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

Abstract

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.