انتخاب تامین کننده در محیط ساخت برای سفارش همراه با ریسک

The problem of allocation of orders for parts among part suppliers in a customer driven supply chain with operational risk is formulated as a stochastic single- or bi-objective mixed integer program. Given a set of customer orders for products, the decision maker needs to decide from which supplier to purchase parts required for each customer order to minimize total cost and to mitigate the impact of delay risk. The selection of suppliers and the allocation of orders is based on price and quality of purchased parts and reliability of on time delivery. To control the risk of delayed supplies, the two popular percentile measures of risk are applied: value-at-risk and conditional value-at-risk. The proposed approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing mean worst-case cost per part simultaneously. Numerical examples are presented and some computational results are reported.

An important issue in supply chain risk management is how to best allocate the orders for parts among various part suppliers to fulfill customer orders for products at low cost and to mitigate the impact of risk. The selection of supply portfolio in the presence of supply chain delay risk, i.e., the supplier selection and order allocation under uncertain quality of supplied materials and reliability of on-time delivery, is based on price, quality (defect rate) and reliability (on-time delivery rate) criteria that may conflict with each other. Furthermore, to reduce the fixed ordering costs, the number of suppliers and the total number of orders should be minimized. However, to mitigate the impact of delay risk the selection of more suppliers sometimes may divert the risk of unreliable supplies. In spite of the importance of supplier selection and order allocation problems, the decision making is not sufficiently addressed in the literature (for a recent review, see [1], in particular for the make-to-order manufacturing environment, e.g. [2], [3], [4], [5] and [6]. The vast majority of the decision models are mathematical programming models with either a single objective, e.g. [7] and [8] or multiple objectives, e.g. [9], [10], [11], [12] and [13]. The models developed for supplier selection and order allocation can be either single-period models (e.g. [9] and [11]) that do not consider inventory management or multi-period models (e.g. [8], [12], [14] and [15]) which consider the inventory management by lot-sizing and scheduling of orders. Since common parts can be efficiently managed by material requirement planning methods, this research is focused on custom parts that can be critical in make-to-order manufacturing. For custom-engineered products no inventory of custom parts can be kept on hand. Instead, the custom parts need to be requisitioned with each customer order and hence the custom parts inventory need not to be considered. When selecting suppliers and allocating orders to generate a supply portfolio, the producer faces uncertain costs and must place orders with a set of suppliers with different quality and reliability. In stochastic supply settings, supplier selection allows the producer to decide whether it should cooperate with low cost, yet risky suppliers over more expensive but possibly more reliable suppliers. A common risk-neutral objective of minimizing expected cost is therefore influenced by uncertainty and risk. As a result, new non-risk-neutral objectives of minimizing the number of outcomes that could occur above an acceptable cost level are observed in practice. Although, the supplier selection problem is stochastic in nature, research seldom considers uncertainty and risk (see, [16]). For example, chance-constrained programming models were developed by Kasilingam and Lee [7] to account for stochastic demand and by Wu and Olson [13] to consider expected losses from quality acceptance inspection or late delivery. Feng et al. [17] use the stochastic integer programming to model the relationship between manufacturing cost, quality loss cost, assembly yield, and discrete tolerances. In Sawik [5], a portfolio approach is proposed for the problem of allocation of orders for custom parts among suppliers in make-to-order manufacturing. The problem is formulated as a single- or multi-objective mixed integer program with the risk of defective or unreliable supplies controlled by the maximum number of delivery patterns (combinations of suppliers’ delivery dates) for which the average defect rate or late delivery rate can be unacceptable. Then, in Sawik [6] the portfolio approach has been enhanced to consider a single-period supplier selection and order allocation in the presence of supply chain disruption risks. In this paper, the portfolio approach presented in [5] and [6] has been enhanced to consider a single-period supplier selection and order allocation in the make-to-order environment in the presence of supply chain delay risk. The mixed integer programming models are proposed for a single- or bi-objective static supplier selection and order allocation, that is for the allocation of orders for parts among the suppliers with no timing decisions. In contrast to the dynamic portfolio, which is the allocation of orders among the suppliers combined with the allocation of orders among the planning periods. The proposed portfolio approach allows the two popular in financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied for managing the risk of supply delays. The proposed mixed integer programming models provide the decision maker with a simple tool for evaluating the relationship between expected and worst-case costs. This paper demonstrates that for a finite number of scenarios, CVaR allows the evaluation of worst-case costs and shaping of the resulting cost distribution through optimal supplier selection and order allocation decisions, i.e., the selection of optimal supply portfolio. VaR and CVaR have been widely used in financial engineering in the field of portfolio management (e.g. [18]). CVaR is used in conjunction with VaR and is applied for estimating the risk with non-symmetric cost distributions. Uryasev [19] and Rockafellar and Uryasev [20] and [21] introduced a new approach to select a portfolio with the reduced risk of high losses. The portfolio is optimized by calculating VaR and minimizing CVaR simultaneously. For example, this approach has been applied to solution of the newsvendor problem (e.g. [22]) or recently to risk averse selection of orders, where the approach is combined with a scenario-based method [23]. The paper is organized as follows. In Section 2 a description of the supplier selection problem in a customer driven supply chain with risks is provided. The mixed integer programs for a single objective selection of supply portfolio to minimize either the expected cost per part or expected worst-case cost part are developed in Section 3. The trade-off (mean-risk) model for a bi-objective selection of supply portfolio is presented in Section 4. Numerical examples and some computational results are provided in Section 5, and final conclusions are made in the last section.

The problem of optimal allocation of orders for parts among a set of approved suppliers in a customer driven supply chain under conditions of risk associated with uncertain reliability of suppliers has been modeled as a portfolio-type stochastic mixed integer program. The proposed portfolio approach is capable of optimizing the supply portfolio by calculating value-at-risk of cost per part and minimizing conditional value-at-risk of cost per part simultaneously, over a set of delivery scenarios. The supply portfolio is selected based on the expected cost per part of ordering, purchasing and delay penalty and/or the expected worst-case cost per part. The two alternative objective functions were either considered separately or simultaneously in a bi-objective optimization problem. While a single objective approach is capable of finding an optimal, either risk-neutral supply portfolio that minimizes the expected cost per part or risk-averse supply portfolio that minimizes the expected worst-case cost per part, the trade-off model: mean–risk, focuses on varying cost/risk preference of the decision maker and provides her/him with a subset of nondominated portfolios. The trade-off model has been formulated as the optimization of a weighted-sum of the expected cost and the CVaR as a risk measure. The limited computational experiments prove that the proposed approach based on mixed integer programming models provides the decision maker with a simple tool for evaluating the relationship between expected and worst-case costs. The optimal risk-neutral or risk averse supply portfolio can be found within CPU seconds for a limited number of scenarios considered, using the CPLEX solver for mixed integer programming. The experiments show that in a risk-neutral environment the more costly suppliers are rarely selected. On the other hand, in a non-risk-neutral environment the number of selected suppliers increases with the confidence level αα, which indicates that the impact of delay risks is mitigated by diversification of the supply portfolio. An important issue that needs to be further considered is the estimation of probabilities and the resulting costs associated with delay risks. Future research on supplier selection in customer driven supply chains with risks should also focus on various enhancements of the proposed approach. For example, the delivery scenarios should combine the low impact supply chain delay risk with a high impact disruption risk referring to the major disruptions to normal activities caused by natural or man-made disasters such as earthquakes, floods, labor strikes, terrorist attacks. In most cases, the business impact associated with disruption risks is much greater than that of the delay risk. Finally, in a more general setting, the selection of a dynamic, multi-period supply portfolio should be considered, with the joint decisions: what, where and when to order, made over a time horizon (see, [8]).