برآورد سطح خدمات مشتری در خطوط تولید خودکار چندبخشی چندنوعی: یک روش تحلیلی

We develop an approximate analytical method to estimate the customer service levels in automated multiple part-type production lines. The production line consists of several processing stations in series with finite intermediate buffers, one for each part-type. The main contributions include the analysis of multiple part-type systems with machine setups, bypass routings and stations having combinations of shared and dedicated machines. This research is motivated by observations of real production lines. We use the continuous material approximation in modeling the system behaviour and develop a new approximate decomposition method to analyze the performance of the system. Validation experiments conducted on production lines with different configurations show good accuracy in the estimation of customer service levels compared to simulation. We use an example case study to demonstrate the application of the model in the performance improvement of a system that is based on a real production line. The analytical model is proposed as a reliable and fast performance analysis tool for the optimization of automated multiple part-type production lines with complex configurations.

Modern-day industrial production lines are generally designed to produce multiple part-types (Goyal & Netessine, 2007). Examples are found in automotive assembly (Patchong, Lemoine, & Kern, 2003), semiconductor manufacturing (Jang, 2007), packaging lines and bottling plants (Colledani, Gandola, Matta, & Tolio, 2008). Manufacturers who operate multiple part-type production lines often aim to achieve high customer service levels for all part-types, while minimizing inventory and other related costs (Christou, Lagodimos, & Lycopulou, 2007). Therefore, it is essential that the production system is designed such that these performance requirements can be fulfilled. In designing any production system, various alternate configurations are often evaluated before selecting the configuration that best meets performance objectives. Analytical methods are increasingly used for evaluating the performance of production systems (Patchong et al., 2003 and Burman, 1995). Compared to simulation, analytical methods are faster and can provide greater insights to the dynamics of the manufacturing system (Colledani et al., 2010). In this paper, we propose an approximate analytical method for estimating customer service levels in automated multiple part-type production systems. The system consists of several interconnected stations with each station having processing machines that may be shared among several part-types (shared machines) or dedicated to a particular part-type. Processing operations and material transportation between stations are automated. An example production system consisting of five stations producing four part-types is shown in Fig. 1, where rectangles represent machines and circles represent inter-station buffers. As shown in the figure, each part-type has its own buffer (homogeneous buffers). This is commonly observed in food product packaging lines and bottling plants ( Colledani et al., 2008). Full-size image (36 K) Fig. 1. A five station, four part-type production system. Figure options Several researchers have contributed to the analysis of automated multiple part-type production systems (Jang, 2007, Colledani et al., 2008 and Nemec, 1999). A literature review is provided in Section 2. These studies mainly focused on estimating the production rate of systems where each station consisted of a single shared machine with negligible setup times. In this paper, we extend the analytical methods to multiple part-type systems with stations having combinations of shared and dedicated machines where shared machines require a setup each time production is switched between part-types. In addition, part-types may also have bypass routings. This work has been particularly motivated by discussions with the authors of a simulation study (Zhou, 2009) of an electrical component production line that involved all of the system characteristics mentioned above. Machine setups are quite common in the production of multiple part-types (Gershwin, 1994). Setup operations may include tool changes, machine calibration, fixture adjustments, cleaning, etc. Although setup times are being constantly reduced through technological advances (e.g. automatic tool changes) and continuous improvement activities, most production systems will still require non-negligible setups (McIntosh, Culley, Mileham, & Owen, 2001). In industrial multiple part-type manufacturing systems, a single shared machine station is primarily used when the machine is too costly to be duplicated (Hopp & Spearman, 2008). However, certain stations may have both dedicated and shared machines, as described by Zhou (2009). In addition, part-types may not require processing at all stations as assumed in previous studies (Jang, 2007, Colledani et al., 2008 and Nemec, 1999). Bypass routings are frequently encountered in multiple part-type production (Diponegoro & Sarker, 2003) and industrial examples include sheet metal fabrication (Diponegoro & Sarker, 2003), electrical component assembly (Zhou, 2009), and garment packing plants. In our analytical approach, we first develop a new building block model of a two-machine system (2M1B model) using the continuous material flow approximation (Alvarez-Vargas, Dallery, & David, 1994). In this model, it is assumed that both machines have equal deterministic processing times and are subject to failures. This is a common assumption in the modeling of automated systems (Li, Blumenfeld, & Huang, 2009). The continuous flow approximation provides the flexibility to later extend the analysis to asynchronous systems, where machines at each stage have different processing times. We then incorporate this new 2M1B building block in the approximate decomposition analysis of automated multiple part-type production lines with general configurations of the characteristics studied in this paper. Numerical results show that the decomposition method provides good accuracy in estimating customer service levels for a range of production line configurations. We also apply the methodology to estimate the customer service levels of a production system with a configuration similar to an existing industrial production line described in the simulation study of Zhou (2009). Using this system as a case study, we demonstrate how the model can be used to identify system improvements that will best enhance system performance. The remaining sections of the paper are organized as follows: Section 2 provides a review of the relevant literature. The system description and modeling methodology is then detailed in Section 3. Section 4 presents results for the model validation and experimental case study. Finally, the conclusions and future research directions are presented in Section 5.

In this paper, we presented an approximate analytical method for estimating the customer service levels of automated multiple part-type production systems. The main contributions of this paper include the incorporation of the following important characteristics: • machine setups, • bypass routings, and • stations comprising of combinations of dedicated and shared machines. In order to capture the deterministic nature of processing times in automated systems, we utilized the continuous material approximation for modeling the discrete flow of parts. This model allowed a tractable analysis of the system using Markov theory. A new building block model was then developed for a two machine line and an approximate decomposition method for longer multiple part-type production systems was introduced. The analytical model was validated for several different system configurations including that of a real production line for electrical component assembly. In all of the experiments, the analytical estimates for the customer service levels were shown to be quite accurate. In addition, the algorithm converged in all instances and provided results in much faster time than simulation. Thus, the analytical model may be used as a fast and reliable alternative to simulation in the optimization of multiple part-type production systems. Finally, we presented a case study using the electrical component line configuration to demonstrate the use of the model in production system improvement. This research work points out interesting new directions for future research. Some natural extensions of this model include the study of non-homogeneous lines, where machines can have different processing times for each part-type. We have provided for part-type dependent failure and repair rates that could be helpful in the analysis of non-homogeneous lines using methods such as homogenization ( Dallery et al., 1989). Another extension of this work would be to incorporate the different switching policies that have been proposed in the literature.