تصمیم گیری مشترک "تعیین اندازه دسته تولید" تأمین تجهیزات با حجم بالا، انتخاب تامین کننده و انتخاب حامل

The joint decision making of procurement lot-size, supplier selection, and carrier selection has potential to reduce buyer's purchasing expenditures. Furthermore, the total logistics cost can also come down through economies of scale in the purchasing and transportation costs, and reduction in supply chain disruptions such as rejections and late deliveries. We study a procurement setting in which a buyer needs to purchase a single product from a set of suppliers over finite discrete time periods to satisfy service level requirements. The suppliers offer all-unit quantity discounts, and transportation cost depends on carrier capacity as well as geographical location of suppliers. This paper proposes an integer linear programming model to simultaneously determine the timings of procurement, lot-sizes, suppliers and carriers to be chosen so as to incur the least total cost over the planning horizon. A numerical example is included to demonstrate the effectiveness of the proposed model in establishing tradeoffs among purchasing cost, transaction cost, and inventory holding cost. Sensitivity analysis has been carried out to understand the effects of the model parameters on the purchasing decisions and total cost. Managerial insights of this study serve as a reference for decision makers to develop effective procurement strategies.

In today's competitive market, the products are to be procured and managed in the most effective manner to minimize costs while satisfying service level requirements. The purchasing strategies of a firm have potential to reduce purchasing and transaction costs and inventories by integrating various internal activities of purchasing process. The purchasing department is completely responsible for supplier selection process, procurement decision process, and sourcing evaluation (Aissaoui et al., 2007). In the supplier selection process, a pool of suppliers is chosen for procurement according to a predefined set of criteria. Based on current academic literature, Ho et al. (2010) have reviewed 78 related articles appeared in the period from 2000 to 2008. They noted that quality is the most popular criterion (68 papers or 87.18%) in the supplier selection process. The second most popular criterion is delivery (64 papers or 82.05%). The price/cost is the third most popular criterion (63 papers or 80.77%). Further, they observed that there was a trend in the supplier evaluation and selection problem to use the multi-criteria decision making approaches from the first five years (2000–2004) to the recent four years (2005–2008). The procurement decision process is concerned with the problem of lot-sizing and other inventory related issues. Finally, in the sourcing evaluation process, overall efficiency and effectiveness of procurement process is assessed. In multi-period horizon, products could be purchased from one or more suppliers in each period. Alternately, excessive products could be carried forward to a future period. Sometimes shortages with backlogging may also be allowed to take advantage of economies of scale in purchasing cost and transaction cost (i.e., ordering cost plus transportation cost) by procuring a few large size lots when suppliers offer discounts for large order quantities. In practice, large quantity of freight or long distance of shipment may reduce per unit transportation cost (Shinn et al., 1996). Considerations like economies of scale concept may be advantageous to incur the least total cost over the decision horizon by optimizing the cost of ordering and transportation as well as purchasing cost when suppliers offer discounts. Indeed, the frequent procurement of small size lots reduces inventory holding cost but increases purchasing and transaction costs. The buyer can reduce purchasing and transaction costs by procuring a few large size lots, less frequently, but this may lead to higher inventory cost or shortage cost. The supplier selection and lot-sizing are two important decisions any purchasing department has to make. In the literature, supplier selection is considered as a strategic decision while lot-sizing is considered as a tactical decision. With regard to supplier selection, the buyer needs to consider the objectives such as cost minimization, and quality and service level maximization. With regard to lot-sizing problem, the buyer needs to consider inventory cost and shortage cost minimization. However, due to the inherent interdependency between these two decisions, a purchasing department cannot optimize them separately (Aissaoui et al., 2007 and Rezaei and Davoodi, 2011). Further, a few studies have reported that a firm can benefit by integrating purchasing quantities and inbound transportation decisions (Russell and Krajewski, 1991, Swenseth and Godfrey, 2002 and Mansini et al., 2012). The buyer can select an appropriate size carrier or negotiate the discounts rates with third party logistics providers (3PL) to reduce the inbound transportation cost. Hence, incorporating the decision to schedule orders over time with the supplier selection and appropriate transportation carrier selection may significantly reduce total cost over the planning horizon. In spite of many advantages, the models that have been proposed in the literature on inventory lot-sizing with supplier selection, have not sufficiently considered economies of scale in the purchasing and transportation costs. Nowadays, disruptions have become more common in supply chains, which lead to supply chain risks (Giannakis and Louis, 2011). Supply chain disruptions such as rejections and late deliveries also affect the procurement decisions (Choudhary and Shankar, 2011). If buyer includes quality and delivery related performance aspects in purchasing decisions then suppliers may be motivated to increase their performance on these criteria in subsequent periods. Above observations have been used to develop an integrated model for inventory lot-sizing, supplier selection, and carrier selection problems. We investigate a problem in which a single product is procured from multiple suppliers, in multiple periods, considering economies of scale concepts in purchasing and transaction costs, and supply chain disruptions such as rejections and late deliveries. Since, logistics cost plays a key role in inventory lot-sizing, supplier and carrier selection, it is necessary to incorporate economies of scale in purchasing and transportation costs. We consider all-unit quantity discount structure for purchasing cost, and carrier size as well as geographical location dependent discount structure for transportation cost at full truck loads (FTL) capacity. We consider all realistic constraints in purchasing and inventory management such as buyer's demand, service level requirement and storage capacity, and suppliers' production capacity, discounts, rejections and late deliveries. The proposed model permits time dependent variations in problem parameters such as suppliers' quality and delivery performance, price, production capacity, and buyer's ordering cost, inventory holding cost, transportation cost, storage capacity, service level, etc. The intent of this model is to determine the right timings of procurement, appropriate lot-sizes and its supplier(s), and carrier(s) for transportation of the items. The paper is further organized as follows: Section 2 presents a brief literature review of the existing relevant quantitative approaches related to multi-period procurement lot-sizing with supplier selection problem. In Section 3, an integer linear programming formulation is proposed for joint decision making of procurement lot-sizing, supplier selection, and carrier selection problem considering all-unit quantity discounts, transportation discounts, and supply chain disruptions. Section 4 presents a numerical example with solution to demonstrate the effectiveness of the proposed approach. Managerial implications of proposed approach are discussed in Section 5. Finally, conclusions, limitations, and directions for future research are provided in Section 6.

Inventory lot-sizing with supplier selection and carrier selection are important decisions any buyer has to make. A buyer cannot optimize them separately due to inherent interdependency among these decisions. Selecting the right suppliers and splitting lot-sizes to the selected suppliers over multi-period decision horizon become a major challenge for a buyer when suppliers offer quantity discounts with unreliable quality and delivery performance. Further, complexity in decision making process increases if a buyer has to select an appropriate size carrier considering economy of scale in transportation cost. Therefore, model-based decision support is required to find optimal procurement strategy for given purchasing environment. This paper presents an integer linear programming approach for joint decision making of multi-period procurement lot-sizing, supplier selection, and carrier selection problem. The proposed model can be used to simultaneously determine the timings of procurement, what lot-size should be procured and from which supplier, and which size carrier should be chosen for transporting procured lot-size from each selected supplier. We have studied a procurement setting in which a buyer needs to purchase a single product from three suppliers using three different size carriers. We considered economies of scale in purchasing and transportation costs, and supply chain disruptions due to rejections and late deliveries in purchasing process. The computational results show that proposed model is sensitive to the problem parameters. In realistic procurement environment, a buyer needs to purchase a product from a large number of suppliers at many price break levels using large number of different size carriers. This makes the problem harder to solve using commercial optimization solver. The complexity of the model can be expressed by the number of constraints and binary variables. Overall, the proposed model has t(4imj+2i+j+4) constraints and t(3imj+i+2) variables, of which t(2imj+i) are binary variables. Therefore, an effective and efficient heuristic or evolutionary algorithm is required to solve a large size problem using proposed formulation. Simulated annealing method or scatter search algorithm appears to be promising methods for this purpose ( Raza and Akgunduz, 2008 and Ebrahim et al., 2009). In this study, we present managerial insights derived from a small size problem. There is a need to analyze large scale problems for generalization of these findings. Furthermore, future research might include several products. If there were two products, both managed by same pool of suppliers, consolidated shipment of a mixed load could be delivered to the buyer. The point is that two or more products would allow additional economies in transportation and purchasing costs.