This article was downloaded by: [Gyeongsang National Uni], [Professor Kwan Hee Han] On: 25 November 2012, At: 20:32 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK International Journal of Production Research Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tprs20 Manufacturing cycle time reduction for batch production in a shared worker environment Kwan Hee Han a, Geon Lee a & Sang Hyun Choi b a Department of Industrial & Systems Engineering, Engineering Research Institute, Gyeongsang National University, Jinju, Korea b Department of MIS, Chungbuk National University, Chungbuk, Korea Version of record first published: 05 Jan 2012. To cite this article: Kwan Hee Han, Geon Lee & Sang Hyun Choi (2013): Manufacturing cycle time reduction for batch production in a shared worker environment, International Journal of Production Research, 51:1, 1-8 To link to this article: http://dx.doi.org/10.1080/00207543.2011.631604 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
International Journal of Production Research Vol. 51, No. 1, 1 January 2013, 1 8 Manufacturing cycle time reduction for batch production in a shared worker environment Kwan Hee Han a *, Geon Lee a and Sang Hyun Choi b a Department of Industrial & Systems Engineering, Engineering Research Institute, Gyeongsang National University, Jinju, Korea; b Department of MIS, Chungbuk National University, Chungbuk, Korea (Received 22 June 2011; final version received 10 October 2011) Responsive delivery without inefficient excess inventory requires short manufacturing cycle times. The manufacturing cycle time is comprised of operation time, loading/unloading time, set up time and machine idle time. The sum of loading/unloading, set up and machine idle times is called downtime. To shorten batch processing time, reduction in downtime must be the first priority. One way to reduce downtime per work unit is to increase batch quantity, while another is to shorten the sum of set up and machine idle times. Whereas fast cycle time is critical for time-based competition, efficient utilisation of labour is also essential to keep a manufacturing company competitive due to the rapid increase in labour costs. Therefore, in many small and medium-sized businesses, one worker simultaneously handles multiple machines. In such a shared worker environment, machine idle time inevitably occurs due to a lack of available workers. The purpose of this paper is to propose a downtime reduction method based on part sequencing in a shared worker environment. The proposed heuristic results in a significant reduction in average downtime when compared to the results from the existing optimal sequencing method of independent machines. Keywords: set up reduction; part sequencing; shared worker; batch processing 1. Introduction In today s dynamic business environment, the ability to improve performance is a quintessential requirement for business organisations. Manufacturing organisations are thus faced with the need to optimise the way in which they function in order to achieve the best possible performance within necessary constraints. While cost and quality remain critical to the performance goals of businesses, time-based competition strategies have been adopted widely in many industries. Responsive delivery without inefficient excess inventory requires short manufacturing cycle times. In a batch manufacturing environment, batch processing time is the sum of the set up time, loading/unloading time, machine idle time and processing time; that is, T B ¼ T SU þ T ID þ Q i ðt LU þ T O Þ ð1þ where T B ¼ batch processing time, T SU ¼ set up time, T ID ¼ machine idle time, Q i ¼ quantity of i-th batch, T LU ¼ loading/unloading time per work unit, and T O ¼ operation time per work unit. Therefore, the average manufacturing cycle time per work unit (T P ) is expressed as: T P ¼ T B =Q i ¼ ðt SU þ T ID Þ=Q i þ T LU þ T O ð2þ In Equation (2), T P consists of operation time (T O ) and downtime ((T SU þ T ID )/Q i þ T LU ). In other words, T P is the sum of operation cycle time (OCT) and downtime cycle time (DCT). Set up time (T SU ), the main component of DCT, is the time to change tooling, and set up and reprogram the machinery. This is lost production time, which is a disadvantage of batch manufacturing systems. Major reasons for machine idle time (T ID ) include the starvation or blocking of parts and worker unavailability. Loading/unloading time (T LU ) is required for the initialisation and release of machine operation. In Equation (2), T O remains constant for a certain period of time in a normal working environment. Therefore, in order to shorten T P in the above equation, downtime cycle time must be reduced. One way to reduce DCT is to *Corresponding author. Email: hankh@gnu.ac.kr ISSN 0020 7543 print/issn 1366 588X online ß 2013 Taylor & Francis http://dx.doi.org/10.1080/00207543.2011.631604 http://www.tandfonline.com
2 K.H. Han et al. increase batch quantity Q i. Since loading/unloading time, dependent as it is on the level of automation of material handling equipment, is varied within a small range, the other way is to shorten the sum of the set up and machine idle times. However, batch quantity is usually determined by due date and priority of orders in a small quantity batch production system, so it is an external variable that is largely outside of a manufacturing company s direct control. Therefore, the latter method is a viable alternative solution for fast manufacturing cycle times. A widely adopted tool these days for the reduction of set up time is the part sequencing method. In addition to the current trend of pursuing speed in manufacturing, efficient use of labour is also important to keep a manufacturing company competitive due to the rapid increase in labour costs. Therefore, in many small and medium-sized businesses, one worker simultaneously operates multiple machines. In such a shared worker environment (SWE), in which the number of workers is smaller than that of the machines operated, idle time inevitably occurs due to worker unavailability when one machine needs a set up or loading/unloading operation while the needed worker sets up or loads/unloads another machine. In contrast to the shared worker environment, idle time due to worker unavailability does not occur in a dedicated worker environment (DWE), in which the number of workers is equal to that of the machines operated. Idle time caused by interruptions between machines operated in an SWE can be put into three categories: (1) a machine needs to be set up while the worker sets up another; (2) a machine needs to be loaded or unloaded while the worker sets up another machine; (3) a machine needs to be loaded or unloaded while the worker loads or unloads another. Whereas there are many approaches to reduce set up times in a dedicated worker environment, there have been no approaches for the reduction of set up and machine idle times in an SWE. Therefore, the purpose of this paper is to propose a heuristic method for the reduction of the total set up and machine idle times based on part sequencing in an SWE. The rest of this paper is organised as follows: Section 2 reviews related works; Section 3 describes incremental approaches for set up and idle time reduction; Section 4 presents experimental results through a case study; and Section 5 summarises the results and suggests directions for future research. 2. Related works In today s current competitive environment, effective sequencing and scheduling has become a necessity for the survival of manufacturing companies in the market place (Pinedo 2008). A considerable amount of research effort has been focused on the area of deterministic scheduling. The static/deterministic scheduling research in which the set up time or cost is of main concern in the problem has been reviewed (Yang 1999). In this survey, the literature is classified into job, class and job-and-class setup situations. Each situation is further classified on the basis of sequence dependence and separability of the setup. The problem of job scheduling with sequence-dependent machine set up times has been the focus of most literature (Allahverdi et al. 1999, Zhu and Wilheim 2006, Allahverdi et al. 2008, Ozkan and Toklu 2010). Pinedo (2008) showed that makespan minimisation on a single machine with sequence-dependent setup time is strongly NPhard. When set up times are dependent on sequence, minimising makespan becomes equivalent to minimising total set up time. This problem corresponds with what is usually called the Travelling Salesman Problem (TSP). Gilmore and Gomory (1964) presented one of the pioneering works on the sequencing-dependent set up time problem which is modelled and solved as a TSP. Due to the NP-hardness of TSPs, the algorithms that will find the shortest sequence of jobs take an unreasonable length of time to execute in a scheduling environment subject to frequent scheduling changes. Therefore, some research has proposed heuristics that can find reasonable solutions quickly (Croes 1958, Lin and Kernighan 1973, Bianco et al. 1988, Tan et al. 2000). Ozgur and Brown (1995) proposed a two-stage travelling salesman heuristic procedure for the problem where similar products produced on the machine can be partitioned into families. Chrisman (1986) developed an optimal sequencing in a gear manufacturing cell as a problem of TSP with rush orders. Efficient grouping procedures, which include machine-specific algorithms for fine-tuning machine operations for a group of PCBs, was proposed to balance the savings in set up time with the increase in assembly time and to minimise the global makespan (Yilmaz et al. 2007). The single machine scheduling problem with independent family (group) set up times where jobs in each family are processed together was proposed to minimise total tardiness using a mixed-integer linear programming (Gupta and Chantaravarapan 2008). An extensive computational investigation concerning the performance evaluation of non-permutation versus permutation schedules for the flow line manufacturing cell with sequence-dependent set up times was presented
International Journal of Production Research 3 through the use of an effective simulated annealing algorithm (Ying et al. 2010). A simulation-based approach was adopted for part sequencing in terms of cost minimisation (Rasmussen et al. 1999). And finally, five new set-uporiented rules were proposed that provide better performance than the seven ordinary rules from the literature for scheduling a dynamic job shop using simulation-based experimentation (Vinod and Sridharan 2009). However, an integrated method for the reduction of set up and machine idle times in a shared worker environment has yet to be presented. 3. Incremental approaches for set up and idle time reduction In Equation (2), since T O remains constant and Q i is not a controllable internal variable, the reduction of the sum of T SU, T ID and T LU is necessary for fast manufacturing cycle time. In a dedicated worker environment, since the major solution used to reduce loading/unloading time is automated material handling equipment, a considerable amount of time and money are required for effect, excluding this element from further consideration. Starvation or blocking of parts and machine failure, major reasons for machine idle time, are also excluded because of the complexities involved in finding solutions. In a dedicated worker environment, worker unavailability, the most common cause of machine idle time, does not occur. Therefore, to achieve a fast cycle time, reduction of the set up time is the most controllable internal variable in a DWE. As explained in the first section, one of the major methods used to reduce set up time is part sequencing. The set up time duration of a current batch is dependent on the part characteristics of the previous batch. Therefore, determination of the part sequence is critical in reducing manufacturing cycle time. The part sequencing method can be divided into three types: first is a random selection of the next batch from the process-ready batches; second is selection of the next batch with the shortest set up time when compared to the current batch; and third is the determination of the entire sequence for batches requiring machine processing. In a dedicated worker environment, each machine runs independently from the others. In this situation, the approach for set up time minimisation is reduced to a problem of sequencing a set of N batches on one machine. When all batches have equal release dates, the one-machine scheduling problem is equivalent to the Travelling Salesman problem which is known to be NP-hard. In a TSP, each city corresponds to the time required for set up. Even if TSP is NP-hard, optimal batch sequencing can be obtained through permutation if the number of batches is moderate. Therefore, a two-stage travelling salesman heuristic procedure (Ozgur and Brown 1995) is adopted in this paper where similar products produced on the machine can be partitioned into families. In a shared worker environment, machine idle time occurs due to worker unavailability in addition to set up time. The problem of reducing worker unavailability is very complex because idle time reduction at one machine cannot be achieved without considering other machines loading schedules. This problem becomes more complex when the number of machines operated by one worker increases. Therefore, a heuristic procedure is needed. It is assumed that all batches are available before the start of production. It is also assumed that the total number of batches is partitioned into sub-groups, and each sub-group is assigned to a machine within a workstation according to their part similarity and the workers experience. The proposed heuristic algorithm for the reduction of set up and machine idle times in an SWE is as follows: (1) Of the total part types ready for the start of production, similar parts are partitioned into sub-groups according to their geometry and machining requirements. Each sub-group is allocated to the appropriate machine for processing within a workstation. S is the average number of batches assigned to the sub-group. (2) For each machine in a DWE, all possible batch sequence alternatives for machining can be generated through permutation. The required number of calculations is m (S)!, where m is the number of machines within a workstation. (3) The best P batch sequence alternatives are selected for each machine. All possible batch sequences are generated at each workstation by a combinatorial calculation of m machine s P alternatives. This creates P m alternatives. (4) P m alternatives are evaluated in terms of average downtime cycle time as calculated in Equation (2), and the best combination of each machine s part sequence at a workstation is selected. In the next section, the procedures and effects of the proposed heuristic method are presented in the experimental results.
4 K.H. Han et al. 4. Experimental results a case study Company S in this case study produces mainly agricultural and construction machinery parts in Korea. Its production characteristics include high product variety (over 300 different part types) and small production volume. As a result, it has adopted a process-centred machine layout and batch production system which requires time for set up before production. Target Workstation, C, with five identical machines, hobs gear teeth. Two workers operate Workstation C. One worker s role is to set up the machines, while the other worker is responsible for loading/unloading operation of the parts. The reason for the separation of tasks between the workers is the difference in skill level needed for each task: setting up is usually more complicated than loading/unloading. An average of 30 part types are produced in one week. Because of different due dates and rush orders, an average of 90 batches are processed at Workstation C in one week. The average quantity of one batch is 182 pieces (ranging from 99 to 269). Table 1 shows processing cycle time statistics for Workstation C. It is assumed that all batches are ready for production at the start of any specific week. Set up time in a hobbing operation is dependent on three determinants; gear type, gear shape and type of cutting tool used. If one of the determinants of the following batches is equivalent to that of the previous batch, setting up for the next batch is shortened by 20 minutes over the base set up time, which is settled at 60 minutes. Therefore, the set up time range for Workstation C is between 0 and 60 minutes. Part of the set up time matrix is depicted in Figure 1. In Equation (2), the average manufacturing cycle time per work unit consists of two parts: operation cycle time (OCT) and downtime cycle time. OCT usually remains constant for a certain period of time. Downtime operation is not value-added, and makes production cycle time longer. As a result, the average downtime cycle time per work unit (ADCT) is chosen as the criterion for the evaluation of cycle time reduction alternatives. ADCT of a workstation K is calculated as:! ADCT K ¼ XM 1 M X N DCT ij ð3þ N Q i j¼1 where M ¼ number of machines within a workstation, N ¼ number of batches, Q ¼ quantity of i-th batch. Table 1. Processing cycle time statistics (seconds). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 0 3 4 5 6 7 8 i¼1 Setup time/batch (sec.) Loading/unloading time/work unit (sec.) Processing time/work unit (sec.) Average time 2500.0 36.0 127.0 9 10 11 0 12 13 14 15 Figure 1. Part of the set up time matrix (seconds).
International Journal of Production Research 5 Downtime reduction is achieved through a part sequencing method in this paper. In a DWE (one worker dedicated to one machine), three experiments were conducted. The first method was a random selection of next batches from among the processing-ready batches. The experimental results are shown in Table 2 after 50 runs of calculation. As shown in Table 2, average DCT was 109.31 seconds, with a wide range from 81.66 to 156.33 seconds. The second method is next batch selection with the shortest setup time (SST). This method is divided into two sub-methods according to tie-breaking rules when there are multiple batches with the same SST. The tie-breaking rules adopted were random selection and shortest processing time (SPT). As shown in Table 3, the ADCT of next batch selection methods with SST is 75.02 and 75.45 seconds individually. There seems to be no difference between the two sub-methods. Last is the optimal sequencing method, which produces the entire batch sequence of production for each machine as a problem of TSP. However, as described in Section 1, this problem is NP-hard. Therefore, in order to solve this problem within a reasonable time, it is necessary that similar parts are grouped into the same sub-group and allocated in advance to each machine according to their physical characteristics. The experiment for the case study was conducted under the condition that the 90 batches were sub-grouped by their geometric similarities, and assigned to each machine in view of the labour specialisation of the worker(s) and conditions of the machine processing. An average of 18 batches was pre-allocated to every five machines. Moreover, to include rush orders in the experiment, some same-part batches were intentionally allocated to different machines. This problem is solved by an average of 18 factorial computations of all possible part production sequences and a selection of best part sequence for each machine. The number of batches pre-allocated to machines was between 17 and 19. Table 4 shows the best sequence and DCT of each machine with the optimal part sequencing method in DWE. The ADCT of the optimal sequencing method is 67.01 seconds as summarised in (Table 3). This result reveals a 38.7% reduction over average random selection (109.31 seconds), which is 10.7% shorter than next-batch selection with SST (75.02 seconds). Table 5 shows the part sequence and DCT of the optimal sequence method in an SWE, in which the SWE s ADCT is comparatively longer than that of the DWE because of worker unavailability during setup or loading/ unloading operations. This phenomenon increases machine idle time considerably at Workstation C in the SWE. In an SWE, as shown in Table 5, the optimal sequence of each machine in a DWE does not guarantee the shortest DCT because of a rapid increase in the machine idle time in the SWE. However, it is almost impossible to generate Table 2. Results of random part sequencing. 1a) Best 1b) Average 1c) Worst ADCT (sec.) 81.66 109.31 156.33 Table 4. Results of optimal sequencing method in DWE. Solution rank Table 3. Summary of next-batch with SST and optimal sequencing method. Part sequence 2a) Next batch with SST (tiebreaking ¼ random) 2b) Next batch with SST (tiebreaking ¼ SPT) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 3) Optimal sequencing ADCT (sec.) 75.02 75.45 67.01 DCT M/C MC_A 1 11 3 7 9 16 22 1 24 26 18 27 20 6 13 17 23 15 14 62.78 MC_B 1 11 3 7 9 16 22 1 4 25 18 27 20 6 13 17 21 10 8 30 65.31 MC_C 1 11 3 7 9 16 22 1 2 28 18 27 20 6 13 17 19 12 5 29 72.02 MC_D 1 26 10 2 8 15 21 14 25 29 4 5 12 19 24 30 23 28 66.67 MC_E 1 26 10 2 8 15 21 14 25 29 4 5 12 19 24 30 23 28 68.28 67.01 DWE: Optimal sequence of each machine.
6 K.H. Han et al. Table 5. Results of optimal sequencing in SWE. Solution rank Part sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 DCT M/C MC_A 1 1 11 3 7 9 16 22 1 24 26 18 27 20 6 13 17 23 15 14 221.43 MC_B 1 11 3 7 9 16 22 1 4 25 18 27 20 6 13 17 21 10 8 30 239.98 MC_C 1 11 3 7 9 16 22 1 2 28 18 27 20 6 13 17 19 12 5 29 248.02 MC_D 1 26 10 2 8 15 21 14 25 29 4 5 12 19 24 30 23 28 237.26 MC_E 1 26 10 2 8 15 21 14 25 29 4 5 12 19 24 30 23 28 218.25 232.99 SWE: Optimal sequence of each machine. Table 7. Results of proposed heuristic method in SWE. Solution rank Part sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 DCT M/C MC_A 1 11 3 7 9 16 22 1 24 26 18 27 20 6 13 17 23 15 14 169.76 MC_B 3 11 3 7 9 16 22 1 8 25 18 27 20 6 13 17 21 10 4 30 179.12 MC_C 4 11 3 7 9 16 22 1 5 28 18 27 20 6 13 17 29 2 12 19 184.43 MC_D 1 26 10 2 8 15 21 14 25 29 4 5 12 19 24 30 23 28 181.24 MC_E 4 26 2 8 10 15 21 14 25 29 4 5 12 19 24 30 23 28 176.21 178.15 SWE: Proposed Heuristic. Table 6. Size of alternatives and their required CPU times. Number of alternatives CPU time (sec.) ADCT (sec.) 5 5 2.87 178.15 10 5 96.02 178.15 15 5 789.76 178.15 20 5 3587.20 178.15 an optimal sequencing to minimise the ADCT of Workstation C because of the problem of NP-hardness, which requires (S!) m computations (where S ¼ the average number of batches assigned to one machine, and m ¼ number of machines within a workstation). Therefore, it must be determined which combination of possible part sequence alternatives at each machine produces reasonably good ADCT in Workstation C even though it does not guarantee an optimal solution. In this paper, small subsets of the total possible combinations are investigated for a reasonable, rather than optimal, solution. In other words, the best P sequencing alternatives for each machine in a DWE are selected first. Then, P m alternatives exist for combinatorial calculations (m ¼ 5 in the case study), and the best solution from these alternatives is selected by comparing their ADCT. In this experiment, P is varied from 5 to 20 as shown in Table 6. The software program for the proposed heuristic algorithm ran on a personal computer with a 2.93 GHz Intel core i7 processor and 4 GB RAM. As shown in Table 6, computational CPU time increases exponentially as the number of alternatives increases linearly, whereas ADCT reduction does not occur. This result reveals that a very small number of best part sequences from each machine can generate a reasonably good solution quickly without consuming much CPU time. Table 7 shows the generated best part sequence of each machine and its DCT in an SWE. As shown in Table 7, for machines B, C and E, rank one solution of a DWE is not selected as the best
International Journal of Production Research 7 Table 8. Comparison of optimal sequencing with proposed heuristic in SWE. 3) Optimal sequencing 4) Proposed heuristic ADCT (sec.) 232.99 178.15 ADCT (sec) 200 92.21 Figure 2. Trends of ADCT and labour utilisation. Labour utilisation(%) sequence in an SWE. In other words, the combination of 1-3-4-1-4th best solutions Table 7 generates a shorter ADCT (178.15 seconds) rather than the combination of 1-1-1-1-1st best solutions (232.99 seconds in Table 5). Table 8 summarises the results of the optimal part sequencing of each machine and that of the proposed heuristic method in the SWE. As shown in Table 4 and Table 8, the result of optimal part sequencing in the SWE (232.99 seconds) is 247.7% longer than that in the DWE (67.01 seconds), in which the main cause of longer ADCT is a rapid increase of machine idle time due to worker unavailability. In the SWE, the proposed heuristic method resulted in 178.15 seconds of ADCT, which is 23.5% shorter than that of the optimal sequencing method (232.99 seconds). The disadvantage of a shared worker environment is the increase in ADCT, although an SWE saves on labour costs. In other words, in an SWE there is a trade-off between ADCT and labour utilisation as shown in (Figure 2). As the number of machines operated by two workers decreased in the case study, ADCT also declined in proportion to the decrease in labour utilisation. In other words, when five machines are operated by two workers at Workstation C, ADCT is 178.2 seconds while labour utilisation is 92.21%. However, if three machines are handled by two operators, this results in a considerable reduction of ADCT (40.6%) whereas labour utilisation is decreased by 34.0%. 5. Conclusions and further research There is no doubt that long-term profit through productivity ranks as the number one goal in manufacturing. However, besides the traditional aim for cost-efficient techniques, additional objectives, such as shorter manufacturing lead time, call for new approaches. To meet the emerging requirements of fast manufacturing cycle time, finding an efficient way to reduce set up and machine idle times in batch production systems is an essential prerequisite for business performance. However, the existing approaches to reducing downtime have been investigated only in a dedicated worker environment where one operator handles only one machine. The proposed heuristic is to reduce set up and machine idle times in a shared worker environment based on the part sequencing method where machine idle time increases due to worker unavailability during set up and loading/ 100% 80.94 178.2 150 75% 60.88 142.9 100 50% 105.8 50 25% 5 4 3 Number of machines operated by two workers
8 K.H. Han et al. unloading operations. In this paper, several part sequencing methods for cycle time reduction are evaluated step by step using a real case to find a reasonable solution in an SWE. By using the proposed method, the average downtime cycle time per work unit is reduced significantly over that of the optimal part sequencing for each machine. However, to better support the situation on a real shop floor, a dynamic part sequencing method is needed rather than a deterministic sequencing method. Thus, further research is needed on the development of an interactive real time part sequencer to minimise manufacturing cycle time in a shared worker environment. Acknowledgements This research was financially supported by the Ministry of Education, Science and Technology (MEST) and the National Research Foundation of Korea (NRF) through the Human Resource Training Project for Regional Innovation. Financial support also came from the Ministry of Knowledge Economy (MKE) for the development of a digitally-based real time adaptive manufacturing system platform. References Allahverdi, A., Gupta, J.N.D., and Aldowaisan, T., 1999. A review of scheduling research involving setup considerations. Omega the International Journal of Management Science, 27 (2), 219 239. Allahverdi, A., et al., 2008. A survey of scheduling problems with setup times or costs. European Journal of Operations Research, 187 (3), 985 1032. Bianco, L., et al., 1988. Scheduling tasks with sequencing dependent processing times. Naval Research Logistics, 35 (2), 177 184. Chrisman, J.A., 1986. Manufacturing cell: analytic setup times and part sequencing. The International Journal of Advanced Manufacturing Technology, 1 (5), 55 60. Croes, G.A., 1958. A method for solving traveling salesman problem. Operations Research, 6 (6), 791 798. Gilmore, P.C. and Gomory, R.E., 1964. Sequencing a one-state variable machine: a solvable case of the traveling salesman problem. Operations Research, 12 (5), 655 679. Gupta, J.N.D. and Chantaravarapan, S., 2008. Single machine group scheduling with family setups to minimize total tardiness. International Journal of Production Research, 46 (6), 1707 1722. Lin, S. and Kernighan, B.W., 1973. An effective heuristic algorithm for the traveling salesman problem. Operations Research, 21 (2), 448 516. Ozgur, C.O. and Brown, J.R., 1995. A two-stage traveling salesman procedure for the single machine sequence-dependent scheduling problem. Omega the International Journal of Management Science, 23 (2), 205 219. Ozkan, U. and Toklu, B., 2010. Balancing two-sided assembly lines with sequence-dependent setup times. International Journal of Production Research, 48 (18), 5363 5383. Pinedo, M., 2008. Scheduling: Theory, algorithms, and systems. 3rd ed. New York: Springer. Rasmussen, R.R., Savory, P., and Williams, R.E., 1999. Integrating simulation with activity-based management to evaluate manufacturing cell part sequencing. Computers & Industrial Engineering, 37 (4), 757 768. Tan, K.C., et al., 2000. A comparison of four methods for minimizing total tardiness on a single process with sequence dependent setup times. Omega the International Journal of Management Science, 28 (3), 313 326. Vinod, V. and Sridharan, R., 2009. Simulation-based meta-models for scheduling a dynamic job shop with sequence-dependent setup times. International Journal of Production Research, 47 (6), 1425 1447. Yang, W.-H., 1999. Survey of scheduling research involving setup times. International Journal of Production Research, 30 (2), 143 155. Yilmaz, I.O., et al., 2007. Development of group setup strategies for makespan minimization in PCB assembly. International Journal of Production Research, 45 (4), 871 897. Ying, K.-C., et al., 2010. Permutation and non-permutation schedules for the flow line manufacturing cell with sequence dependent family setups. International Journal of Production Research, 48 (8), 2169 2184. Zhu, X. and Wilheim, W.E., 2006. Scheduling and lot sizing with sequencing dependent setup: a literature review. IIE transactions, 38 (11), 987 1007.