in the planning period p, and x _k,p is a decision variable;

Step S2: Since the arrival process and service time of the queuing system in the multi-product production line follow a general distribution, the priority processing rule of urgent parts is considered and the GI/G/1 queuing model is used to model each workstation, and the expectation of the waiting time in the queuing system is obtained as E(W);

Step S3: Calculate the total waiting time Z _k,m,p of products of type k at workstation m within period p under a specific arrival rate λ:

The total waiting time Z _k,m,p of a product of type k at workstation m in period p consists of the following three parts: the time τ _k,m,p from the arrival of the product to the appearance of at least one idle resource at workstation m, the processing time σ _k,m,p of all urgent parts in the waiting queue before the product, and the processing time δ _k,m,p of the newly arrived urgent parts of the product during the waiting process;

Z _k,m,p =τ _k,m,p +σ _k,m,p +δ _k,m,p ;

σ _k,m,p =T _m ·E(W)·λ _out,m,p ;

δ _k,m,p =T _m ·Z _k,m,p ·λ _out,m,p ;

Where, μ _m = 1/T _m , λ _out,m,p represents the arrival rate of urgent parts to be processed at workstation m within period p, The squared coefficient of variation corresponding to the general distribution of the arrival interval of the product at workstation m is represented by: The squared coefficient of variation corresponding to the general distribution of the service time of workstation m;

Step S4: Calculate the time f(k,p,l) required for a product of type k to be put into the lth process in cycle p until the process is completed, and the total processing cycle time F(k,p, _Lk ) of the product of type k under a specific arrival rate λ:

Process l of type k product is processed by workstation m, denoted as M _k,l = m; for any process l∈{1,…,L _k } of type k product, the product stay time at the corresponding workstation M _k,l is given by the processing time and waiting time Composition, therefore

Among them, processing time is known;

Step S5, based on the time f(k,p,l) required for the product of type k to be put into the lth process in period p until the process is completed, and the total processing cycle time F(k,p,L _k ) of the product of type k, calculate the output quantity y _k,p of the product type k in the planned period p under the specific arrival rate λ;

Step S6: Calculate the WIP quantity _wk,p of product type k in the system at the end of planning period p, the inventory quantity hk _,p of product type k in the system at the end of planning period p, and the delayed delivery quantity bk _,p of product type k in the system at the end of planning period [ under a specific arrival rate λ:

Where D _k,[ represents the demand for product type k within the planning period [, and D _k,p is known in a multi-variety production line;

Step S7: Calculate the sum of the work-in-process cost, inventory cost and delayed delivery cost minimized under a specific arrival rate λ. Minimizing the sum of the work-in-process cost, inventory cost and delayed delivery cost is the objective function, which is expressed as:

Among them, W _k represents the unit work-in-process cost corresponding to product type k, H _k represents the unit inventory cost corresponding to product type k, and B _k represents the unit delayed delivery cost corresponding to product type k;

Step S8: traverse the minimum sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, compare the total cost results and select the optimal solution.

Through the above steps, the multi-variety production line order placement optimization method considering the priority processing of urgent parts of the present invention can calculate the minimized sum of work-in-process cost, inventory cost and delayed delivery cost when considering the arrival of urgent parts at the workstation, and select the optimal solution by traversing the minimized sum of work-in-process cost, inventory cost and delayed delivery cost corresponding to different arrival rates λ, so as to find the optimal placement plan for the multi-variety production line order placement problem.

The above contents are only preferred embodiments of the present invention. For ordinary technicians in this field, according to the concept of the present invention, there will be changes in the specific implementation methods and application scopes. The content of this specification should not be understood as limiting the present invention.

Claims (3)

1. The multi-variety production line order placement optimization method considering emergency part preferential processing is characterized by comprising the following steps of:

Step S1, calculating the utilization rate rho _k,m,p of the product of the work station m processing type k under the specific arrival rate lambda:

Lambda _0,m (k, p) represents the raw material arrival rate of the type k product on the workstation m in the period p, lambda _n,m (k, p) represents the semi-finished product reentry arrival rate of the type k product on the workstation m in the period p, and mu _m represents the service rate of the workstation m;

M _k,l represents a workstation corresponding to the first process of the type k product, and an arrival rate λ _0,m(k,p)＝x_k,p·[M_k,1 =m of the raw material corresponding to the type k product to the workstation M in the period p;

arrival rate of semi-finished product corresponding to type k product to workstation m in period p

Wherein K represents a product type, p represents a planning period, m represents a workstation type, K represents the number of product types processed by a multi-variety production line, L _k represents the number of procedures of the product type K, L represents the number of procedures, L epsilon {1,2, …, L _k};x_k,p represents the number of raw material throwing of the product type K in the planning period p, and x _k,p is a decision variable;

S2, modeling each workstation by taking the emergency part priority processing rule into consideration and using a queuing model of GI/G/1, and obtaining the waiting time expectation E (W) on the queuing system because the arrival process and the service time of the queuing system in the multi-product production line are subject to general distribution;

step S3, calculating the total waiting time Z _k,m,p of the type k product in the period p at the specific arrival rate lambda on the workstation m:

The total waiting time Z _k,m,p of the type k product on station m during period p comprises the following three parts: the time τ _k,m,p from the arrival of the product to the occurrence of at least one free resource at workstation m, the processing time σ _k,m,p of all the emergency parts in the waiting queue that precede the product, the processing time δ _k,m,p of the emergency parts that the product newly arrives in the waiting process;

Z_k,m,p＝τ_k,m,p+σ_k,m,p+δ_k,m,p；

σ_k,m,p＝T_m·E(W)·λ_out,m,p；

δ_k,m,p＝T_m·Z_k,m,p·λ_out,m,p；

wherein mu _m＝1/T_m,λ_out,m,p represents the arrival rate of the emergency parts to be processed by the workstation m in the period p, A coefficient of square variation corresponding to a general distribution of inter-arrival times indicative of product arrival at workstation m,The square variation coefficient corresponding to the general distribution obeyed by the service time of the workstation m;

Step S4, calculating the time F (k, p, L) required for the product of type k to be put into the first process in the period p until the process is completed at the specific arrival rate lambda, and the total processing period time F (k, p, L _k) of the product of type k:

process l of the type k product is processed by station M, noted M _k,l =m; for any procedure L e {1, …, L _k } for a product of type k, the residence time of the product on the corresponding workstation M _k,l is determined by the processing time And waiting timeComposition, therefore

Wherein the processing time isAre known;

Step S5, calculating the output quantity y _k,p of the product type k in the planning period p at the specific arrival rate lambda based on the time F (k, p, L) required for throwing the product of the type k to the first process in the period p until the process is completed and the total processing period time F (k, p, L _k) of the product of the type k;

Step S6, calculating the work-in-process quantity w _k,p of the product type k in the system at the end of the planning period p, the stock quantity h _k,p of the product type k in the system at the end of the planning period p and the delayed delivery quantity b _k,p of the product type k in the system at the end of the planning period p at the specific arrival rate lambda:

Wherein D _k,p represents the demand for product type k during the planning period p, D _k,p is known in multi-variety production lines;

Step S7, calculating the sum of the minimum product cost, the inventory cost and the delay delivery cost under the specific arrival rate lambda, wherein the sum of the minimum product cost, the inventory cost and the delay delivery cost is an objective function, and the objective function is expressed as:

Wherein W _k represents the unit work-in-process cost corresponding to the product type k, H _k represents the unit inventory cost corresponding to the product type k, and B _k represents the unit delay delivery cost corresponding to the product type k;

And S8, traversing the sum of the minimum product cost, the inventory cost and the delay delivery cost corresponding to different arrival rates lambda, and comparing the total cost results and selecting an optimal solution.

2. A multi-breed line order placement optimization method considering emergency preferential processing as claimed in claim 1, wherein: in this multi-variety production line, the product process path, processable equipment and processing time are known and determined.

3. A multi-breed line order placement optimization method considering emergency preferential processing as claimed in claim 1, wherein: in the multi-variety production line, each workstation comprises at least one device, wherein the devices are processed according to the first-come first-serve rule, and one device can process only one product at the same time.