In this work, a mixed-integer linear programming model is formulated to allocate the appropriate orders to the right suppliers for recyclable raw materials. We modify the previous model for the supplier selection and order allocation problem for stochastic demand to cope with the supply risks of recyclable raw materials such as insufficient supply quantity, defective rate, and late delivery. The optimal solution of the mathematical model is the benchmark for small-sized problems. Then, a hybrid meta-heuristic of Particles Swarm Optimization and Grey Wolf Optimization (PSO-GWO) is proposed to search for the best solution for large-sized problems. A real-life case study of a steel manufacturer with two factories in Vietnam is presented to validate the proposed approach. Some experiments have been tested to confirm the performance of the hybrid PSO-GWO approach.

Integrated supplier selection and order allocation is a complex problem that is important for both designing and operating supply chains. It becomes especially complicated when quantity discounts are considered at the same time. Under such circumstances, most studies often formulate the problem as a Multi-Objective Linear Programming problem (MOLP), and then transform it to a Mixed Integer Programming problem (MIP) to handle the inherited multi-objectives, simultaneously. But, objectives are not of equal importance and in this approach scaling and subjective weighting often are not considered. In addition, some of the studies that use weighting method to solve the MOLP, usually ignore to normalize the coefficients. However, as different coefficients have different units such as cost or number coefficients, so weighted summation will be meaningless. Furthermore, in most of the studies only quantitative criteria are considered in mathematical model. But, the importance of some qualitative criteria persuade decision maker to consider other affective criteria as well as cost. In this study, in order to ease the problem and to obtain a more reasonable compromised solution for order allocating among suppliers, an integration of analytical hierarchy process and linear integer and multi-objective programming is proposed. The large number of criteria and attributes are employed in this problem and they are employed in a comprehensive model to solve the multi-objective problem and to find the most preferred non dominated solutions by considering decision maker’s (DM) preferences. Some illustrative examples are solved using LINGO and the results are compared. The sensitivity analysis and comparing the results with one of the well-known studies in the literature has demonstrated the flexibility and efficiency of the proposed model to deal with large sized problems and incorporate different purchasing policies, easily and in a short amount of time.

Today, with the advancement of technology in the production process of various products, the achievement of sustainable production and development has become one of the main concerns of factories and manufacturing organizations. In the same vein, many manufacturers try to select suppliers in their upstream supply chains that have the best performance in terms of sustainable development criteria. In this research, a new multi-criteria decision-making model for selecting suppliers and assigning orders in the green supply chain is presented with a fuzzy optimization approach. Due to uncertainty in supplier capacity as well as customer demand, the problem is formulated as a fuzzy multi-objective linear programming (FMOLP). The proposed model for the selection of suppliers of SAPCO Corporation is evaluated. Firstly, in order to select and rank suppliers in a green supply chain, a network structure of criteria has defined with five main criteria of cost, quality, delivery, technology and environmental benefits. Subsequently, using incomplete fuzzy linguistic relationships, pair-wise comparisons between the criteria and sub-criteria as well as the operation of the options will be assessed. The results of these comparisons rank the existing suppliers in terms of performance and determine the utility of them. The output of these calculations (utility index) is used in the optimization model. Subsequently, in the order allocation process, the two functions of the target cost of purchase and purchase value are optimized simultaneously. Finally, the order quantity is determined for each supplier in each period.