## 2 Literature Review  
Determination of the order quantity among suppliers takes an important place in the relations of suppliers and buyers. As the purchasing decisions are based on multiple suppliers, companies split their orders among suppliers. Therefore, the power of suppliers over the buyers reduces. This is how companies can reach low prices. Buyers split order quantities among selected suppliers to keep secure working with them [1].  
Several studies on the supplier selection and order allocation problem have been conducted by several researchers [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. [PERSON] et al. [11] studied a procurement problem simultaneously taking into consideration the transportation and purchasing costs, introducing both an integer programming model and a heuristic solution. Inventory holding cost has also been taken into consideration in some studies. [PERSON] and [PERSON] [12] develop two mixed-integer nonlinear programming models for supplier selection and order allocation while minimizing total cost, which consists of ordering, inventory holding, and purchasing costs subject to quality and suppliers' capacity constraints. [PERSON] et al. [13] consider the multi-product multi-period inventory lot-sizing with supplier selection problem. Their model considers ordering, holding, and purchase costs.  
Some articles tackle purchasing, transportation, and inventory decisions simultaneously. [PERSON] and [PERSON] [14] propose a mixed-integer nonlinear programming model in order to allocate order quantities to the selected set of suppliers considering purchasing, transportation, and inventory costs subject to quality and suppliers' capacity constraints. [PERSON] et al. [15] present a mixed-integer programming model for the supplier selection problem with multiple products and multiple periods in an international context, which takes into account inventory and transportation decisions. [PERSON] et al. [16] introduce a mixed-integer nonlinear programming model which includes transportation costs. [PERSON] et al. [17] presented a mixed-integer programming model to solve the lot-sizing problem with multiple suppliers, multiple periods, and quantity discounts. Their objective was to minimize the total cost, which includes ordering, inventory holding, purchasing, and transportation costs. However, price discount was not included in their model. Our study considers ordering, purchasing, transportation, and inventory holding costs, as well as price discounts.  
Many papers have addressed the traveling purchaser problem. Their models were handled with different constraints [18; 19; 20; 21; 22].  
In the literature, there are studies which separately examine either the supplier selection, order quantity allocation or traveling purchaser problems mentioned above; however, no studies have been found that integrate these problems. This study aims to fill this gap using a single integrated mathematical programming model. Furthermore, in the literature, decision models and techniques for supplier selection do not often consider issues related to inventory, vehicle routing, and price discounts simultaneously. This study deals with all these real-life constraints and situations.  
In this article, a mixed-integer nonlinear programming model is proposed to select the best set of suppliers and determine the proper allocation of order quantities while minimizing total cost, including the annual ordering, inventory holding, purchasing, and routing costs under suppliers' capacity and price discount constraints.