The main goal of this research is to present new efficient methods and optimization models to enhance the Green Supply Chain Planning (GSCP). As a first objective, we focus on developing a novel optimization planning model in a green supply chain network consisting of suppliers, assemblers, distribution centers, and retailers. This model is subjected to various constraints which are related to the inventory and forward logistics management. We applied the proposed model for a vacuum and floor machines manufacturer case study located in the Midwestern, U.S. The main objective functions include: minimizing the costs of assembling, transporting, holding inventory at assembling sites and distribution centers, and shortage at retailers under carbon dioxide (CO2) emissions constraints throughout the logistic network; maximizing service levels and determining the acceptable service levels to meet final customers’ demands. We applied three different solution methods including a gradient-based algorithm in MATLAB “Find Minimum of Constrained nonlinear multivariable function (FminCon)”, a novel metaheuristic algorithm “Grey Wolf”, and the “Branch and Bound (B&B)” algorithm in Lingo to find optimal solutions for the proposed optimization model, which has a specific complexity. We compared the achieved optimal solutions by these methods. The case study and expanded numerical example verify whenever the parameter of the minimum service level at retailers’ sites increases or decreases, the amount of produced CO2 emissions and the total costs of the supply chain will directly correlate. It also demonstrates the trade-offs among the total costs of the supply chain network, CO2 emissions, and service levels. The achieved results reflect the efficiency of the proposed model for GSCP. As a second objective, we concentrate on revealing more information about optimal points in which performance measures of various adaptive (X ) ¯quality control charts hold their optimal minimum values. In this way, better quality control systems can be applied to detect defective parts and errors sooner, reduce the wastes, and find the related causes for the various processes involved in supply chain networks/production systems in order to achieve more effective GSCP and improve the quality control. Previous researches applied a forward viewpoint and evaluated the performance of adaptive models only for a specific and limited set of design parameters. However, in this research, we use a reverse perspective and search all possible sets of design parameters in the response space to find optimal minimum values for three performance measures, including adjusted average time until signal, average number of observations to signal, and average number of samples to signal. For this purpose, similar to recent studies, the Markov-chain approach is applied to develop performance measures. Then, a coded algorithm is proposed that explores the entire response surface and evaluate the value of each performance measure to find the optimal points. As an output, this algorithm obtains sets of initial parameters resulting in optimal minimum values of performance measures for adaptive models with respect to broad ranges of shifts in mean. It also computes the values of other performance measures and their improvement percentages in comparison to a fixed parameters control chart at obtained optimal points. The presented new guideline provides decision makers and quality managers with more knowledge about optimal points to choose a proper adaptive model, select an appropriate performance measure, and set economical and viable values for design parameters for specific ranges of shifts in mean that are estimated to have a higher priority in their process control. Finally, the third objective of this research is to evaluate the waste streams and recycling opportunities for various echelons of a supply chain. A real case study categorized in health care systems is considered for this purpose.
Keywords: Quality Control Charts, Supply Chain Management, Supply Chain Modeling, Mathematical Modeling, Fuzzy, VIKOR method, MCDM methods, Healthcare Supply Chain, Inventory Control, CO2 emissions, Grey Wolf Algorithm, Gradient-based algorithm