Aisle layout method considering the separation of human-machine aisles

Abstract

The present invention discloses an aisle layout method considering the separation of man-machine channels, which belongs to the technical field of facility layout design, collects basic data of layout sites and facilities to be distributed, and establishes a facility layout mathematical model with the goal of minimizing material handling costs; in the facility layout mathematical model, when workers carry materials between facilities in different rows, their transportation paths must pass through sidewalks; S2, solve the facility layout mathematical model to obtain a facility layout plan. While optimizing production costs, the present invention also separates man-machine channels for material handling by people and machines, respectively, which greatly improves the safety performance of the layout.

Description

Technical Field

[0001] The present invention relates to the technical field of facility layout design, and in particular to aisle layout, specifically to an aisle layout method that takes into account the separation of human-machine channels, and is suitable for optimizing the layout of facilities that are arranged in double rows and have material conveyance. Background Art

[0002] Aisle layout is a common layout form in facility layout. It is used in various scenarios due to its advantages such as simple configuration, regular layout and high transportation efficiency. In specific layout, the facilities (production units) are divided into two rows in sequence. The passage between the two rows of facilities is a road, which is used for the interaction of materials between facilities and the transfer of personnel and equipment. Whether the aisle layout is reasonable determines, to a certain extent, whether the production activities are smooth and whether the transportation costs are expensive.

[0003] In real workshops, the transportation of small parts is usually completed by workers, and the transportation of large and heavy parts is completed by transportation equipment (such as forklifts, etc.). Therefore, there is a mixture of manual and machine handling in the workshop. The traditional aisle layout research directly ignores the difference in handling methods. The planning paths of workers and handling machines are the same, both entering the road from the starting point and then reaching the end point. According to this method, the material transportation distance is short, but people and vehicles use the same channel, which poses a great safety hazard. In the actual production process, for safety reasons, sidewalks are set on both sides of the road for workers to pass, and zebra crossings are set on the road so that workers can cross the road. When workers need to carry materials between different rows, they must pass through the zebra crossing to ensure safety. Therefore, it is necessary to study this aisle layout method that is consistent with reality and separates human-machine channels to provide scientific guidance for actual production. Summary of the invention

[0004] To solve the above problems, the main purpose of the present invention is to provide an aisle layout method that takes into account the separation of human-machine channels. While optimizing production costs, the present invention also separates the human-machine channels for material handling by people and machines respectively, which greatly improves the safety performance of the layout and takes into account the safety and economy of the layout.

[0005] The technical solution of the present invention is as follows:

[0006] The aisle layout method considering the separation of human-machine aisles includes the following steps:

[0007] S1. Collect basic data of the layout site and facilities to be distributed, and establish a facility layout mathematical model with the goal of minimizing material handling costs; in the facility layout mathematical model, sidewalks extending along the length of the road are set on both sides of the road, and zebra crossings are set on the road as passages for workers to cross the road. In this way, the human and machine passages are separated. During the material handling process, the handling routes of workers and vehicles are formulated according to the following rules:

[0008] When transporting materials between facilities in different rows, workers start from the starting point and move to the zebra crossing via the sidewalk, then cross the zebra crossing, and finally move to the end point via the pedestrian walkway. Vehicles start from the starting point and enter the road and then move to the end point. When transporting materials between facilities in the same row, workers start from the starting point and move to the end point via the sidewalk, and vehicles start from the starting point and enter the road and then move to the end point. Please refer to Figure 1 , which shows the road layout structure of the embodiment with separated human-machine channels. Compared with the traditional facility layout, in this embodiment, workers must pass through the zebra crossing to complete the transportation activities between different rows of facilities.

[0009] S2, solving the facility layout mathematical model to obtain a facility layout plan;

[0010] The facility layout mathematical model of the present invention includes an objective function and a constraint function.

[0011] The objective function is as follows:

[0012]

[0013] Where F is the material handling cost (MHC); n is the number of facilities; i, j is the number of facilities; f ij is the vehicle logistics interaction between facility i and facility j; m ij is the human-carrying flow interaction between facility i and facility j; dv ij is the vehicle travel distance between facility i and facility j; dm ij is the walking distance of workers between facility i and facility j; c1 is the transportation cost per unit distance of vehicle transportation per unit logistics volume; c2 is the transportation cost per unit distance of worker transportation per unit logistics volume;

[0014] The constraint functions include:

[0015]

[0016]

[0017] In the formula, α ir is the decision function, if facility i is in the rth row, then α ir =1, otherwise α ir=0; r is the facility allocation row number, r∈R; R is the facility allocation row set, R={1,2}; N is the set of facility numbers, N={1,2,…,n};

[0018] Formula (2) and (3) are facility allocation constraints. Formula (2) stipulates that facilities must be allocated to each row on both sides of the road, and formula (3) constrains that each facility given can only be allocated to one row.

[0019]

[0020]

[0021] In the formula, z ijr is the decision function. If facilities i and j are both allocated in row r and i is to the left of j, then z ijr =1, otherwise z ijr =0; z jir is the decision function. If facilities j and i are both allocated in row r and j is to the left of i, then z jir =1, otherwise z jir =0; α jr is the decision function. If facility j is in the rth row, then α jr =1, otherwise α jr =0;

[0022]

[0023] In the formula, x i is the horizontal coordinate of the material interaction point of facility i; l i is the length of facility i along the road length direction; l j is the length of facility j along the road length direction; x j is the horizontal coordinate of the material interaction point of facility j; M is a large positive number,

[0024] Formula (6) is used to restrict the boundaries of adjacent facilities allocated on the same row in the layout space from overlapping.

[0025]

[0026] In the formula, z kir is the decision function, if facilities k and i are both allocated in row r and k is to the left of i, then z kir =1, otherwise z kir =0; l k is the length of facility k along the road length direction;

[0027] Formula (7) is used to determine the horizontal coordinate of the center point of the facility.

[0028]

[0029] In the formula, p m is the horizontal coordinate of the midpoint of the sidewalk;

[0030] Formula (8) is used to limit the range of the zebra crossing horizontal coordinate.

[0031] dv ij ≥x i -x j +w,1≤i<j≤n ⑼

[0032] dv ij ≥x j -x i +w,1≤i<j≤n ⑽

[0033] Where w is the width of the road;

[0034] Formulas (9) and (10) are used to limit the distance between vehicles traveling between facilities.

[0035]

[0036]

[0037] Formulas (11) and (12) are used to limit the walking distance of workers between facilities in the same industry.

[0038] When facilities are located in different rows, workers' transport routes can be divided into Figure 2 The walking distance between workers in different rows of facilities is (|x i -p m |+|x j -p m |+w), this embodiment introduces the variable into the model The above formulas are linearized into equations (13) to (15).

[0039]

[0040]

[0041]

[0042] In the formula, represents the horizontal distance between facility i and the horizontal coordinate of the zebra crossing, Represents the horizontal distance between facility j and the horizontal coordinate of the zebra crossing.

[0043]

[0044] After linearization, it should be:

[0045]

[0046]

[0047]

[0048]

[0049] Through a large number of experiments, it is found that there are a large number of symmetric solutions in the CAP problem, which further expands the solution space. To this end, this paper introduces a symmetry-breaking constraint and uses the q method to limit the location of facility 1 to the first row, as shown in equation (16). This constraint greatly eliminates redundant solutions and improves the solution speed of the model.

[0050] α 11 =1 ⒃

[0051] Beneficial effects:

[0052] (1) The present invention also separates the human-machine channel for material handling by humans and machines respectively, which greatly improves the safety performance of the layout and takes into account both the safety and economy of the layout.

[0053] (2) The present invention establishes a mathematical model for the layout of aisles with separated human-machine channels, which is conducive to screening, quantifying and evaluating various layout schemes, so as to obtain the optimal scheme and reduce costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below.

[0055] Figure 1 It is a schematic diagram of the layout of the facility for separating the man-machine passage of the present invention;

[0056] Figure 2 It is the planning diagram of the transportation route when the inventor carries goods across the road;

[0057] Figure 3 It is the schematic diagram of the optimal facility layout for Case S9;

[0058] Figure 4 Schematic diagram of the optimal facility layout for Case Am13b. DETAILED DESCRIPTION

[0059] The present invention will be further described in detail below in conjunction with the embodiments and drawings.

[0060] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. The described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Example

[0062] The aisle layout method considering the separation of human-machine aisles includes the following steps:

[0063] S1. Collect basic data of the layout site and facilities to be distributed, and establish a facility layout mathematical model with the goal of minimizing material handling costs; in the facility layout mathematical model, sidewalks extending along the length of the road are set on both sides of the road, and zebra crossings are set on the road as passages for workers to cross the road. In this way, the human and machine passages are separated. During the material handling process, the handling routes of workers and vehicles are formulated according to the following rules:

[0064] When transporting materials between facilities in different rows, workers start from the starting point and move to the zebra crossing via the sidewalk, then cross the zebra crossing, and finally move to the end point via the pedestrian walkway. Vehicles start from the starting point and enter the road and then move to the end point. When transporting materials between facilities in the same row, workers start from the starting point and move to the end point via the sidewalk, and vehicles start from the starting point and enter the road and then move to the end point. Please refer to Figure 1 , which shows the road layout structure of the embodiment with separated human-machine channels. Compared with the traditional facility layout, in this embodiment, workers must pass through the zebra crossing to complete the transportation activities between different rows of facilities.

[0065] S2, solving the facility layout mathematical model to obtain a facility layout plan;

[0066] The facility layout mathematical model of the present invention includes an objective function and a constraint function.

[0067] The objective function is as follows:

[0068]

[0069] Where F is the material handling cost (MHC); n is the number of facilities; i, j is the number of facilities; f ij is the vehicle logistics interaction between facility i and facility j; m ij is the human-carrying flow interaction between facility i and facility j; dv ij is the vehicle travel distance between facility i and facility j; dm ijis the walking distance of workers between facility i and facility j; c1 is the transportation cost per unit distance of vehicle transportation per unit logistics volume; c2 is the transportation cost per unit distance of worker transportation per unit logistics volume;

[0070] The constraint functions include:

[0071]

[0072]

[0073] In the formula, α ir is the decision function, if facility i is in the rth row, then α ir =1, otherwise α ir =0; r is the facility allocation row number, r∈R; R is the facility allocation row set, R={1,2}; N is the set of facility numbers, N={1,2,…,n};

[0074]

[0075]

[0076] In the formula, z ijr is the decision function. If facilities i and j are both allocated in row r and i is to the left of j, then z ijr =1, otherwise z ijr =0; z jir is the decision function. If facilities j and i are both allocated in row r and j is to the left of i, then z jir =1, otherwise z jir =0; α jr is the decision function. If facility j is in the rth row, then α jr =1, otherwise α jr =0;

[0077]

[0078] In the formula, x i is the horizontal coordinate of the material interaction point of facility i; l i is the length of facility i along the road length direction; l j is the length of facility j along the road length direction; x j is the horizontal coordinate of the material interaction point of facility j; M is a large positive number,

[0079]

[0080] In the formula, z kir is the decision function, if facilities k and i are both allocated in row r and k is to the left of i, then z kir =1, otherwise z kir=0; l k is the length of facility k along the road length direction;

[0081]

[0082] In the formula, p m is the horizontal coordinate of the midpoint of the sidewalk;

[0083] dv ij ≥x i -x j +w,1≤i<j≤n ⑼

[0084] dv ij ≥x j -x i +w,1≤i<j≤n ⑽

[0085] Where w is the width of the road;

[0086] When facilities are on the same row:

[0087]

[0088]

[0089] When facilities are on different rows:

[0090]

[0091]

[0092]

[0093] In the formula, represents the horizontal distance between facility i and the horizontal coordinate of the zebra crossing, Represents the horizontal distance between facility j and the horizontal coordinate of the zebra crossing.

[0094] α 11 =1 ⒃

[0095] In this embodiment, 16 working conditions are selected for simulation. The basic data of each working condition comes from the reference, specifically: Ji Dan, Zhang Zeqing, Liang Wei, et al. Mathematical formulation and a novel two-stage algorithm for double-row layout problem with fixed loading and unloading points [J]. Journal of Manufacturing Systems.

[0096] All experimental data were calculated on a personal computer. The processor configuration of the computer is: 12thGen Intel(R)Core(TM)i5-124002.50GHz. The mixed-integer linear programming (MILP) model established in this embodiment was accurately solved using the GUROBI 9.5.1 optimizer. The corridor allocation problem with separated man-vehicle passage (CAP_SMVP) has NP-hard properties, and the difficulty of solving it increases exponentially with the scale of the problem. In order to balance the quality and speed of the solution, the upper limit of the solution time of the optimizer is set to 18,000 seconds. If the running time exceeds the upper limit, the operation stops and the current feasible solution is output. "—" means that when the running time reaches the upper limit, no feasible solution has been obtained. In Table 1, Gap is the deviation percentage of the upper and lower bounds in the optimizer, and the bold font indicates the optimal value.

[0097] Table 1 Model solution results

[0098]

[0099]

[0100] As can be seen from Table 1, the MILP model can obtain the optimal solution for problem sizes less than 15, and its Gap value is 0. Figure 3 and Figure 4 The optimal layout diagrams of scales 9 and 13 were drawn, showing the details of the workshop facility layout, the location of the sidewalk (2 meters wide) and the MHC consumed, verifying the correctness of the model solution.

[0101] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. Aisle layout method considering the separation of human-machine aisles, characterized in that: The following steps are involved: S1. Collect basic data of the layout site and each facility to be distributed, and establish a facility layout mathematical model with the goal of minimizing material handling costs; in the facility layout mathematical model, sidewalks extending along the length of the road are set on both sides of the road, and zebra crossings are set on the road as passages for workers to cross the road; During material handling, the routes of workers and vehicles are formulated according to the following rules: When transporting materials between facilities in different rows, workers start from the starting point and move to the zebra crossing via the sidewalk, then cross the zebra crossing, and finally move to the end point via the pedestrian walkway. Vehicles start from the starting point and enter the road and then move to the end point. When transporting materials between facilities in the same row, workers start from the starting point and move to the end point via the sidewalk, and vehicles start from the starting point and enter the road and then move to the end point. S2, solving the facility layout mathematical model to obtain a facility layout plan; The facility layout mathematical model of step S1 includes an objective function and a constraint function. The objective function is as follows: Where F is the material handling cost; n is the number of facilities; i, j is the facility number; f ij is the vehicle logistics interaction between facility i and facility j; m ij is the human-carrying flow interaction between facility i and facility j; dv ij is the vehicle travel distance between facility i and facility j; dm ij is the walking distance of workers between facility i and facility j; c1 is the transportation cost per unit distance of unit logistics volume; c2 is the transportation cost per unit distance of logistics workers; The constraint functions include: dv ij ≥x i -x j +w,1≤i<j≤n⑼dv ij ≥x j -x i +w,1≤i<j≤n⑽When the facilities are located in the same row: When facilities are on different rows: In the formula, α ir is the decision function, if facility i is in the rth row, then α ir =1, otherwise α ir =0; α jr is the decision function, if facility j is in the rth row, then α jr =1, otherwise α jr =0; r is the facility allocation row number, r∈R; R is the facility allocation row set, R={1,2}; N is the set of facility numbers, N={1,2,…,n}; z ijr is the decision function. If facilities i and j are both allocated in row r and i is to the left of j, then z ijr =1, otherwise z ijr =0; z jir is the decision function. If facilities j and i are both allocated in row r and j is to the left of i, then z jir =1, otherwise z jir =0; z kir is the decision function, if facilities k and i are both allocated in row r and k is to the left of i, then z kir =1, otherwise z kir =0;x i is the horizontal coordinate of the material interaction point of facility i; j is the horizontal coordinate of the material interaction point of facility j; l i is the length of facility i along the road length direction; l j is the length of facility j along the road length direction; l k is the length of facility k along the road length direction; M is a preset positive number, p m is the horizontal coordinate of the midpoint of the sidewalk; w is the width of the road; represents the horizontal distance between facility i and the horizontal coordinate of the zebra crossing, Represents the horizontal distance between facility j and the horizontal coordinate of the zebra crossing.

2. The method for arranging aisles considering the separation of human-machine aisles according to claim 1, characterized in that: The constraint function also includes: α 11 ＝1。 3. The method for arranging aisles considering the separation of human-machine aisles according to claim 1, characterized in that: In the constraint function, equations (13) to (15) are replaced by:

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