The integration of supply chain decisions aims to reduce costs and delivery time for customers. However, uncertainty in supply chain parameters, particularly demand, can disrupt this integration. The increased interest in probabilistic planning and simulation models in supply chain modeling is a response to this demand uncertainty. Therefore, the main objective of this study was to develop a multi-level, multi-product, multi-period supply chain network model that considers conflicting objectives such as cost minimization, delivery time minimization, and system-wide reliability maximization. The supply chain network under investigation consisted of four levels or subsystems: suppliers, manufacturers, distributors, and retailers. In this study, it was assumed that demand follows a random probabilistic distribution function. Consequently, simulation techniques were employed to estimate costs, including shipping costs, lost sales costs, and other expenses. After developing the multi-objective model, various scenarios were created based on different perspectives of inventory levels, namely minimum inventory, maximum inventory, and average inventory level. For each scenario, objective-related values were estimated. Ultimately, based on the Pareto optimal solutions obtained for each case of the model, the Vickor decision-making method was used to rank the answers and select the best solution from the proposed model. The results indicated that the second scenario, considering the average inventory level, was identified as the optimal solution for the described model.IntroductionToday, supply chain management (SCM) encompasses the entire production planning process for the supply chain, from raw material suppliers to the final customer. This has become a focal point for numerous researchers. In most supply chain designs, the objective has been to transfer products from one layer to another in order to meet strategic, tactical, and operational demands while minimizing complications arising from interrelationships and uncertainties across the chain. These challenges have posed significant decision-making hurdles in the supply chain domain. Supply chains can be regarded as complex systems wherein various factors interact with each other, resulting in emergent properties. Designing a versatile supply chain to address conflicting and diverse objectives requires considering them simultaneously and striking a balance among different criteria. The dynamic and intricate nature of the supply chain introduces a high level of uncertainty, thereby impacting the decision-making process in supply chain planning and influencing overall network performance. Based on the aforementioned issues, the focus of investigation includes the following: The examined supply chain network comprises four levels or subsystems, namely suppliers, manufacturers, distributors, and retailers. Raw materials are sourced from suppliers and sent to production factories, where each product is manufactured using a specific combination of raw materials. The products are then transported from manufacturers to distribution centers, and subsequently forwarded to retailers. The market is divided into different regions, and customer demands are fulfilled through visits to the retailers. Demand is assumed to be random and follows a probability distribution pattern. Consequently, simulation techniques are employed to estimate costs, including transportation costs, lost sales costs, and other expenses. Scenarios are created based on different perspectives at each level, focusing on inventory levels (minimum, maximum, and average). For each scenario, the values associated with the investigated objectives are estimated.Materials and methods In this research, data collection involved the examination of relevant literature, including articles published in international journals, books, and treatises. Documentary studies were conducted to gather information. To analyze the collected data, simulation and multi-objective programming concepts and methods were employed. Minitab and ED software were utilized for statistical analysis and simulation purposes.ConclusionsConsidering that the model can be solved under different conditions, including the current situation and various scenarios, the answers obtained for each state are Pareto optimal. This means that it is not possible to determine a single best answer for each state of the model. Therefore, before comparing the scenarios with each other, the Pareto optimal answers for each scenario should be ranked to identify the best options. In this research, a model for designing the supply chain network was presented, taking into account demand randomness. To better understand the proposed model and demonstrate its practicality, numerical examples were examined and evaluated using different scenarios and the Lingo software. It is important to note that the developed model in this study is independent of the number of facilities at each level of the supply chain and the parameter values. Therefore, the general form of this model can be applied to any production environment that aligns with the patterns presented in this research. The proposed model initially employed the design of experiments to estimate the mathematical relationship related to the cost objective function. After developing the multi-objective model, the Lingo software was used to solve the sample problem and evaluate the results under different scenarios. Finally, based on the Victor decision-making method, the Pareto optimal solutions for each state of the model were used to rank the answers and determine the best mode for the proposed models. Based on the obtained results, the third option or the second scenario is suggested as the preferred choice for the described model, considering the index values associated with each optio
