انتخاب تامین کننده مشترک و برنامه ریزی سفارشات مشتری تحت ریسک های اختلال : تامین منابع واحد در مقابل دوگانه تامین منابع

This paper presents a stochastic mixed integer programming approach to integrated supplier selection and customer order scheduling in the presence of supply chain disruption risks, for a single or dual sourcing strategy. The suppliers are assumed to be located in two different geographical regions: in the producer's region (domestic suppliers) and outside the producer's region (foreign suppliers). The supplies are subject to independent random local disruptions that are uniquely associated with a particular supplier and to random semi-global (regional) disruptions that may result in disruption of all suppliers in the same geographical region simultaneously. The domestic suppliers are relatively reliable but more expensive, while the foreign suppliers offer competitive prices, however material flows from these suppliers are more exposed to unexpected disruptions. Given a set of customer orders for products, the decision maker needs to decide which single supplier or which two different suppliers, one from each region, to select for purchasing parts required to complete the customer orders and how to schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The problem objective is either to minimize total cost or to maximize customer service level. The obtained combinatorial stochastic optimization problem will be formulated as a mixed integer program with conditional value-at-risk as a risk measure. The risk-neutral and risk-averse solutions that optimize, respectively average and worst-case performance of a supply chain are compared for a single and dual sourcing strategy and for the two different objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported.

In make-to-order manufacturing, a typical customer driven supply chain consists of a number of part suppliers at different locations and one or more producers, where parts are supplied and assembled into finished products and next distributed to customers. In such supply chains, supply of parts and schedule of customer orders for finished products should be coordinated in an efficient manner to achieve a high customer service level at a low cost. The coordination is much more important in view of supply disruptions by unexpected natural or man-made disasters such as earthquakes, fires, floods, hurricanes or labor strikes, economic crisis, terrorist attack that may occur in global supply chains. The probability of such disaster events is very low, however their business impact can be very high. For example, the recent disruptions in the electronics supply chains due to the great East Japan earthquake of March 11, 2011 and then the catastrophic Thailand flooding of October 2011, where many component manufacturers were concentrated, resulted in huge losses of many Japanese companies, e.g., [1] and [2]. Most work on coordinated supply chain scheduling focuses on coordinating the flows of supply and demand over a supply chain network to minimize the inventory, transportation and shortage costs. For example, Chen and Vairaktarakis [3], Chen and Pundoor [4] and Pundoor and Chen [5] studied simplified models for integrated scheduling of production and distribution operations. The authors have analyzed computational complexity of various cases of the problem and have developed heuristics for NP-hard cases. Lei et al. [6] considered an integrated production, inventory and distribution routing problem involving heterogeneous transporters with non-instantaneous traveling times and many capacitated customer demand centers. A mixed programming approach combined with a heuristic routing algorithm was proposed to coordinate the production, inventory and transportation operations. Bard and Nananukul [7] developed a mixed integer programming model and a reactive tabu search-based algorithm for a transportation scheduling problem that included a single production facility, a set of customers with time-varying demand and a fleet of vehicles. Wang and Lei [8] considered the problem of operations scheduling for a capacitated multi-echelon shipping network with delivery deadlines, where semi-finished goods are shipped from suppliers to customers through processing centers, with the objective of minimizing the shipping and penalty cost. The three polynomial-time solvable cases of this problem were reported: with identical order quantities; with designated suppliers; and with divisible customer order sizes. Liu and Papageorgiou [9] developed a multi-objective mixed integer programming approach to address production, distribution and capacity planning of global supply chains considering cost, responsiveness and customer service level simultaneously. An integrated approach to deterministic coordinated supply chain scheduling was proposed by Sawik [10] to simultaneously schedule manufacturing and supply of parts and assembly of finished products. Given a set of part suppliers and a set of customer orders for finished products, the problem objective was to determine which orders were provided with parts by each supplier, to schedule manufacturing of parts at each supplier and delivery of parts from each supplier to the producer, and to schedule customer orders at the producer, such that a high customer service level was achieved and the total cost was minimized. The selection of part supplier for each customer order was combined with a due date setting for some orders to maximize the number of orders that can be completed by customer requested due dates. A monolithic mixed integer programming model was presented and compared with a hierarchy of mixed integer programs for a sequential selection of suppliers and scheduling of manufacturing and delivery of parts and assembly of products. Different enhancements of the above mixed integer programming approach for the coordinated scheduling in multi-stage supply chains were presented in Sawik [11]. Various perspectives on supply chain coordination issues were reported and reviewed by Arshinder et al. [12] and the gaps existing in the literature were identified. Li and Wang [13] reviewed coordination mechanisms of supply chain systems in a framework that was based on supply chain decision structure and nature of demand. A review of methods and literature on supply chain coordination through contracts was provided by Hezarkhani and Kubiak [14]. The supplier selection and order quantity allocation problem is a complex stochastic optimization problem, however the research on supplier selection under disruption risks is very limited. For example, risks associated with a supplier network was studied by Berger et al. [15], who considered catastrophic super events that affect all suppliers, as well as unique events that impact only one single supplier, and then a decision-tree based model was presented to help determine the optimal number of suppliers needed for the buying firm. Ruiz-Torres and Mahmoodi [16] considered unequal failure probabilities for all the suppliers. Berger and Zeng [17] studied the optimal supply size in a single or multiple sourcing strategy context, under a number of scenarios that are determined by various financial loss functions, the operating cost functions and the probabilities of all the suppliers being down. Yu et al. [18] considered the impacts of supply disruption risks on the choice between the single and dual sourcing methods in a two-stage supply chain with a non-stationary and price-sensitive demand. Yue et al. [19] introduced frontier sourcing portfolios to support manufacturers sourcing decisions, which consider the cost and probability of finishing the order on time. Ravindran et al. [20] developed multi-criteria supplier selection models incorporating supplier risks. In the multi-objective formulation, price, lead-time, disruption risk due to natural event and quality risk are explicitly considered as four conflicting objectives that have to be minimized simultaneously. Four different variants of goal programming were used to solve the multi-objective optimization problem. Xanthopoulos et al. [21] developed newsvendor-type inventory models for capturing the trade-off between inventory policies and disruption risks in a dual-sourcing supply chain network, where both supply channels are subject to disruption risks. The models were developed for both risk neutral and risk-averse decision-making. Sawik [22] and [23] proposed a portfolio approach for the supplier selection and order quantity allocation under disruption risks and applied the two popular in financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) (e.g., Sarykalin et al. [24], Yao et al. [25]) for managing the risk of supply disruptions. The two different types of disruption scenarios were considered: scenarios with independent local disruptions of each supplier and scenarios with local and global disruptions that may result in all suppliers disruption simultaneously. The resulting scenario-based optimization problem under uncertainty was formulated as a single- or bi-objective mixed integer program. In view of the recent trend of outsourcing and globalization, coordinated selection of part suppliers and allocation of order quantities and scheduling of customer orders may significantly improve performance of a multi-stage supply chain under disruption risks. However, the research on quantitative approaches to the coordinated supplier selection and customer order scheduling in the presence of supply chain disruption risks has not been reported in the literature. In a make-to-order environment, the supplier selection and order quantity allocation are a medium- to short-term decision, driven by the time-varying customer demand. Thus, the scheduling horizon for supplies of parts coincides with the scheduling horizon for customer orders and to achieve the best results the supplier selection and order quantity allocation decisions should also be made for the same time horizon. The advantage of a joint decision making can be shown especially in the presence of supply chain disruption risks. The major contribution of this paper is that it proposes a new stochastic mixed integer programming approach to integrated supplier selection and customer order scheduling in the presence of supply chain disruption risks, for a single or dual sourcing strategy. The suppliers are assumed to be located in two different geographical regions: in the producer's region (domestic suppliers) and outside the producer's region (foreign suppliers). The supplies are subject to independent random local disruptions that are uniquely associated with a particular supplier and to random semi-global (regional) disruptions that may result in disruption of all suppliers in the same geographical region simultaneously. The domestic suppliers are relatively reliable but more expensive, while the foreign suppliers offer competitive prices. However the foreign suppliers are more prone to breakdowns and material flows from these suppliers are more exposed to unexpected disruptions due to natural or man made disasters and longer shipping times and distance. Given a set of customer orders for products, the decision maker needs to decide which single supplier or which two different suppliers, one from each region, to select for purchasing parts required to complete the customer orders and how to schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The problem objective is either to minimize total cost of ordering and purchasing of parts plus penalty cost of delayed and unfulfilled customer orders due to the parts shortages or to maximize customer service level, i.e., the fraction of customer orders filled on or before their due dates. The resulting allocation of total demand for parts among the selected suppliers and the schedule of customer orders for every potential disruption scenario should be determined ahead of time, either to minimize the average or worst-case cost or to maximize the average or worst-case customer service level. The obtained combinatorial stochastic optimization problem will be formulated as a mixed integer program with conditional value-at-risk as a risk measure. The risk-neutral and risk-averse solutions that optimize, respectively average and worst-case performance of a supply chain are compared for a single or dual sourcing strategy and for the two different objective functions. Finally, some managerial insights on the choice between the two sourcing strategies are discussed. The paper is organized as follows. In Section 2 description of the integrated selection of suppliers and scheduling of customer orders in the presence of supply chain disruption risks is provided. The mixed integer programs for risk-neutral and risk averse solutions for both single and dual sourcing and the two objective functions are developed in Section 3. Numerical examples and some computational results are provided in Section 4, and final conclusions are made in the last section.

The integrated supplier selection, order quantity allocation and customer order scheduling studied in this paper arise in customer driven supply chains with disruption risks. The problem is a computationally difficult one because of its inherent combinatorial nature and the stochastic setting. The proposed mixed integer programming approach with conditional value-at-risk as a risk measure provides the decision maker with a simple tool for coordinating the flows of parts from suppliers to producer and the flows of finished products from producer to customers. The approach allows the decision maker for shaping the distribution of cost or customer service level by selecting the optimal supply portfolio and scheduling of customer orders. Given a set of customer orders for products with customer requested due dates as well as the corresponding demand for parts, an assignment of the demand to a single supplier or an allocation between two different suppliers is determined and the schedule of customer orders is found for each disruption scenario in such a way as to optimize the potential average or worst-case performance of a supply chain. Implicitly, the subsets of accepted and rejected (unfulfilled) customer orders are determined for each disruption scenario. Comparison of single and dual sourcing strategies indicates that for both the risk-neutral and the risk-averse solutions with a low confidence level, the same single supplier is selected only; a low price, risky supplier to minimize cost or an expensive, reliable supplier to maximize customer service level. In order to minimize the expected cost per product or CVaR of cost per product for low confidence levels, the cheapest supplier is usually selected. In contrast, to maximize the expected service level or CVaR of service level for low confidence levels, the most reliable supplier (with the lowest disruption probability) is mostly selected. For a higher confidence level, both single and dual sourcing models select a single, reliable supplier to minimize worst-case cost of unfulfilled customer orders or maximize worst-case customer service level. A difference between single and dual sourcing solutions arises only for the highest confidence levels. Then, for a dual sourcing and the risk-averse solutions with the highest confidence levels, an expensive, reliable supplier selected for lower confidence levels is additionally supported with a low price, risky supplier to allocate the total demand for parts between the two suppliers. However, the selection of the supporting risky supplier depends on the objective function: a cheaper and less reliable supplier is selected to reduce the risk of high costs and a more expensive and more reliable supplier is selected to reduce the risk of low service level. In general, the computational results indicate that the supplier reliability is a key selection parameter. To maximize service level the most reliable supplier is selected as the main one (for a dual sourcing) or the only one (for a single sourcing), whereas to minimize cost, the cheapest one is selected from among most reliable suppliers, respectively. For the limited number of scenarios considered, the proven optimal solution can be found, using the CPLEX solver for mixed integer programming. However, in the proposed models the number of scheduling variables x jts is O (hnq ) and the number of constraints is O((h+n)q)O((h+n)q), i.e., they grow linearly in the number q of disruption scenarios and hence exponentially in the number m of suppliers, if all q=2mq=2m potential scenarios are considered. In the proposed models the suppliers differ in price of offered parts and transportation time, while the quality of supplied parts is not considered. However, the models can be easily enhanced to account for the suppliers defect rates, e.g., [22] and [23] and also for quantity discounts and transportation costs, e.g., Mansini et al. [31]. Future research should concentrate on the enhancement of the proposed dual sourcing models for a multiple sourcing with multiple, more than two geographical regions, each subject to independent semi-global (regional) disruption risks. The future research should also focus on comparison of the proposed integrated supplier selection and customer order scheduling with a common hierarchical approach, where first the supplier selection and order quantity allocation subject to disruption risks is accomplished and then, given a schedule of part supplies, the optimal schedule of customer orders is determined for each disruption scenario, subject to parts availability constraints. The hierarchical approach can be based either on a two-stage stochastic programming or on a two-level deterministic equivalent of stochastic mixed integer programming.