Analysis of Closed Loop Production System Using Orthogonal Array and Integer Programming Optimization

Sustainable production systems require optimal utilization of resources. Raw material acquisition is one of the costly processes in a production system. EOL (End-of-Life) products re-manufacturing through reverse logistics can help in decreasing excessive raw material cost. In this study, we consider production system of closed loop supply chain in which both forward and reverse production systems are active. DOE (Design of Experiments) methodology is incorporated which is a statistical approach adopted in dealing with complex workplace problems. We employ L9 orthogonal array using Taguchi experiment in Minitab 17 and DOE for plotting the results. Dependent variables used in this study are productivity, P (number of forward and reverse products produced per period) and quality accuracy of product (measured in percent deviation from reference standards). A trade-off analysis between the control variables is presented on the basis of SNR (Signal to Noise Ratio). Control variables used in the analysis are tools employed in production system (tu), number of machines being used (m) and dedicated manufacturing cells (dc). We use three levels of analysis for each control factor. Optimum result conditions are calculated using signal to noise ratio with larger-the-better-criteria as well as smaller-the-better criteria and study is concluded with main effects of the mean plots. DOE optimization analysis for productivity suggests combination set of 32, 8, and 6 for tools, machines in use and manufacturing cells, respectively. Similarly, for optimal dimensional accuracy, tools used are 24; number of machines in use is 14 with 3 manufacturing cells. All result indices are accomplished within a confidence interval of 95% with p-values less than 0.05. MILP (Mixed Integer Linear Programming) analysis considers cost function of production and transportation between tools, machines and levels and Taguchi based experimental findings are validated by mathematical optimization findings.


Analysis of Closed Loop Production System using Orthogonal Array and Integer Programming Optimization
of resources such as batch-sizing, work in process quality inspection and leagile practices [1]. Due to competitive market dynamics, cost optimality is of no use if it comes as a result of compromise on quality. In this article, we discuss one of the efficient ways to optimally use resources in the form of raw material usage by considering case of a CLSC (Closed Loop Supply Chain). CLSC is an alternative and modernized way to look at SC (Supply Chain) issues in a way that product liability rests upon the production system for its entire life cycle [2]. SC involves multiple business activities such as acquisition of raw materials, production, logistics management and distribution of the product to customer [3]. A normal SC moves the product line in one direction starting from accessing raw material from supplier and delivery to the end customer; however, in CLSC, both forward and reverse movements of the product (to and fro from the customer) are considered. CLSC is implemented to moderate the economic and environmental consequences of the products;for instance, minimization of products containing Carbon contents (environmental degradation) [4]. CLSC is defined as "design, control and operation of a system to maximize value creation over the entire life cycle of a product with dynamic recovery of value from different types and volumes of returns over time" [5]. Reverse logistics deal with collection of products from customer once they serve their useful life which is quite opposite to the traditional logistic services [6].
Reverse logistic operations have created more hype in the wake of corporate social responsibility [7] and it is one of the leading practices adopted by giants such as BMW, Howard Packard and General Motors [8].

Analysis of Closed Loop Production System using Orthogonal Array and Integer Programming Optimization
Reverse logistics provides with efficient centralized system for controlling, implementing and planning in accordance with requirements of the production system [11]. To re-emphasize, it is not necessary that the product through reverse chain enters into the system from the start but rather it can enter into the production system at any point depending upon the condition of the product and services/processes needed to be performed. RL (Reverse Logistics) serves for extracting value from the collected items and thus it follows start to a new SC [12], which in connection to the existing SC creates problems such as productivity, quality of production, work scheduling and demand completion [13][14]. RL extends the vision of production system and SC management by triggering more confounding factors into consideration [15]. Both forward and reverse logistics form closed loop supply chain which is a sustainable approach for managing and recovering end of life products [16]. In the past two decades, closed loop supply chain in general and reverse logistics in particular has been focus of research attention in the academic arena [17]. From operational research viewpoint, much attention is provided to economic aspects [18][19][20], environmental footprints [21][22][23] and performance analysis [24][25] of reverse logistics. Most of the performance analysis studies are centered on remanufacturing optimization with an assembly line approach [26]; however, reverse logistics is a time varying phenomena [27] for which production system is urged to react in a dynamic manner. Production system needs to be aligned with flexibility to cope with the manufacturing requirements of both forward and reverse items. This requires combination of resources to optimize the efforts in meeting customers' requirements as well as profitability concerns. In the larger context, RL affects quality of products and productivity ofproduction system along with other variables [28]. In research literature of RL, in house production resources optimization for production of both streams (forward and reverse) is still unexplored. This study contributes to the literature of reverse logistics by suggesting optimal combination of tools, machines and cells used in the manufacturing assembly line of a CLSC in order to optimize productivity and dimensional accuracy. We address the following research question: "In CLSC. What is the optimal number of tools, machines and manufacturing cells employed in the production system to enhance productivity and quality of production system?" In order to analyze the quality and productivity of a reverse logistics, Taguchi method is employed for examining the closed loop supply chain. In the next section, methodology of the study is outlined.

METHODOLOGY
We analyze manufacturing line of CLSC using Taguchi method which is a statistical robust technique for process parameters examination. Taguchi method has been in practice for more than 3 decades now and its utility can be found in contexts such as manufacturing, process design and SC [29]. Taguchi method is used in diverse range of reverse logistics problems such as polyethylene bottles [30], in the context of uncertain pricing of used products [31], for environmental consideration [32] and reverse logistics network design [33]. Taguchi (Table 1).
Next, we identify three levels for the selected control machines are assigned to level 3 ( Table 2).  Table 4).
Taguchi method full factorial orthogonal array is applied for analysis purposes. Since we had 3 control factors, we applied L 9 orthogonal array with three runs on each

FIG. 2. SIX STEPS APPROACH TOWARDS TAGUCHI
METHOD [34] For analysis of the study, we considered a French manufacturing assembly line of automotive engines and performed statistical analysis of parts in high need of repair and replacement through reverse logistics. We considered three parts for the study investigation which were; Piston, Case and Connecting rod as shown in Fig. 3.

EXPERIMENT DESIGN
As a result of both forward and reverse channeling;    As mentioned in Table 5, total of 27 experiment runs were performed for analysis of productivity with the mean values also tabulated. Against the mean values, SNR is also provided and since we prefer higher productivity, we will select on the basis of larger the better criteria.
Next, we analyze data for our second non-controllable variable which is dimensional accuracy. Dimensional accuracy in this case is defined in terms of deviation of overall dimensions from standard specifications. It is expressed in terms of percentage and smaller the value of deviation (da), the better it is. SNR criteria of smaller the better is considered and

TABLE 5. TWENTY SEVEN (27) ITERATIONS FOR PRODUCTIVITY AND S/N RATIO ERIMENTS
In Table 7 sum and average of SNR for all control variables is presented for productivity factor and the same is depicted in Fig. 4.
As can be seen in Table 8 Table 9 exhibits values of sum and average for all control variables and against their three distinct levels. Here the "noise" variable is dimensional accuracy and the criteria used was smaller the better. Graphical depiction through design experts is provided in Fig. 5 where data of SNR for control variables is plotted on y axis against levels on xaxis.

Analysis of Closed Loop Production System using Orthogonal Array and Integer Programming Optimization
In Table 10, parameters variation analysis results are presented. We can conclude from the Table 9 that "machines" factor explains the variation in "productivity" by 39.5% which is the highest and next to it, tools explains it by 33.1%. Similarly, error in "productivity" analysis is 3.4% which is less than the error value for dimensional accuracy (4.8%). Variation explanation by percentage follows the same trend for "dimensional accuracy" as for productivity and it is accounted for by    5(a-c)

DISCUSSION
Reverse logistics starts with collection of EOL products from customer followed by subsequent recycling for energy extraction and introduction into secondary market [35]. There are two coping mechanisms for RL products; either they can be process through a dedicated production line or these products can be processed with the forward assembly line [36]. Allocation of dedicated production line can be quite costly and thus it is suggested that RL might be processed with the forward production for cost optimality and enhancement in performance [37]. In this study, we have considered combined framework of closed loop supply chain in which both forward and reverse production are being performed as shown in the framework (Fig. 6).
When forward production is assisted by reverse production, enterprises needs to re-evaluate their strategy as flexibility might be required in the resource mobilization [38]. There can be a compromise on the quality of production and productivity due to the dynamic induction of reverse products in manufacturing lines. Reverse logistics are reported to pose challenges of quality as such products have already completed their useful life [39] and right combination of resource mix can provide optimal results as accomplished in the current study. In competitive production environment, businesses tend to optimize on multiple fronts besides quality production and thus this study has two fold objectives of meeting quality and improving productivity.
As discussed in introduction section of this study, a follow up methodology was used to validate the experimental study findings. We employed MILP to evaluate the robustness of statistics. MILP tool was used   Fig. 7 provides with an extra plot of overall production cost and transportation cost. On average, level 1 value of each dependent (control variable) results into an overall minimization of production as well as transportation cost.
Similarly, analysis based on mathematical optimization was performed for dimensional accuracy noise factor.

CONCLUSION
In this study, we have provided optimal assignment of control factors for two different conditions. In the first case, we have optimized (maximized) the productivity while in second case we optimize (minimize) dimensional variation in the product.