Key Engineering Materials Vol. 344 (2007) pp 913-920 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/Jul/15
Modeling sheet metal integrated production planning for laser cutting and air bending Bart Verlinden1, a, Dirk Cattrysse2,b , Joost Duflou3,c , Dirk Van Oudheusden4,d 1,2,3,4
Celestijnenlaan 300A, 3001 Heverlee, Belgium
a
[email protected],
[email protected],
[email protected],
[email protected]
c
Keywords: production planning, laser cutting, air bending
Abstract. Over the past few years both sheet metal process planning and production planning issues received increased attention. For process planning of the laser cutting process, nesting algorithms are developed in order to decrease the waste material. Additionally, algorithms are available for path planning, i.e. determining the best sequence for cutting the different parts. Production planning is mainly performed based on the ability to fill a sheet. For air bending, process planning focuses on bend sequencing and tool selection, while production planning optimization aims at minimizing time consuming setups between the different production layouts at the press brake. However, when integrating both processes, the benefits from individual optimization counteract one another: good nestings at the laser machine can create additional setups at the press brake, hence increasing the makespan. An integrated approach is proposed to verify whether this problem can be solved by already taking into account possible setups at the press brake in the early nesting stage. Integration of both processes aims at an optimal combination of parts on a sheet and minimization of the setups at the press brake. In this paper, an overview of a modeling effort addressing both goals is proposed. When combining parts on a sheet, preference is given to parts requiring the same production layout at the press brake. If this is impossible, production layouts with low changeover times are preferred. Industrial cases are used to verify the applicability of the proposed model. The results are compared to a reference approach where nesting is performed with dedicated software and planning for air bending is based on an operator’s experience. Compared to this reference approach, a makespan reduction and a setup time reduction can be observed. The planning is generated almost instantaneously and no additional sheets are required compared to the reference approach. Future research will focus on expanding the model and verifying its applicability on a larger data-set. Introduction The last two decades, amongst others due to the introduction of CNC machines and new processes such as laser cutting, a renewed interest in sheet metal operations can be observed [1]. Nowadays, sheet metal processes are considered a viable option, not only for structural components but also for durable consumer goods. The increased demand for sheet metal parts and the need for shorter throughput times have placed new requirements on the corresponding process planning and production planning systems. Fortunately, CAD/CAM systems allow automating different processes and computers offer opportunities for improvements. In this paper two sheet metal processes, i.e. laser cutting and air bending, are considered in a flow shop environment. Certain aspects of the distinct processes can be optimized. Process planning of the laser cutting process focuses on optimal nestings of different parts on a sheet. A cutting sequence can be determined, taking into account all constraints inherent to the cutting process [1,2,3]. Production planning of the cutting process is based on the ability to fill up sheets with waste material minimization as the driving factor [1,2,3,4,5]. For air bending, process planning focuses on bend sequencing and tool selection [6,7]. To avoid collisions between the part, machine and tools, a clever choice of both the production layout (i.e. toolsets positioned on the press brake) and bend sequence (i.e. the sequence for executing the different bend strokes of a part) is required.
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Production planning for air bending focuses on setup time minimization [8,9]. Interchanging production layouts is time consuming and should thus be avoided if possible. An experienced press brake operator can reduce these setups to some extent already, but a large gap for improvement can still be observed. Although both processes can be individually optimized, some problems arise in real-life production situations. Optimal nesting of parts at the laser machine provides no guarantee for minimal setups at the press brake. Indeed, it can happen that every part of the generated nesting requires a different production layout for bending. The effort spent on guaranteeing good material utilization rates at the cutting stage is counteracted by an increased setup time at the press brake, increasing the makespan of the products. To overcome those problems, an integrated approach is proposed. In the early nesting stage, possible setups at the press brake are taken into account. This paper offers an overview of our modeling effort to tackle the production planning problem from an integrated point of view and has 4 sections. Next section discusses the individual optimization of the processes considered. Also a first model for integrated production planning is discussed. Section 3 analyzes the possible improvements and proposes an alternative way for modeling sheet metal planning operations in an integrated way. Section 4 summarizes the results and concludes the paper. Individual optimization Laser cutting optimization. Many sheet metal processing companies are producing relatively small lot sizes, resulting in additional waste material [1,9,10]. Since material is an important cost factor, optimization methods are needed to tackle this problem. In order to reduce the waste material, parts requiring the same material and thickness can be grouped on a larger sheet. The problem of combining different patterns on a flat blank or coil is known as the cutting stock problem and can be observed in different industries (metal, paper, cardboard, leather, wood, plastic, textiles…). A recent overview of solution approaches and techniques for this cutting stock problem is given by de Carvalho [11]. More information on nesting algorithms specifically for sheet metal operations can be found in [4,5]. So far, different algorithms have been developed to optimally nest different sheet metal parts on a sheet while minimizing the waste material. Those powerful algorithms and heuristics have been implemented in commercial CAM software for cutting applications, allowing process planners and machine operators to combine different parts on a sheet, while taking into account specific constraints inherent to the cutting process (clamping zone, heat building zone etc.). In general, three steps can be distinguished in those commercial packages[1]. In a first stage, powerful algorithms are used to generate good nestings while minimizing the waste material. Next, the laser cutting technology such as cutting speed, piercing method, lead-in etc. is selected. Finally, the cutting path is optimized, taking into account cutting distance minimization, best cutting direction and lowest heat build-up. Air bending optimization. The 3D sheet metal parts considered in this research consist of a number of flanges, connected through a weld line or bend line as can be seen from Fig. 1. Each bend line of a part requires a certain punch/die combination, i.e. a toolset. The type of toolset is determined by the geometrical properties of the part. To produce a single part, different toolsets might be needed. Those different toolsets are positioned on the press brake with the required space between them, resulting in a production layout (Fig. 1).
Fig. 1 - A typical sheet metal part and production layout
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Interchanging production layouts is time consuming and should be avoided as much as possible. Fortunately, some production layouts can be used for multiple parts. In some cases a bend line with length (k) can be made with a toolset length (k+x) if that bend line does not contribute to forming a box-type part. The other way around is impossible: a bend line with length (k) cannot be made with a toolset length (k-x). Besides this restriction, some bend lines require dedicated tools such as a horn tool or a gooseneck. Those tools allow certain bend lines to be produced avoiding collisions between the machine, part and tools. Research on the bending process mainly focuses on process planning issues. A good overview is offered by Duflou et al. [6]. Production planning for air bending is still mainly experience-based [9,10]. All parts with duedate below a certain threshold are combined in a pool for scheduling. After the nestings are created and the parts are cut sheet by sheet, the parts are sent to the press brake for bending. The press brake operator will, based on his experience, knowledge and preference, schedule the different parts. He will reduce the number of time consuming setups between production layouts as much as possible. Identical parts will, for example, be bent consecutively, but depending on the operator’s personal preferences, different schedules will be generated for bending the pool of jobs. A survey in Belgian sheet metal companies [9] revealed that tool changes are indeed an important aspect of the air bending process. It contributes for about 9% to the total bending time of a part. Executing the bend strokes amounts to 59%, while manipulations of the part (handling, positioning, putting away) contributes on average 32% to the total bending time of a part. Tool changes 9%
Bending 59%
Part Manipulation 32%
Fig. 2 - Average time distribution for air bending Only limited research is available on optimization of production planning for air bending. Cattrysse et al. [8] formulate the problem as a traveling purchaser problem (TPP). The main goal is minimization of the time consuming setups. The proposed approach results in both a makespan reduction and a reduction in the number of setups. So far, this approach has not been implemented in software. Although the individual processes can be optimized to some extent, integrating both processes poses some problems from a planning perspective. At the cutting stage no information regarding the required bending tools is taken into account. This implies that nestings can be created where many parts require a different production layout for bending. The generated nestings might thus result in multiple setups at the press brake. The reduced material cost will be counteracted by an increased setup cost at the press brake. It is possible that nesting with somewhat more scrap material creates less setups at the press brake due to the fact that parts requiring the same production layout are combined on a sheet. A trade-off between material cost and throughput time is thus required. This research investigates whether an integrated approach can indeed decrease the number of setups at the press brake by cleverly combining the jobs for nesting. The integrated model should hence simultaneously optimize three important aspects: 1) the different parts to be combined on a sheet, 2) the sequence for bending the different parts and 3) the production layouts to be used at the press brake. The sequence for bending the parts does not determine the bend sequence for an individual part (e.g. bend line 1 - bend line 3 - bend line 2), but the order for bending the different parts (e.g. part A - part D - part C - part B). For modeling sheet metal operations from an integrated perspective, a first mathematical model was proposed [12]. The objective function is two-fold, consisting of minimization of the number of setups on the press brake and minimization of the makespan of the parts. The model minimizes the number of different layouts used for producing the batch, taking into account the production time of
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the different parts if a certain production layout is used. Every time a new production layout is required, an average setup time for that layout is added to the objective value. The constraints of the model take capacity restrictions for the sheets into account and verify part-layout combinations and sheet-part combinations. The interested reader is referred to Verlinden et al. [12] for more details on the model and the approach. For this mathematical model, good results can be obtained as far as makespan reduction, setup time reduction and reduction of the number of toolchanges is concerned. For small scale problems, computational times stay within acceptable limits, but as the number of parts increases, the generation time increases drastically. A feasible solution can be found within dozens of minutes, but for larger cases, optimal solutions cannot be reached within a reasonable amount of time. To tackle the problem of large computational times and the use of sequenceindependent setups at the press brake, another formulation of the integrated production planning problem is investigated and explained in this paper. Since the integrated sheet metal production planning problem is a combination of nesting the parts (can be seen as bin packing) and setup time minimization (can be seen as travel time minimization), the problem can be reformulated as a vehicle routing problem. The well-known vehicle routing problem lies indeed at the intersection of those two problems[13]. Alternative modeling for integrated production planning The vehicle routing problem. The vehicle routing problem (VRP) is a well-known integer programming problem, which falls into the category of NP-hard problems. The problem was first formulated by Dantzig [14] as the truck-dispatching problem. The goal of solving vehicle routing problems is to determine optimal routes (delivery or collection) from a certain given depot to a number of geographically dispersed customers, given that a number of independent vehicles with limited capacity can be used. The vehicle routing problem has many variants allowing to include capacitated trucks [15], time windows [16], multiple depots [17], etc. Many practical applications such as waste-collection, furniture home-delivery, pizza-delivery etc. can be found in literature. A general overview of heuristics methods for solving VRP instances is given in [13]. Modeling sheet metal operations as a VRP. The integrated sheet metal planning problem can be reformulated as a vehicle routing problem where the sheets with a limited usable sheet area represent the trucks with a limited and fixed capacity. The parts with a certain surface represent the different customers with a specific demand and the setup times between the production layouts (PL) required for the different parts represent the traveling distances between the different customers (Fig. 3).
Fig. 3 - Reformulation as a vehicle routing instance
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In the VRP formulation [18], the objective function minimizes the total sequence-dependent setup time between the production layouts of the different work pieces. The constraints of the model assure that every part is produced and the sheets are filled as good as possible. The vehicle routing approach for sheet metal production planning can hence be formulated as follows: fill each sheet as good as possible with parts requiring the same production layout for bending. If no such parts can be found or if no such parts fit on the sheet, add parts with a production layout that requires a minor setup at the press brake. Note that the sheets can only be filled with parts with the same material and same thickness and with a surface smaller than the remnant available surface of the sheet at that moment. In order to generate an integrated production plan with this vehicle routing approach, a number of procedural steps need to be followed. In a first stage, each part is assigned a production layout by minimizing the number of different production layouts required for bending the complete batch. In this step, one starts from all possible part-layout combinations and tries to find the minimal number of common layouts required for producing the batch. This results in a unique part-layout combination. The algorithm to be used for this step is explained in [8]. Next, the capacitated vehicle routing problem approach is used to determine the different parts to group on a sheet and to determine the order for bending the parts at the press brake. In a last step, the sheets are scheduled with a traveling salesman problem (TSP) such that the setups between sheets are minimized and if possible avoided. In this last step only the order of the sheets can be changed. The order for bending the parts cannot be altered anymore. So, first each part is assigned a production layout, minimizing the total number of layouts used. Next, the parts are grouped on sheets (filling the trucks) and the sequence for bending the parts is determined (minimizing the travel distance). Last, the sequence of the sheets can be altered to avoid certain time-consuming setups between sheets. Computational experience Instances to test. A number of cases has been worked out to verify the proposed model for integrated production planning. In reality, some companies focus on piecewise production of complex parts, while others mainly produce larger series. The batch considered in this research consists of 276 parts comprising both profiles and complex parts. Two materials are included (i.e. steel and stainless steel) and in total 201 feasible production layouts are selected for bending the parts, dependent on the available tool segments and tool types. From the complete batch, different combinations of parts are selected resulting in 10 cases, representing typical industrial situations (Table 1). The results of the production planning model are for each situation compared to a reference approach for which nesting is carried out with dedicated software and planning at the press brake is based on some rules representing the experience of an operator. This reference approach represents the current way of planning [9]. For this reference approach, all parts are grouped in a pool of jobs for nesting. The sheets are cut one after another, and once a single sheet is cut, the parts of that sheet are sent to the press brake. At the press brake, all profiles are bent first in increasing surface order, followed by complex parts in increasing surface order. Identical parts follow one another and useless setups are avoided, i.e. if possible, the last layout of the previous sheet is used for bending a part of the next sheet. The production layouts to use for bending are selected from the 201 possibilities by an experienced press brake operator. Alternatively, this layout can be determined by using dedicated CAD/CAM software for bending. Such software typically allows to model the part, unfold the part, determine a collision-free bend sequence and assign tools to the different bend lines. Computational results. Table 2 displays a typical output of the production planning module for one of the ten cases considered. Such production plan indicates the parts to combine on a sheet, the order for cutting the sheets, the order for bending the parts at the press brake and the production layout (PL) to use at the press brake.
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Table 1: Different cases to test # parts # sheets Thick_1mm 17 Thick_1.5mm 17 Thick_2mm 12 Thick_3mm 80 Thick_6mm 150 Thick_Small 46 Thick_small_profiles 24 Thick_small_complex 22 Thick_large_profiles 152 Thick_large_complex 78
Table 2: Typical output of the VRP approach Sheet1 Demostuk (PL181) Voorbeeld (181) Schofbeurs (PL 181) Autodemo (PL 25) 1657_Test (PL 25) Multifan (PL 64) Cutting time (s) 223 Bending time (s) 1125 Setup press brake (s) 372
6 3 2 3 23 12 8 7 18 9
Parts Complex, Profiles Complex, Profiles Complex, Profiles Complex, Profiles Complex, Profiles Complex, Profiles Profiles Complex Profiles Complex
Sheet2 L_prof_1.5(PL4) L_prof_1.5(PL4) Banister_3(PL66) Banister_3(PL66)
594 718 376
Total
817 1843 748
The procedure as described on previous page is applied on all ten cases and the results are compared to both the initial mathematical model [12] and the reference approach. Table 3 displays the results for the vehicle routing approach and indicates the setup time reduction (STR) and makespan reduction (MR) compared to the reference approach. For all ten cases, the integrated model has been run for 600 seconds since one expects the planning to be generated every morning in a limited amount of time. If within these preset 600 seconds the optimal solution could not be reached, the gap between the linear relaxation and the best solution found so far is mentioned in Table 3. In those cases the search procedure was interrupted before reaching the optimal solution. For the ten cases, an average setup time reduction of 46% is obtained compared to the reference approach. Since less changeover time is required at the press brake, extra time is generated for the press brake operator to perform additional tasks (administrative, helping at other processes…) or bending extra parts for e.g. building an internal stock of common parts. When taking into account possible waiting times in front of the press brake, the makespan of the products can be calculated. The makespan indicates for each case the finishing time of the last part of the batch at the bending stage. This makespan comprises cutting time, waiting time in front of the press brake, setup time at the press brake and bending time of the parts. On average a makespan reduction of 6% is observed. To quantify this somewhat, the makespan reduction is calculated expressed in equivalent saved working days per year. For this calculation we assume that the batches are continuously repeated for a whole year. If 244 working days are available per year, this results in a savings of 14 working days compared to the reference approach. These savings mainly occur due to the fact that less changeovers are required at the press brake. It can be observed that for some cases the makespan reduction is negligible. A closer look at those instances reveals that it concerns cases with large amounts of thick parts (thickness > 3mm). For those cases the laser cutting time increases exponentially with the thickness, while the bending
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time does not increase accordingly. A reduction of the total setup time at the press brake only has a marginal influence on the makespan since cutting the parts requires far more time compared to bending the parts. To indicate those cases, the cutting time is compared to the bending time and mentioned in the column “RATIO”. One of the machines is considered dominant if the ratio is smaller than 0.5 or larger than 2. Although for non-balanced cases (i.e. a dominant machine exists) other approaches are preferred as far as makespan reduction is concerned, using the integrated approach is still beneficial over the current way of planning. The makespan reduction will be negligible, but the process of planning both machines is automated. The decreased makespan and setup time need to be balanced against the material requirements. For the ten cases considered, no additional sheets are required with the VRP approach compared to the reference approach (optimal nesting with dedicated software). The main difference between nesting software and the integrated model is the fact that in some cases other parts are combined on a sheet, resulting in a different final layout of the sheets and hence a different layout for the remnant sheets, i.e. sheets that are partially used and stored for later use. Table 3: Computational results for the VRP approach GAP Ratio # parts # sheets [%] Thick_1mm 1.24 17 21 6 Thick_1.5mm 0.58 17 3 0 Thick_2mm 0.90 12 0 2 Thick_3mm 0.91 80 3 16 Thick_6mm 11.78 150 23 0 Thick_Small 0.78 46 12 29 Thick_small_profiles 1.87 24 8 14 Thick_small_complex 0.54 22 7 0 Thick_large_profiles 11.11 152 18 0 Thick_large_complex 3.80 78 9 16 AVERAGE
STR [%] 44 45 41 6 90 37 47 25 85 42 46.20
MR MR [%] [days/yr] 10.90 26.70 9.60 23.40 9.10 22.30 4.70 11.40 0.32 0.79 3.80 9.41 15.90 38.90 2.68 6.60 1.17 2.90 2.26 5.50 6.04 14.79
Conclusions If the individual sheet metal processes are optimized separately, benefits might counteract one another. To avoid this sub-optimization, an integrated approach is proposed. A previously developed mathematical model allows generating integrated production plans, resulting in an average makespan reduction of about 4% compared to the reference approach. The biggest drawback of this formulation is the fact that average setup times are used for interchanging production layouts and the huge computational complexity. To overcome this drawback, the problem is reformulated as a well-known vehicle routing problem where the sheets represent the trucks and the parts with a certain surface represent the customers with a specific demand. The setup times between production layouts represent the travel distances. This alternative approach results in an average makespan reduction of about 6% and an average setup time reduction over 46% compared to the current way of planning. The computational time is reduced drastically compared to the previous mathematical model. It can be observed that if the number of thicker parts increases, the benefits from an integrated approach, as far as makespan reduction is concerned, decrease since the laser machine becomes more dominant in those cases. The integrated approach automates the planning process and overcomes problems due to experience-based planning at the press brake. Ongoing research focuses on the inclusion of individual due-dates to model rush orders entering the system. Individual due-date requirements will be included in the model by introducing soft time windows. For each part a violation penalty is included, expressing the importance of the part. If the part goes beyond its preset due-date, a penalty needs to be paid per unit delay.
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