HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 46(2) pp. 55–62 (2018) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2018-0019 WORKER MOVEMENT DIAGRAM BASED STOCHASTIC MODEL OF OPEN PACED CONVEYORS TAMÁS RUPPERT1 AND JÁNOS ABONYI *1 1MTA-PE Lendület Complex Systems Monitoring Research Group, Department of Process Engineering, University of Pannonia, Egyetem u. 10, Veszprém, H-8200, HUNGARY Human resources are still utilized in many manufacturing systems, so the development of these processes should also focus on the performance of the operators. The optimization of production systems requires accurate and reliable models. Due to the complexity and uncertainty of the human behavior, the modeling of the operators is a challenging task. Our goal is to develop a worker movement diagram based model that considers the stochastic nature of paced open conveyors. The problem is challenging as the simulator has to handle the open nature of the workstations, which means that the operators can work ahead or try to work off their backlog, and due to the increased flexibility of the moving patterns the possible crossings which could lead to the stopping of the conveyor should also be modeled. The risk of such micro-stoppings is calculated by Monte-Carlo simulation. The applicability of the simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process. Keywords: Industry 4.0, Operator 4.0, Monte-Carlo simulation, Process development, Line balanc- ing, Wire-harness assembly 1. Introduction Conveyor lines are more productive than regular assem- bly lines [1]; therefore there are more prevalent in the au- tomotive industry [2]. The movement of these conveyors mostly has paced and cyclic characteristic where at the beginning of the cycle, every station moves to the next position [3]. It can happen that the operator cannot finish his/her work before the product leaves the workstation. There are two alternative approaches for completing the unfinished work. We speak about close station produc- tion when the operator must stop the conveyor even in case of a minor delay [4]. Such processes are typical in Japan. In U.S.-type production systems, the operator does not have to finish his or her job, he or she can move with the product to the next station to work off the backlog. In these open stations the operators can work ahead or can be delayed [5], and the production stops only when the delay exceeds a critical limit. These open workstations reduce capacity loss by decreasing the risk of stopping the conveyor, but the modeling and optimization of these processes is much more challenging as the model has to handle idle and delay times [6]. Worker movement dia- grams are widely used to model the work of operators at conveyor belts [7]. Such models can be used to reduce the risk of conveyor stoppage [8] and optimize production se- quence [9], since the optimal distribution of the products can also reduce the probability of critical backlogs [10]. *Correspondence: researcher@abonyilab.com Worker movement diagrams focus only one station. In open paced conveyors the operators effect on each other; therefore the model should handle the interactions be- tween the workstations, especially for the prediction of the conveyor stoppage. Our goal is to develop a worker movement diagram based model for open paced conveyors, which model con- siders the stochastic nature of production and recognizes the meeting point of operators and analyzes the idle times due to working in the same zones and risk of stopping the production in case of unmanageable backlogs. We in- troduce stochastic variables into the movement diagram representation based model and apply Monte-Carlo sim- ulation to evaluate the risk of conveyor stoppage and give robust estimates of the effects of different parameter set- tings. The simulator is developed in Python environment. The applicability of the proposed model and simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process. Section 2 describes the worker movement diagram and the sections defined based on the relative position of the operators and the conveyor. The model of the paced conveyor is based on equations that represent the movement of the operators in these sections. Based on these equations we calculate when the conveyor should be stopped. Section 3 describes the applicability of the developed simulator in a wire harness production system. mailto:researcher@abonyilab.com 56 RUPPERT AND ABONYI 2. Model of the paced conveyor 2.1 Problem definition The most widespread paced open station conveyors are used to produce wire harnesses in the automobile in- dustry. The optimization and cost estimation of these processes are an economically significant problem [11]. These modular assembly lines consist of manual work- stations (tables) shown in Fig. 1. Human operators work at the tables that are moving similarly as a conveyor belt (see Fig. 2). These tables move with a fixed speed which is determined based on the tact time, tc. After the cycle, every table moves to the next station. The modeling the relative position of the operators and the tables can be represented by worker movement diagrams that will be presented in the next section. 2.2 Movement diagram of an open station The paced conveyor has k,k = 1, . . . ,K is number of workstations that moves in every n = 1, . . . ,N cycle. The speed of the conveyor is vc, and the walking speed of operator is vw. The tc is the tact time determines the assembly speed: vkn = L tk π(n−k) (1) where L represents the length o the workstation, the tk π(n−k) the assembly time which is dependent on the produced product. The sequence of the products is rep- resented by a π vector of the labels of the types, so π(k) = pj states that type product pj started to be pro- duced during the k-th production cycle. The modeling of the paced conveyor is complex task as the conveyor moves only for a tcm < tc period of the time, which de- fines several sections of the tack time according to the speed and position of the table and the operators. As it is depicted in Figs. 3 and 4, the worker move- ment diagram is divided for six sections (s = 1, . . . ,6) . 1. The operator moves to the starting point of the table Figure 1: An example assembly table in wire harness man- ufacturing. The dashed line with an arrow represents the worker motion at the table. The operator works on the ta- ble from left to right. The assembly speed is vkn. Figure 2: The most widely used open station paced con- veyors are used in wire harness assembly, where the oper- ators are working at tables that moving in every cycle of the production [12]. 2. The operator works before the new cycle 3. The operator and the table move together 4. The operator works and the table stays 5. The operator and the table move together after the end of tact time 6. The operator works and the table stays after the end of tact time In the first section, s = 1, the operator walks to the left side of the table, F(1)kn. After reaching this posi- tion the operator starts the assembly process and moves with the conveyor till the conveyor moves to its next workspace. After this F(3)kn position the operator works at the standing table with a vkn speed. When the job is fin- ished, the operator reaches the end of the table, F(4)kn = kL, as it is shown at Fig. 5). The second, fifth and sixth sections happen when operator deviates from this normal case (work ahead or delayed). In the following, we present a model that describes how the positions of the table and the operators are chang- ing in time. In the model F(s)kn denotes the position of kth operator at nth cycle step in sth section of diagram, where the positions are measured from the starting point of the first table. Section 1. - The operator moves to the starting point of the table At the beginning of the cycle, the operator moves the starting point of the next table which is 2L far from its actual position. The F(1)kn position when the kth opera- tor reaches the staring point of table should be calculated as F(1)kn = F(6) k n−1 −T(1)knvw (2) T(1)kn = NWT + DWT + CDWT + IWT (3) where F(6)kn−1 is the kth operator finishing position in the previous cycle step (n−1), while the T(1)kn required Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 57 Figure 3: Worker movement diagram of the sections when the operator works ahead. Lines with arrow represent the motion of the operator, while dashed lines represent movement of the table. Figure 4: Worker movement diagram of the sections when the operator has a backlog. Lines with arrow represent the motion of the operator, while dashed lines represent movement of the table. Figure 5: Worker movement diagram of one station. The first meeting point with the table and the operator is F(1)kn. F(3) k n and F(4)kn are the positions at the end of the second and third sections. When there is no delay or the operator does not work ahead F(4)kn = F(6) k n, where F(6) k n is the finishing position. 46(2) pp. 55–62 (2018) 58 RUPPERT AND ABONYI time can be decomposed into four components, which will be modeled in the following subsections: • NWT - Normal Walking Time • DWT - Delayed Walking Time • CDWT - Critically Delayed Walking Time • IWT - Idle Walking Time NWT: Normal Walking Time In the normal case, the operator and the conveyor move together at the beginning of the cycle with vc+vw relative speed. The effect of the akn−1 idle time and the l k n−1 late time of the previous cycle is represented by the NWTa and NWTb variables that are used to calculate the NWT walking time: NWT = max[min(NWTa; NWTb); 0] (4) NWTa = max ( 2L−akn−1vw vc + vw ; 0 ) (5) NWTb = min ( tcm − lkn−1, 2L vc + vw ) , (6) where akn−1vw represents the walking distance of opera- tor at the end of the previous cycle. When tcm − lkn−1 is less than zero, then operator does not have to walk, be- cause he or she still works on the last (n−1) product (In this case we should calculate DWT). DWT: Delayed Walking Time When the assembly time in the previous cycle exceeds tc, DWT is equal to the time which necessary for the reaching the table after tc. DWT = IF [tcm − lkn−1 > 0 OR l k n−1 = 0]; (7) THEN DWTh; ELSE 0 DWTh = (8) max [ 2L vc + vw −max ( tcm − lkn−1; 0 ) ; 0 ] vcw where vcw = vc+vw vw is the walking speed of operator, when the conveyor is moving. CDWT: Critically Delayed Walking Time When lkn−1 is more than tcm, the operator moves to the beginning of the table when the conveyor is standing. CDWT = IF [tcm − lkn−1 <= 0 (9) OR lkn−1 = 0]; THEN 2L vw ; ELSE 0 IWT: Idle Walking Time When the conveyor does not move and akn−1 is bigger than the necessary walking time, 2L vw , then IWT = min ( akn−1, 2L vw ) (10) Section 2. - The operator works before the new cycle The F(2)kn staring position and T(2) k n duration of the The second section is calculated as: F(2)kn = F(1) k n + T(2) k nv k n (11) T(2)kn = max ( akn−1 − 2L vw ; 0 ) (12) where vkn is the average speed of the assembly. Section 3. - The operator and table move together In this section, operator and the conveyor are moving to- gether for a time period shorter than tcm, so they will meet at: F(3)kn = F(2) k n + T(3) k n(vc + v k n) (13) T(3)kn = min ( max [ (n−1)tc + tcm −Tk; 0 ] ;tcm ) (14) where (n−1)tc + tcm describes the time instant the sec- tion will finish. In normal situation T(3)kn equals to tcm, while in extreme case the operator has as significant idle time as he or she finishes his or her job before the end of this section. Section 4. - The operator works and table stays In this section the operator works with vkn linear speed until the conveyor does not move, so this section finishes at: F(4)kn = F(3) k n + T(4) k nv k n (15) T(4)kn = min{max[ntc −T; 0]; (16) L vkn −T(2)kn −T(3) k n} , where L vkn −T(2)kn−T(3)kn defines the remaining assem- bly time before the end of the tact time. The idle and delay times At the end of the cycles the akn idle or l k n delay time is calculated as: lkn = max ( L vkn + T(1)kn −akn−1 + lkn−1 − tc; 0 ) (17) akn = max ( tc − Lvkn −T(1) k n + a k n−1 − lkn−1; 0 ) (18) The prediction of conveyor stoppage is the most impor- tant ability of the model which will be calculated based on the delay time as it will be presented in the following subsection. Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 59 Section 5. - The operator and the table move together after the end of tact time This section can be considered as the modification of the third section with the delay of the operator. As we already know lkn and the operator can work in this section maxi- mum till tcm, the calculation is straightforward: F(5)kn = F(4) k n + T(5) k n(vc + v k n) (19) T(5)kn = min ( lkn, tcm ) (20) Section 6. - The operator works and the conveyor stays after the end of tact time As the duration of this section is limited as tc − tcm, the variables that define the end of the section are calculated as: F(6)kn = F(5) k n + T(6) k nv k n (21) T(6)kn = min [ max ( lkn − tcm; 0 ) ;tc − tcm ] (22) Calculation of the stoppage and the idle time The open station type operation of the paced conveyor has increased flexibility as the conveyor has to be stopped only when the delay of the kth operator is as significant as it disturbs the work of the neighboring k−1th operator. We define this situation as: Tk + T(1)kn <= T k−1 + T(1)k−1n−1 + tc 4 (23) In this case the idle Ikn time has to be modified by T(1) k n and reset the value of akn to zero. Ikn = (n−1)tc −T(1) k n (24) When the lkn − T(6)kn is smaller than tcm, the operator stops the conveyor. The lkn is reset and the stoppage time is: Skn = max(l k n −T(6) k n − tcm; 0) (25) 2.3 KPIs and the developed simulator The developed simulator handles the stochastic and open nature of the conveyor, simulates all workstations, the in- teractions between the operators and predicts stoppage. The worker movement diagram representation helps in the stoppages prediction (see Fig. 6). Production planners can use the developed simulator to try sequencing strategies and analyze a new production lines capability. The following key performance indica- tors (KPIs) calculated based on Monte-Carlo simulation gives a realistic picture about the production. • The balance of conveyor line is depended on the maximum of the late times of operators, lk = [lk1, l k 2, . . . , l k n]: B = K∑ k=1 max(lk) K 1 tc (26) • The efficiency of production is calculated based on to the sum of the L vkn assembly times di- vided by the maximum of the T(6)k = T(6)k1,T(6) k 2, . . . ,T(6) k n) finishing times and the sum of stoppage times multiplied by the number of workstations. P = K∑ k=1 L vkn {max[T(6)k] + N∑ n=1 K∑ k=1 Skn}K (27) • The sum of the S stoppage times (Eq. 25). • The mean of the assembly times. The simulator and the movement diagram are devel- oped in Python environment. d The developed simulator and the related dataset is freely and fully available on the website of authors: www.abonyilab.com. 3. Application to wire harness production To demonstrate the applicability of the simulator three typical types of production sequencing strategies were analyzed. In the first case, the sequence follows the ran- dom customer demand which case often happens in Just In Time (JIT) production. Batch production is a more ef- ficient sequencing strategy. In this case, batches of lower and higher complexity products are following each other. One of the best solutions is the π = m1,m2,m1, . . . high/low sequencing strategy because it utilizes the open station nature of the conveyor. The studied conveyor contains K = 5 workstations. The number of manufactured products is N = 100, and two different group of products (M = 2) are produced. The assembly times are represented by a normal distribu- tion, which is t1 = N(250,30) for the lower complexity product and t2 = N(310,30) for the higher complexity product. The tact time of the conveyor is constant and set to tc = 280s which is the average assembly time of the products. Fig. 7 shows the results of 1,000 simulations of the three sequence types. This scatter matrix plot shows the main KPIs, the balance, the number of the manufactured products, the number of stoppages, and the average as- sembly times. The green dots represent the High/Low, the blues the batched, and the red the random sequences. As shown in Fig. 7, the difference between the ran- dom (blue) and high/low (green) sequences is significant on all KPIs. The batched sequence (red) has similar per- formance to the high/low sequence, but many times this batch production is not manageable because of the high variance of the products and the short delivery times. 4. Conclusions As human resources are still necessary for many man- ufacturing systems, the development of production pro- cess should also focus on the performance of operators. 46(2) pp. 55–62 (2018) www.abonyilab.com 60 RUPPERT AND ABONYI −5 0 5 10 15 20 25 30 Distance [m] 0 1000 2000 3000 4000 5000 6000 Ti m e [s ] Figure 6: The developed worker movement diagram of five stations and 18 cycle steps. The distance begins at −5 m to represent the previous workstation. Figure 7: The result of a Monte-Caro simulation of three different sequencing strategies. The scatter plot shows all of KPIs. The high/low sequence is denoted by green, the batch by red, and the random by blue dots. The difference between the random and high/low sequences is significant on all KPIs. Hungarian Journal of Industry and Chemistry Worker Movement Diagram Based Model Of Open Paced Conveyors 61 According to the digital twin concept, this development should be based on the model of the production sys- tem, which necessaries the development of simulators that can handle uncertainties related to the human nature of the operators. The developed worker movement dia- gram based model handles the paced and open worksta- tions of the conveyors and the stochastic nature of pro- duction. The worker movement representation helps in the analysis of the operators which is needed to predict production stoppages. The introduction of stochastic vari- ables and the Monte-Carlo simulation-based evaluation of the key performance indicators provide a realistic pic- ture about the production. The applicability of the simula- tor in the analysis of the effect of production sequencing is demonstrated by a well-documented benchmark prob- lem of a wire-harness production process. The developed simulator is not specialized to the studied wire harness production; it can be used to model all of the types of paced conveyors even open or closed workstations. Acknowledgement This research was supported by the National Research, Development and Innovation Office NKFIH, through the project OTKA-116674 (Process mining and deep learn- ing in the natural sciences and process development) and the EFOP-3.6.1- 16-2016- 00015 Smart Specialization Strategy (S3) Comprehensive Institutional Development Program. Notations KPI Key Performance Indicator NWT Normal Walking Time DWT Delayed Walking Time CDWT Critically Delayed Walking Time IWT Idle Walking Time k index of workstation k = 1, . . . ,K K number of workstations n index of cycle step n = 1, . . . ,N N number of cycle steps s index of section s=1, . . . ,6 vkn assembly speed of th operator [ m s ] vw walking speed of the operator [ m s ] vc speed of the conveyor [ m s ] vcw walking speed of the operator when the conveyor is moving [m s ] tc tact time [s] tcm conveyor movement time [s] tk (π(n) assembly time of actual the product at kth operator [s] T(s)kn duration of the actual s section in nth cycle step a kth workstation [s] T(6)k finishing times of the kth operator [s] akn work ahead time in nth cycle step at kth operator [s] lkn late time in nth cycle step at kth operator [s] lk late times of kth operator [s] T actual simulated time [s] Ikn final idle time in nth cycle step at kth workstation [s] Skn stoppage time in nth cycle step at kth workstation [m] F(s)kn position of operator at the actual s section in nth cycle step a kth workstation [m] Tablekn table position in nth cycle step at kth operator [m] π(n) sequence of products [−] L length of the workstation [m] Tkn position of the tables [m] REFERENCES [1] Estrada, F., Villalobos, J.R., Roderick, L., Estrada, F., Villalobos, J.R., Roderick, L.: Evaluation of Just- In-Time alternatives in the electric wire-harness in- dustry, Taylor and Francis, 1997 35(7), 1993–2008, DOI: 10.1080/002075497195038 [2] Lodewijks, G.: Two Decades Dynamics of Belt Conveyor Systems Bulk Solids Handling, 2002 22(2), 1–2 [3] Xiaobo, Z., Zhou, Z., Asres, A.: Note on Toyota’s goal of sequencing mixed models on an assembly line, Computers and Industrial Engineering, 1999 36(1), DOI: 10.1016/S0360-8352(98)00113-2, 57–65 [4] Sarker, B.R., Pan, H.: Designing a Mixed-Model, Open-Station Assembly Line Using Mixed-Integer Programming, The Journal of the Operational Re- search Society Palgrave Macmillan Journals, 2001 52(52), 545–558 DOI: 10.1057/palgrave.jors.2601118 [5] Bukchin, J., Tzur, M.: Design of flexible assembly line to minimize equipment cost, IIE Transactions (Institute of Industrial Engineers), 2000 32(7), 585– 598 DOI: 10.1080/07408170008967418 [6] Bautista, J., Cano, J.: Minimizing work overload in mixed-model assembly lines, International Journal of Production Economics, 2008 112(1), 177–191 DOI: 10.1016/j.ijpe.2006.08.019 [7] Xiaobo, Z., Ohno, K.: Algorithms for sequencing mixed models on an assembly line in a JIT pro- duction system, Computers ind. 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