ادغام موضع عدم قطعیت در درون مسئله انتخاب تأمین کننده

Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.

Under the pressure of global competition, companies strive to achieve excellence in delivering high quality and low cost products to their customers on time and rely on the efficiency of their supply chain to gain competitive advantage. At the frontier of a supply chain, suppliers act as a key component for success because the right choice of suppliers reduces costs, increases profit margins, improves component quality and ensures timely delivery. Current supplier management trends show increasing interests in global sourcing, reducing the supplier base and establishing long-term relationships with the suppliers (Minner, 2003). Selecting suppliers is no longer an operational function but becomes a strategic level decision (Crama et al., 2004). When consolidating and reducing the number of suppliers, companies run the risk of not having sufficient raw materials to meet their fluctuating demand. These risks may be caused by natural disasters or man-made actions. A recent example is the fire that happened at one of Phillips’ microchip plants in 2000. Phillips lost about $40 million in sales. As a major customer of the chip plant, cell phone manufacturer Ericsson lost $2.34 billion in its mobile phone division (Bartholomew, 2006). The risks are further amplified by the current focus on supply chain efficiency and lean practices. A small disruption may ripple along the whole supply chain and cause significant business losses. As a result, there is a need to be able to evaluate the tradeoffs between the benefits of managing a few selected suppliers and the risks of not being able to meet the required demand. There can be substantial benefits if the companies plan flexibility into their supply chain to handle risks proactively. Another source of risk is associated with global sourcing. With long lead times and transportation routes, the expanded supply chain is vulnerable to disruptions along the routes. Even though overseas suppliers offer competitive price schedules, they also increase the risk of late delivery of sufficient quantity. Instead of increasing inventory levels to ensure a sufficient supply of raw materials, another option is to strategically determine the number and location of suppliers. By establishing relationships with carefully selected local and overseas suppliers, companies can add flexibility to their supply chain and reduce the risks of disruption without stockpiling. We develop stochastic mathematical programming models to capture the risk associated with uncertain customer demand and supplier capacity and to create a strategic purchasing plan. Moreover, we use multi-parametric programming techniques to analyze tradeoffs and determine a robust set of suppliers with balanced costs and risks. Recognizing the importance of the supplier selection decision, an extensive literature exists to address this kind of decision. These existing decision making models are essentially trying to answer the following basic questions: how many suppliers are appropriate, which suppliers to choose, and what is the optimal ordering/replenishing policy. Many deterministic models have been developed to answer these questions with varying considerations of quantity discount, lot size, or inventory management decisions (e.g., Dahel, 2003, Dai and Qi, 2007, Ghodsypour and O’Brien, 2001 and Narsimhan et al., 2006). The main disadvantage of deterministic models is their incapability of handling randomness embedded in the real system. Other researchers have been working on various probabilistic models and demonstrate the importance of incorporating randomness in the supplier selection problem. Typically they study the effect of random customer demand but do not incorporate uncertainty in the supply and the impact of potential disruption (Gutiérrez and Kouvelis, 1995, Kasilingam and Lee, 1996 and Velarde and Laguna, 2004). Two studies make an all-or-none assumption for supplier availability (Berger and Zeng, 2006 and Ruiz-Torres and Mahnoodi, 2007). Another complication to the supplier selection decision is the multi-criteria aspect. However, most of the literature that addresses uncertainties focuses on a single objective (e.g., Basnet and Leung, 2005, Bollapragada et al., 2004, Dada et al., 2007 and Yang et al., 2007). Dickson (1966) listed 23 selection criteria; however, quality, delivery and price have been identified as the prime criteria when purchasing industrial raw materials (Akarte et al., 2001 and Cameron and Shipley, 1985). Price mentioned here has a broader meaning nowadays; it includes the costs associated with the whole purchasing process and over the purchased item's entire life in addition to the purchasing price. Among these costs, transportation and inventory costs constitute a significant bulk. Therefore, our models consider quality, delivery, and cost (including the transportation and inventory costs) as selection goals in addition to a probabilistic measure of risk. We develop two optimization models to find a minimal set of suppliers to achieve quality and delivery goals while minimizing cost and the risk of having insufficient supply to meet demand. We incorporate uncertainties that may originate at the suppliers, or may be due to uncertain demand in our models. We also include business volume discounts to represent financial advantages in consolidating the supplier base. Globalization in the supplier base is reflected implicitly by the supplier capacity, the quoted price, the transportation cost, and the pipeline inventory cost in this study. Our models provide a means to explore the balance between the risk of not meeting the demand, the benefits of reduced number of suppliers, and the cost. The uncertainties in demand and supplier capacity are captured either by scenarios or with a probability distribution in the models. Not only the optimal supplier set but also ordering quantities are determined by the models. A multi-parametric analysis provides a means to explore tradeoffs between cost, risk, and number of suppliers in a closed form. A sample problem demonstrates the possibility to guard against supplier disruption by carefully weighing costs and risks in selecting a robust set of suppliers. This paper is organized as follows: Section 2 gives the problem formulations of a stochastic programming model and a chance-constrained programming model. Section 3 presents numerical results obtained from a sample problem and provides some guidelines for the sourcing decision. Section 4 discusses the multi-parametric programming approach to analyze the robustness of solutions and illustrates it on the sample problem. Section 5 summarizes this paper, points out the importance of inclusion of uncertainties into modeling, and the advantages of using a chance-constrained programming model with multi-parametric analysis to determine the robustness of the supplier selection decisions.

Selecting a robust set of suppliers requires balancing cost and risk, somewhat akin to a portfolio investment problem. A diverse set of suppliers, with respect to large versus small, local versus far away, high costs versus low costs, can be selected to reduce risk while managing costs. A multi-objective stochastic supplier selection problem with business volume discounts is studied in this paper. The problem is formulated as a SP model and a CCP model. Demand and supplier capacity uncertainties are considered explicitly in these models. The best set of suppliers and order quantities are optimized in these two models. The ɛ-constrainedɛ-constrained method is used to generate Pareto-optimal solutions. These Pareto-optimal solutions give decision makers a clear picture about the tradeoffs between number of suppliers, cost, and system reliability. Moreover, the developed models provide more robust solutions as compared to a deterministic MIP model. If the uncertainty is represented by scenarios, the SP model is preferable to a deterministic MIP model. If distributions are available, the CCP model can provide the Pareto-frontier in a straightforward manner, and in less computational time than the SP model. However, the relationship between the number of selected suppliers, the risks and the total costs is discretized. With the multi-parametric programming techniques, we are able to describe the relationship more completely using explicit linear functions. A benefit of the chance-constrained model becomes manifest here: the ability of applying multi-parametric programming techniques to address multi-criteria and uncertainty.