One of the most popular fields in production planning is to determine the sequencing and quantity of products. In every manufacturing system, lot sizing and scheduling are two fundamental issues to improve production efficiency and effectiveness of customer service. On the other hand, firm can accomplish competitiveness by reducing total logistics costs through integration of its various internal activities of purchasing process. The purchasing function of a firm consists of three activities: lot-sizing decision, supplier selection decision, and carrier selection decision. While a lot-sizing decision aims to minimize inventory and shortage costs by optimizing timings and order sizes. The intent of supplier and carrier selection decisions is to minimize inbound logistics costs and to attain a high degree of quality and delivery performance. Due to the inherent interdependency among these three decisions, a firm cannot optimize them separately. Most studies in the field of supplier selection, are related to an organized system of suppliers, buyer and customers which the buyer, select the best suppliers and then purchase the product from them and without any manufacturing operation, sell to customers. Given that in a production system, supplier selection and purchase of raw materials from them could have a great impact on the size and timing of production, and so far no research has been observed in this area, in this study we have discussed. we consider a single machine capacitated lot-sizing and scheduling problem with supplier selection and carrier selection. We address a problem in which a buyer procures multiple ingredients in multiple periods from multiple suppliers. Each supplier has limited production capacity and a different unit price of the ingredients. In addition, each supplier offers all-unit quantity discounts to motivate the buyer for procuring large quantity. Ingredients could be shipped by using different size carriers. A particular size carrier can ship any lot-size up to its full truck load capacity. The traortation cost will be different for different carriers as well as for different suppliers because of carrier size and geographical locations. The problem is to select one or more suppliers as well as carriers and determine the lot-sizes and sequence of products while satisfying the demand requirements and the machine capacity in each period of a planning horizon. In particular, we consider sequence-dependent setup costs that depend on the type of the lot just completed and on the lot to be processed. The objective is to minimize the sum of setup costs, inventory holding costs for products and ingredients, purchasing costs and transaction costs. The resulting optimization problem is strongly NP-hard. We develop a mixed-integer programming (MIP) formulation of the problem and devise MIP-based Relax Fix , Fix Optimize heuristics and a meta-heuristic based on genetic algorithm. By comparing the numerical results obtained that the fix and optimize method has better answers in all problems.