APEM jowatal Advances in Production Engineering & Management Volume 11 | Number 3 | September 2016 | pp 192-206 http://dx.doi.Org/10.14743/apem2016.3.220 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper Scheduling batches in multi hybrid cell manufacturing system considering worker resources: A case study from pipeline industry Yilmaz, O.F.a*, Cevikcan, E.a, Durmusoglu, M.B.a industrial Engineering Department, Istanbul Technical University, Ma?ka/Istanbul, Turkey A B S T R A C T A R T I C L E I N F O This study considers batch scheduling problem in the multi hybrid cell manufacturing system (MHCMS) taking into account worker resources. This problem consists of determining sequence of batches, finding the starting time of each batch, and assigning workers to the batches in accordance with some pre-determined objectives. Due to a lack of studies on the batch scheduling problem in the MHCMS, a binary integer linear goal programming mathematical model is developed for bi-objective batch scheduling problem in this study. The formulated model is difficult to solve for large sized problem instances. To solve the model, we develop an efficient heuristic method called the Hybrid Cells Batch Scheduling (HCBS) heuristic. The proposed HCBS heuristic permits integrating batch scheduling and employee (worker) timetabling. Furthermore, we construct upper and lower bounds for the average flow time and the total number of workers. For evaluation of the performance of the heuristic, computational experiments are performed on generated test instances based on real production data. Results of the experiments show that the suggested heuristic method is capable of solving large sized problem instances in a reasonable amount of CPU time. © 2016 PEI, University of Maribor. All rights reserved. Keywords: Batch scheduling Hybrid manufacturing cells Hybrid cells batch scheduling Goal programming Heuristic HCBS heuristic *Corresponding author: ofyilmaz@itu.edu.tr omer.faruk.ylmaz89@gmail.com (Yilmaz, O.F.) Article history: Received 24 June 2016 Revised 14 August 2016 Accepted 24 August 2016 1. Introduction Cellular manufacturing (CM), described as the applications of the group technology principles in a manufacturing environment, is a production system in which the parts with similar processing requirements and machines are grouped in distinct manufacturing cells [1, 2]. The main advantages offered by CM are reduction in setup time, reduction in lead time, reduction in work-in-process inventory, enhanced visibility and quality, efficient material handling, simplified scheduling and production control, and an increase in flexibility [3, 4-7]. The problems in a CMS are classified mainly into design and operational aspects. Design problems contain formation of cells and layout planning of cells while operational problems involve assignment of workers (employees) and scheduling of parts/batches-groups into the cells [1]. Operational problems have not been considered extensively in the extant literature compared to design problems [8]. This paper considers the problem of batch scheduling in the MHCMS which is a type of CMS consisting of a number of parallel independent hybrid cells. Most of the real CMSs are composed of hybrid cells, and both automatic and manual operations are performed in these cells [9]. The importance of the worker assignment on batch scheduling problems comes to light more clearly especially in the hybrid cells. Worker involvement is not 192 Scheduling batches in multi hybrid cell manufacturing system considering worker resources: A case study from pipeline... bounded in these cells and the number of workers in cells plays an important role and directly affects the cell cycle times. Due to the manual operations within the hybrid cells, cell cycle times vary from high to low and the flow times of the batches depend on the number of workers assigned to work on these batches. Therefore, the decisions must be made simultaneously for the batch scheduling problem in the MHCMS are the sequence of batches on each cell, the starting time of each batch and the workers assigned to operations of batches on cells. In the current study, scheduling in multi hybrid manufacturing cells, which are arranged as flowline, is addressed. A goal-programming model has been developed for scheduling of batches within cells by considering worker resource. Two conflicting objectives are identified for the problem: minimization of the average flow time and minimization of the total number of workers in the system. Since the average flow time can be used as a performance indicator for resource utilization [10], it is determined as one of the conflicting objectives in this study. To the best of our knowledge, the batch scheduling problem for the MHCMS is examined here for the first time. Due to the computational complexities, it is fairly challenging to obtain optimal solutions to scheduling problems in real sized problem instances with exact optimization methods [11]. As such, a heuristic method, namely the HCBS heuristic, is developed for this problem. Computational results show that the heuristic method presented in the paper has the capability of solving large sized problem instances with industrial pertinence efficiently. The motivation of this study is the batch scheduling problem arising in a real life CMS. Therefore, the study has the ability of adding value to industry in the way of effectively raising engineering control for scheduling activities in CMSs. In this context, the aim of the study is to propose a new batch scheduling method for multi hybrid cell manufacturing system under resource constraints and to verify this method on an industrial application. Furthermore, this study has the originality of proposing a novel goal programming model and a heuristic method via the parallel consideration of the total number of workers and the average flow time in the MHCMS. The flow of this study is as follows: review of the relevant literature is included in Section 2. Problem definition, mathematical model and a numerical example are presented and explained in Section 3. The developed heuristic method is introduced in Section 4. The experimental data and the computational results of the proposed heuristic method are reported in Section 5. The conclusions and recommendations for future research are offered in Section 6. 2. Literature review In this study, batch scheduling problem in the MHCMS is investigated by considering worker resource. Therefore, the literature is reviewed two headlines as the worker assignment and allocation problems in the CMS and the batch scheduling problem in multi cell manufacturing system. Jensen [12] used the simulation method to examine performance advantages of labor flexibility for departmens, hybrid cells and strict cells. Askin and Huang [13] proposed a multi-objective model to improve the fitness of individual workers to tasks performed in cells, and to create effective teams. Norman et al. [14] examined the problem of allocating workers to cells to improve organizational effectiveness which is affected by productivity, quality and training cost Suer and Dagli [15] examined cell loading and labor allocation problems. They created a three-stage structure and examined solutions to sequencing, labor allocation and cell loading problems. Cesani and Steudel [16] used the simulation method to investigate the effects of varied labor allocation policies on system performance. Their results show that balance in the number of workers is a significant determinant of system performance. Suer and Tummaluri [7] studied the problem of assigning operators to operations in labor intensive cells. They proposed a three-stage approach for the solution of the problem. Fowler et al. [17] examined differences between workers, in terms of their general cognitive ability (GCA), and developed a mathematical model to minimize worker-related costs over multiple periods. Davis et al. [18] used the simulation method to examine the relationship between cross training and workload imbalance, and found that workload imbalance increased the need for worker flexibility. Fan et al. [19] examined multi-objective cell formation and operator assignment problems. Suer and Alhawari [20] examined Advances in Production Engineering & Management 11(3) 2016 193 Yilmaz, Cevikcan, Durmusoglu the use of two different operator assignment strategies (Max-Min and Max) in labor intensive manufacturing cells. Azadeh et al. [21] examined the problem of operator allocation in a CMS by combining fuzzy data envelopment analysis (FDEA) and fuzzy simulation techniques. Egilmez et al. [22] examined the problem of stochastic skill-based workforce assignment in a CMS where both operation times and demand are uncertain. Niakan et al. [23] developed a new bi-objective model of the cell formation problem to handle worker assignment and environmental and social criteria. Liu et al. [24] developed a decision model for employee assignment and production control in a CMS with considering learning and forgetting effects of employees. As the body of the literature addressing the worker assignment and allocation problems in the CMS ruled out up to the present the effect of number of workers on the flow time of batches on the cells, the present study moves in that direction. Batch scheduling problem in CMS is also addressed in this study. Little research has been conducted on batch scheduling problem in multi-cell manufacturing system in the literature. The following is a review of studies that examine the batch scheduling problem in multi-cell manufacturing system. Das and Canel [25] proposed a branch and bound solution method to seek solution to the problem of scheduling of batches in the multi-cell flexible manufacturing system (MCFMS). Celano et al. [26] used simulation method to analyze the batch scheduling problem within a manufacturing system consisting of multiple cells. Hachicha et al. [2] utilized simulation method to design a CMS consisting of multiple cells in which parts are produced in batches. Balaji and Por-selvi [27] proposed a model for batch scheduling problem in a MCFMS having sequence dependent batch setup time with flowline structure. When considering the large body of the extant literature, it is revealed that there have been studies in the literature that focus on the batch scheduling problem in CMSs having multi cells. However, there has not been any published study addressing the influence of assignment of workers on flow times of batches for the batch scheduling problem in the CMSs. This problem has been observed in a real cellular manufacturing system in the pipeline industry and it has not been addressed in the literature before. This study bridges this gap in the literature. 3. Descriptions of the problem and mathematical model 3.1 Description of the problem In the current study, the batch scheduling problem in the hybrid cells having missing operations (some parts may skip some operations on some machines) is examined. The distinctive feature of this problem is the dependence of the batch flow times on the number of workers assigned to the main operations of batches on cells. The hybrid cells need attendance of workers constantly. Because of the presence of manual operations, changing the number of workers assigned to the operations in this type of manufacturing cells causes changes in cell cycle times, which in turn changes flow times of batches on cells. An increment in the number of workers in cells results in a decreases in flow times of batches, and vice versa. For this reason, determination of number of workers, which are assigned to cells to perform operations of batches, is important in the hybrid cell scheduling studies. Therefore, when seeking solutions to the batch scheduling problem in a CMS which consists of parallel hybrid cells, it is necessary to consider the sequence of batches, the starting times of batches and the worker assignment to the batches. There are K unrelated parallel labour-intensive hybrid cells in the CMS. The hybrid cells consist of M machines, designed as flowlines, dedicated to process I batches. The assumptions which have been made in the study are as follows: • The cell compositions and the assignment of batches to cells are known in advance. • Each machine in a cell corresponds to an operation, and these operations combine to form main operation. Pre-emption of operations and main operations is not allowed. 194 Advances in Production Engineering & Management 11(3) 2016 Scheduling batches in multi hybrid cell manufacturing system considering worker resources: A case study from pipeline... • Parts are produced in batches, and one-piece flow is applied within the cells. The flow is uni-directional and no back-tracking is allowed. • Batches are processed from only one family in each cell and at most one batch can be processed in a cell at the same time. • The batch sizes are equal to order sizes and batch splitting is not permitted. • Batchesareavailableforprocessingattime zero and processing times include setup times. • Each worker has same multi-skills to perform all operations on cells. 3.2 Mathematical model In this section, to describe the problem more clearly, a binary integer linear goal programming mathematical model is developed to address conflicting objectives which are the total number of workers and the average flow time. The purpose of the proposed mathematical model is to contribute to the apperception of the scheduling problem addressed in the study. The indices, parameters, variables, deviational variables, decision variables and mathematical models are introduced in this section. Indices i,j - Indices of batches (i,j = 1,..., N) z - Index of workers (z = 1,., Z) m - Index of machines (m = 1,., M) k,t - Indices of cells (k,t = 1,., K) Parameters W1 - Weight of the first objective (average flow time) W2 - Weight of the second objective (total number of workers) akijk - If batch i is allocated to cell k, 1; if not, 0 avewalkingk - Average walking time of workers in cell k totalwalkingk - Total walking time of workers in cell using,k,m - If machine m is used for operation of batch i on cell k, 1; if not, 0 manualpro,k,m - Manual processing time for parts in batch i on machine m in cell k autoproi,k,m - Automatic processing time for parts in batch i on machine m in cell k pti,k,m - Processing time of parts in batch i on machine m in cell k Ipt,k - Longest processing time for parts in batch i on cell k FLTi,k - Completion time for the first part in the batch i on cell k cycmini, k - Minimum cell cycle time for batch i on cell k cycmaxi, k - Maximum cell cycle time for batch i on cell k qi - Number of parts in batch i Variables fi, k - Flow time of batch i on cell k c,k - Completion time of batch i on cell k cyci, k - Cell cycle time for batch i on cell k timej, t - Starting time of batch j on cell t workforcej, t - Total number of workers at the start of main operation of batch j on cell l mw - Maximum number of workers in the system woz,i,k,m - If worker z is assigned to machine m for main operation of batch i on cell k, 1; if not, 0 Xi,k - Number of workers assigned for batch i on cell k gi,kj,t - If main operation of batch i on cell k and the main operation of batch j on cell t overlap in time, 1; if not, 0 Deviational Variables d1-d2 - Positive deviational variables for the average flow time and the total number of workers, respectively Decision variables w1z, i, k - If worker z is assigned to main operation of batch i on cell k, 1; if not, 0 Advances in Production Engineering & Management 11(3) 2016 195 Yilmaz, Cevikcan, Durmusoglu bi,j,k - If batch i is processed after batch j on cell k, 1; if not, 0 (Note that after does not necessarily means immediately after) The mathematical formulation of the binary integer linear goal programming model is as follows: Objective Function min objective =w1x (d1/(UP1 - LB1)) +w2x (d2/(UP2 - LB2)) (1) Constraints Efc=i (maxck/maxck) — d1 = LB1 (2) mw — d2 = LB2 (3) cilk >(clk +filk)-Mx(l-biijik) Vi,j, k (4) Ci,k ^fi,k k (5) maxck >cik Vi, k (6) bijik + bj,i,k = akik xak]k Vi,j, k i^j (7) timeJt = cJt -fJt Vj, t (8) (ci,fc ~fi,k)~ timej,t workloadjt Vj,t (25) bij,k 0 or 1 ; xi k integer ; d1 > 0 ; d2 > 0 (26) The objective function (Eq. 1) involves two terms, one for each of the conflicting objectives, and presents a weighted average of deviations from developed lower bounds. The first term minimizes the deviation of the average flow time from LB1 (Eq. 32). The second term attempts to minimize the deviation of the total number of workers from LB2 (Eq. 34), and is in conflict with the first term. In Eq. 1, a zero-one normalisation scheme is used to scale all unwanted positive deviations (d1 and d2) onto a zero-one range [28]. Eq. 2 and Eq. 3 are soft constraints which 196 Advances in Production Engineering & Management 11(3) 2016 Scheduling batches in multi hybrid cell manufacturing system considering worker resources: A case study from pipeline... represent positive deviations from target levels (LB1 and LB2) for the average flow time and the total number of workers objectives, respectively. Eq. 4 ensures that each cell can process at most one batch at the same time. Eq. 5 implies that the completion time of a batch is greater than or equal to the flow time of this batch. Eq. 6 implies that the total completion time in a cell (Ck) is greater than or equal to the largest completion times of batches in this cell. Eq. 7 ensures that if batches i and j are allocated to the cell k, then bjk or b,ijk gets value equal to one. Eq. 8 represents the time points (timej, t) at which the total number of workers can change, that is to say, the starting times of the main operations. Eqs. 9-14 are used to determine main operations which coincide with the time points (timej, t) . Eq. 15 is used to calculate the flow times of the batches. Eq. 16 and Eq. 17 are used to determine the cell cycle time for each batch. Eq. 18 is used to assign workers to machines where the operations are performed. Eq. 19 ensures that worker assigned to machine for operation is also assigned to the cell that contains the machine in question. Eq. 20 prevents the assignment of the same worker to two main operations which overlap in time. Eq. 21 is used to calculate the number of workers assigned for operation of batch i on cell k. Eqs. 2224 are used to calculate the total number of workers at each time point (workforcej, t). Eq. 25 indicates that the total number of workers in the system is greater than or equal to the total number of workers at each time points. Eq. 26 is used for the binary, integer and sign bounds on the variables. The constant M in the equations should be sufficiently large. Since the mathematical model is developed considering the parallel cells in this study, the related studies involve parallel machine/cell scheduling problems and mathematical models constructed by Yang et al. [11] and Dalfard et al. [29] can be examined by interested readers to obtain comprehensive perspective. It is also important to emphasize that although Eqs. 17-19 are proposed to calculate the cell cycle times in case of dedicated assignment of workers to the hybrid cells. Eq. 27 is developed to obtain the cell cycle times. Since each worker has the same multi-skills in the MHCMS, theoretical values of the cell cycle times, which are the best values that can be reached, are calculated by using Eq. 27 and it is used in the solution of the model instead of Eqs. 17-19. cyci,k = {cycmaxiik/xiik) Vi,k (27) The parameters cycmax,k and cycmin,k are calculated using Eq. 28 and Eq. 29, respectively. cycmaxiik = YJm=iiiotalwalkingk+manualproiikm) Vi,k (28) cycminik = lptiik Vi, k (29) The longest processing time for parts on a cell is equal to maximum of processing times of machines in this cell. This fact is stated in Eq. 30. The processing time for parts on each machine is equal to sum of manual processing time and automatic processing time. This fact is stated in Eq. 31. Iphk =maxVrn(p£i,fc,rn) (30) pti,k,m = manualproikm + autoproikm Vi,k,m (31) In this paper, we put forward lower and upper bounds for the average flow time and the total number of workers. The derivation of lower bound (LB1) and upper bound (UP1) for average flow time are expressed as follows: LB1 = (Z^=1ZjL1(cycmini,fc x (qt -1) +FLTLk)/K) (32) UP1 = (ELiZiLi(<-ycmaxi,k X fa -D+FLTiik)/K) (33) The derivation of lower bound (LB2) and upper bound (UP2) for the total number of workers are expressed as follows: LB2 =El=1{minvi{cycmaxiik/cycmaxik)) (34) UP2 = ££=1 (maxvi(cycmaxiik/cycminik)+^ (35) Advances in Production Engineering & Management 11(3) 2016 197 Yilmaz, Cevikcan, Durmusoglu 3.3 Numerical illustration To explain the problem considered in this paper, we present a MHCMS with missing operations (MO). In this system, batches between 1 and 6 are to be scheduled in the first cell and batches between 7 and 12 are to be scheduled in the second cell. The maximum and minimum cell cycle times for each batch, the batch sizes, the automatic and the manual processing times of parts of batches on machines and the total walking time in cells are presented in Table 1. As seen in this table, the operations on machine 3 are missing operations for batch 1 to batch 6 and the operations on machine 2 are missing operations for the batch 7 to batch 12. There is a worker pool which is consists of five different workers. The mathematical model was coded in the GAMS CPLEX software package for equal weights of objectives (w1 = 0.5; w2 = 0.5). The optimal solution was derived in 676 min. of computational time. The results of the CPLEX software are reported below. Fig. 1 illustrates optimum solution of this problem. In Fig. 1, the best sequence of batches on Cell 1 and Cell 2 is obtained as 1-4-3-5-2-6 and 9-8-7-10-11-12, respectively. The starting and completion times of each batch are shown in Fig. 1. The average flow time is equal to 1800, the total number of workers is equal to 3 and the objective function is equal to 0.26. Table 1 Data for a 12-batch 2-cell batch scheduling example Cell Cycle Times Batch Machine! Machine2 Machine3 Machine4 Total Walking Max Min Size Aut. Man. Aut. Man. Aut. Man. Aut. Man. Batch 1 60 30 5 5 15 0 10 MO MO 10 20 15 Batch 2 80 30 10 0 20 0 15 MO MO 0 30 15 1 Batch 3 55 30 5 10 10 0 15 MO MO 15 15 15 20000 gl 15000 < 10000 5000 " so -H il M ï C* C1 ff1 NN« S S S a .ÈP S C .a S -SP î = ■= S o = e SP J J ,ÏP 7,3 7,2 7,1 7,0 6,9 6,8 6,7 6,6 6,5 v* - '' O <=>- fC f- NBEC BS MPT TWEC ï C -O S J s .SP I J '■s s u S NBEC s .SP o 5 -SP o = .SP = = = S BS S MPT E TWEC (a) (b) Fig. 4 Results for average flow time (a), and total number of workers (b) The average flow time and the total number of workers for different levels of factors are provided in Fig. 4. According to this figure, the average flow time is crucially increasing with the rising level of the NBEC, BSEC and MPT. The observed trend of TWEC can be regarded as consistent with Table 4. The average flow time reaches its maximum value when the level of BSEC is high and its minimum value when the level of BSEC is low. Also, the total number of workers reaches its maximum value when the level of NBEC is high and its minimum value when the level of NBEC is low. As far as the total number of workers is concerned, slight differences among different levels have been observed for each factor. The results also show a non-monotonic trend of BSEC, MPT and TWEC in respect of the total number of workers. The reason for the small changes in total number of workers along with different levels of factors is that the sensitivity of the total number of workers to different level of factors is quite low compared to sensitivity of average flow time. As mentioned before, a new mathematical formulation can be developed and used in the method to increase the sensitivity level of the total number of workers to the factor levels. Table 5 Multiple comparisons among factor levels Factor Dep. var. I J Mean difference (I-J) Sig. (P) Factor Dep. var. I J Mean difference (I-J) Sig. (P) NBEC AFT Low Medium High -4413.296* -18311.111* 0.000 0.000 MPT AFT Low Medium High -8943.148* -17272.704* 0.000 0.000 Medium High -13897.815* 0.000 Medium High -8329.556* 0.000 TNW Low Medium High -0.074 -0.333* 0.415 0.000 TNW Low Medium High 0.007 -0.104 0.935 0.255 Medium High -0.259* 0.005 Medium High -0.111 0.223 BSEC AFT Low Medium High -6479.741* -19770.778* 0.000 0.000 TWEC AFT Low Medium High 215.481 -83.778 0.839 0.937 Medium High -13291.037* 0.000 Medium High -299.259 0.778 TNW Low Medium High -0.015 0.074 0.870 0.415 TNW Low Medium High -0.111 -0.074 0.223 0.415 Medium High 0.089 0.329 Medium High 0.037 0.683 (*)The mean difference is significant at the 0.05 level. 204 Advances in Production Engineering & Management 11(3) 2016 Scheduling batches in multi hybrid cell manufacturing system considering worker resources: A case study from pipeline... As seen in Table 5, each of the pairwise differences among the different levels of NBEC, BSEC and MPT is found to be statistically significant (p < 0.05) for the average flow time (AFT). However, the reverse results have been observed for TWEC. The results show that the factor levels of NBEC, BSEC and MPT have an important effect on the performance of the proposed method for the HCBS when the performance is evaluated in terms of the average flow time. Table 5 also indicates that the slight differences between different factor levels (except NBEC) are not found to be statistically significant for the total number of workers (TNW). Regarding TNW, it is concluded that the factor levels of NBEC, MPT and TWEC have not an important effect on the performance of the proposed method for the HCBS when the performance is evaluated in terms of the total number of workers. 6. Conclusion This paper addresses the batch scheduling problem in the MHCMS by considering worker resource and flow times simultaneously-something that is largely overlooked in the literature of batch scheduling in CMS. A goal programming mathematical model is proposed, in which the first objective is minimization of the average flow time and the second is minimization of the total number of workers. Due to the complexity of the problem, we developed a heuristic method, namely the HCBS heuristic. To validate the suitability and applicability of the heuristic, it is implemented in a real life expansion joint production system in a pipeline industry. Hence, this research is thought to assist to the engineering managers with important insights to enhance control level for batch scheduling in CMS. By the end of this research, the findings dealing with capacity requirements show that the proposed HCBS heuristic creates different level of freed-up workforce capacity for different combinations of objective function coefficients. It should also be noted that critical success factors, which are accuracy and topicality of production data, lean applications in manufacturing environment and work study, were made critical contribution to the findings of research. For this reason, attention should be paid to these critical success factors in other studies. For the extension of the present research, other worker related issues can be considered, such as different worker skills for assignment and worker skill levels to perform operations. Moreover, in order to represent the real manufacturing systems more realistic, uncertain parameters and stochastic approaches can be added in future research. 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