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This paper focuses on the issues of the purchase of bill of materials, production planning, and inventory management in materials and products warehouses under demand uncertainty, simultaneously. The purpose of this study is to determine the optimal volume of purchasing the raw materials from different vendors, transportation methods, and production planning over the time horizon so that with proper inventory management in the warehouses of materials and manufactured products, the total cost is minimized. This issue is defined as a multi-region, multi-supplier, multi-component, multi-product, and multi-period problem. There is a time interval between ordering and delivering the bill of materials, which depends on the region where the supplier is located. Customer demands are not predetermined, and robust optimization is employed to handle this uncertainty. Three numerical examples, based on increasing or decreasing the nominal customer demands, are presented to evaluate the robustness of the solutions and to examine the effect of conservatism level on the performance of the proposed model. Finally, the price and importance of proposed robust planning are evaluated based on random data. Introduction Today, successful companies monitor consumer communities and estimate potential needs to provide or produce products that are in high demand. The correct analysis of customer desired quality, estimation of demand volume, producing high-quality materials, and delivering them on time are crucial for a company to survive in today's competitive market. For quality and timely production, several factors need to be considered, including selecting suitable suppliers in terms of quality, price, and timely supply, employing appropriate transportation and storage methods, ensuring accurate timing for production or assembly, and effective inventory management throughout different months. Failure to properly coordinate these stages can lead to continuous interruptions in production and supply. For instance, if the lead time between ordering and receiving raw materials is not considered, there is a risk that materials will not reach the production line on time, resulting in production halt or early delivery causing storage space shortages. In supply chains with a higher number of suppliers, raw materials, manufactured products, and longer time horizons, coordination becomes even more critical, yet challenging. Therefore, a comprehensive model is necessary to determine raw material quantities ordered from suppliers, transportation methods and timing, and the type and volume of products in production. Choosing a supplier or determining the purchase amount from each supplier depends on various factors such as quality, price, discount offers, and lead time. There are three types of discounts: all-unit quantity discounts, incremental quantity discounts, and carload-lot discounts (Jucker and Rosenblatt, 1985). Inventory management of raw materials depends on many factors like warehouse capacity and warehousing costs, which can become more complicated when storing different types of materials in a single warehouse. In production lines, we should consider raw material inventory and customer demand in the coming months, aiming to minimize production costs and maintain input-output balance. However, the uncertainty of customer demand poses a challenge to this planning process, and ignoring it can lead to shortages or surpluses of raw materials and products in different months. To address these challenges and reduce associated costs, presenting a comprehensive mathematical model for simultaneous planning of raw material purchase, inventory management, and production planning is a worthwhile task. This model should ensure minimal disruption to the coordination among supply chain components, despite demand uncertainty. As a motivating example, consider a home appliance factory that produces various products. A unit of each product requires a bill of materials and a specific assembly time. The bill of materials can be purchased from several suppliers in different regions, and they can be transported to the factory using rented or public containers from any region. The time interval between ordering and receiving of materials (lead time) varies depending on the region. Each supplier offers a discount based on quantity discount policy, where in each purchase period, if the total purchase amount exceeds a certain amount, the discount is applied, and a specified percentage of the total purchase amount is deducted. The purchased parts are stored in a limited-capacity warehouse before entering the production line. The bill of materials is assembled and turned into products, which are stored in a warehouse with limited capacity before being delivered to customers. The time required to produce each unit of products and the cost of producing goods in different months may be different, and production line planning should be based on meeting customer demand and reducing production cost. In each time horizon, planners must make decisions about the amount of purchase from each supplier, how to transport the purchased items, production scheduling, and inventory management in different periods in such a way that, according to the market demand and the aforementioned limitations, customer satisfaction is provided and minimize the company's costs. The monthly demand of the products is not precisely known and it is only possible to predict its floor and ceiling. However, the proposed program should be such that the possibility of shortage or excess of stock in the warehouse is negligible. In this study, we aim to develop a comprehensive mathematical model that simultaneously schedules the ordering of bill of materials from different suppliers (with varying lead times and discount policies), multi-period production planning, and inventory management in warehouses of materials and products. We consider tender offers to minimize costs related to purchase, transportation, production, and storage while meeting customer demand on time. In the second stage, we account for the uncertainty of monthly product demand and provide a robust program that results in a low probability of inventory shortage and excess. We structure the rest of this article as follows: In section 2, the literature review is presented. In Section 3, the problem is defined and formulated regarding data certainty. In Section 4, the uncertainty conditions are formulated as a robust model. In Section 5, we solve a numerical example and analyze the obtained results. Section 6 discusses the necessity of robust planning. Finally, the conclusion is stated in section 7. Section snippets Literature review As mentioned above, for production planning, various factors must be taken into consideration, such as determining the supplier of raw materials, the amount of orders and discount policy, lead time, scheduling the production line, monitoring the inventory level in the warehouses of raw materials and final goods, and demand uncertainty. Each of these cases has been investigated and studied independently or comprehensively in the form of practical problems in the past, and we refer to some of Defining and formulating the problem under data certainty Consider a factory, for example, a home appliance plant that orders a bill of materials from various domestic or foreign markets and produces various products by assembling them. Several regions are considered to purchase bill of materials. There are some suppliers in each region, and we assume that the time interval between ordering and delivery from all suppliers in a region is equal and definite. Each supplier has a discount policy based on the minimum purchase amount. In this case, the A Γ-robust framework for planning under demand uncertainty In many real cases, for various reasons, such as system malfunctions or the time distance between decision-making and implementation, the exact values of some parameters are not known from the beginning. In this study, the decisions about buying a bill of materials and producing products are made at the beginning of the time horizon, and the estimated demand may change at the time of demand delivery in different periods. In some cases, to deal with data uncertainty, reactive planning is used so Implementing the proposed model and analyzing the results In this section, the performance of the proposed model are examined by providing a numerical example. In this example, the goal is to investigate the effect of conservatism level parameters on the components of the objective function. The effects of these parameters on all components of the objective function will be investigated cumulatively over the entire time horizon. Consider a home appliance assembly plant that buys 15 types of materials from 5 suppliers. The suppliers are located in Conclusions In this study, several issues were considered simultaneously, including the scheduling of the order the bill of materials, production planning, and inventory management in a warehouse for bill of materials and another warehouse for all finished products. Some real assumptions such as discounts, transportation ways, and lead time are considered, and a comprehensive mathematical model was presented. Due to the extensive time gap between the supply of materials and the production of final Funding This research received no specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References (39) R. Aldrighetti et al. 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