供应商选择群决策建模与多源多时段采购优化
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摘要
供应链环境下供应商选择的战略作用日益突出,它直接关系着企业的运营成本、运作效率及客户服务水平。由于资源限制和供需不确定性,大型企业或工程建设单位往往根据多个目标或准则先选定几个固定的供应商,再根据实际情况进行订单分配。为了减少供应链不确定性的影响及促进合作伙伴关系的需要,供需方之间往往签订一定形式的采购契约。安全库存作为应对供应链不确定性的一种重要手段,对于降低成本和提高客户服务水平具有重要作用。因此,如何根据供应链环境的特点,建立支持供应商选择、订单分配与安全库存配置优化的决策方法,对于丰富和发展供应链管理与决策分析理论,促进供应链成功运作具有重要的学术价值与实践意义。
本文在对供应商选择、订单分配与安全库存配置的研究现状与发展趋势进行总结和分析的基础上,针对供应商选择群决策建模,以及需求随机、资源有限和特定契约环境多时间段多供应商订单分配与安全库存配置进行了较深入的研究。
首先,提出几种新的多属性群决策方法并应用于供应商选择。基于群体理想解的方法,将TOPSIS法扩展到群决策,始终基于群体理想解进行求解,利用群体理想解取代群体效用,利于区分方案优劣。偏好序下对专家综合赋权的逼近理想解法,给出基于专家主观权重一次性求解专家综合权重的方法,避免将主观和客观权重合成综合权重时无法有效确定加权系数的难题;将TOPSIS法扩展到序数偏好,避免逆序的产生。最小化序数偏好距离法,定义两种序数偏好距离,并证明其中一种满足Cook等从社会选择角度提出的几个条件,将Cook-Seiford社会选择函数扩展到多属性决策且考虑权重的情形,可较好地避免排序结果的非唯一性。
然后,研究特定契约下多供应商多时间段订单分配优化。针对多对一的两层供应链,每个供应商对采购方各时段采购量有最小、最大约束,对总采购量有最小约束的情形,先假设需求确定、不允许缺货,以采购方多时段货物、库存、运输成本总和最小为目标建立优化模型,给出多维动态规划与启发式算法相结合的两阶段解法。进而假设各时段需求随机且独立、允许缺货,以采购方多时段货物、库存、缺货成本总和与期末库存残值的差的期望值最小为目标,先考虑阶段采购量区间约束及多供应商,扩展基本报童模型得出单时段的最优采购策略,再以此为基础建立多时段启发式算法,然后通过仿真分析多个参数对最优采购策略及其总成本的影响。从而将最小总量承诺契约扩展到多供应商及时变需求情形,也是对传统报童模型向多供应商、多时间段、资源有限与特定契约四个方向的同时扩展。
最后,讨论需求随机与资源有限的多周期安全库存配置。针对一对一的两层供应链,假设需求随机、供应商有订货批量约束、采购方库容有限,采用粒子群算法求得使采购方相邻两次订货时点之间单位时间的订购、货物、库存及缺货成本总和期望值最小的(R,Q)库存控制策略,并对相关参数进行敏感性分析,结果表明最优再订货点和最优订货批量均与产品价格有关,有时不持有安全库存可能更优。而后进一步考虑累进制数量折扣,给出基于粒子群算法的求解方法,通过算例和仿真讨论了供应商选择问题。从而纠正了(R,Q)策略研究的一些不妥之处,将安全库存研究扩展到资源有限与特定契约情形;可为采购方选择具有不同固定订货费、产品价格、订货批量约束以及数量折扣菜单的供应商提供依据。
Supplier selection in supply chains plays a more and more important strategic role in reducing cost, increasing efficiency and improving service. In view of resource constraints and uncertainties of demand and supply, large enterprises and project construction units usually select several suppliers according to multiple objectives or attributes at first, and then allocate orders among them. In order to reduce the impact of supply chain uncertainties and promote cooperation relationship, suppliers and demanders usually sign some bilateral contracts with each other. As an effective method for disposing the uncertainties in supply chains, setting up safety stock plays an important role in reducing cost and improving customer service. So developing some methods supporting supplier selection, order allocation and safety stock placement is of important academic and practical significance to enrich and perfect supply chain management and decision analysis theories and promote effective operation of supply chains.
This paper summarized and analyzed the situation and development trend of researches on supplier selection, order allocation and safety stock placement, and then did some research on supplier selection group decision-making modeling, and multi-period and multi-supplier order allocation and safety stock placement in the presence of stochastic demands, resource constraints and supply chain contracts.
Firstly, several new multi-attribute group decision-making models were developed for supplier selection. The method based on group's ideal solutions which extended the technique for order preference by similarity to ideal solution (TOPSIS) to group decision-making, substituted group's ideal solution for group utility and was beneficial to differentiate the alternatives. The TOPSIS with experts' synthetic weights under ordinal preferences in which a new expert's synthetic weights setting method was proposed and this methodology can avoid the conundrum of set the weighting coefficient when synthesizing subjective expert' weights with objective ones to synthetic weights, generalizes TOPSIS to ordinal preferences and eliminates rank reversal. The method minimizing the distances of ordinal preferences in which two distance functions for ranking vectors were defined and one of which was been proved to satisfy the conditions proposed by Cook and Seiford in social selection theory and the methodology extends Cook-Seiford social selection function to multi-attribute decision-making with weights and may avoid non-uniqueness of the solutions for the same decision-making problem.
Secondly, multi-supplier and multi-period order allocation optimization under some supply chain contracts was investigated. The order allocation problems in multi-supplier and one-buyer scenario where every supplier specified the minimum and maximum of the quantity purchased each period and the total minimum purchased over the predetermined plan horizon were researched as follows. Under the conditions of certain demands and no short a model minimizing the sum of purchase cost, inventory cost and transportation cost of the buyer over the plan horizon was developed and for which a solution integrating multi-dimensional dynamic programming and heuristic algorithm was proposed. For the scenario where demands in every period are stochastic and independent and the stockout is permitted, an optimization model was developed and which minimized the expected value of the total cost including purchase, inventory, stockout cost and salvage value of the ending inventory for the buyer over the plan horizon. At first, the optimal procurement policy in single period was obtained according to the newsboy model after the order constraints and multiple suppliers were considered. Then the heuristic policy for multi-period procurement was derived from the one in single period. Some simulations were made to show the effect of the parameters on the optimal policy and the minimum cost. This work extends the total minimum contract to the stochastic and non-stationary demands and multiple suppliers setting, and extends newsboy model to the setting with multi-supplier, multi-period, resource constraints and supply chain contracts.
Finally, multi-period safety stock placement with stochastic demands and resource constraints was dealt with. For a one-supplier and one-buyer supply chain with stochastic demands, order lot size constraints from the supplier and the buyer's storage capacity constrains, an optimization model was developed and which minimized the expected value of the sum of order, purchase, inventory, and stockout cost in unit time between two successive order when the buyer used (R, Q) policy. A solution based on particle swarm optimization (PSO) was proposed and some case study and simulations were made. The results showed that the optimal reorder point and the optimal order quantity is dependent on the product price and that holding no safety stock may be optimal in some cases. Then the incremental quantity discounts was taken into account and a PSO-based algorithm was developed to obtain the optimal (R, Q) policy and selection supplier for the buyer. The works correct some mistakes in published literatures on (R, Q) optimization and extend safety stock research to the settings with resource constraints and supply chain contracts. These results can provide a theoretic basis for the buyer to select the suppliers with different ordering cost, product price, order quantity constraints and quantity discount menu.
本文在对供应商选择、订单分配与安全库存配置的研究现状与发展趋势进行总结和分析的基础上,针对供应商选择群决策建模,以及需求随机、资源有限和特定契约环境多时间段多供应商订单分配与安全库存配置进行了较深入的研究。
首先,提出几种新的多属性群决策方法并应用于供应商选择。基于群体理想解的方法,将TOPSIS法扩展到群决策,始终基于群体理想解进行求解,利用群体理想解取代群体效用,利于区分方案优劣。偏好序下对专家综合赋权的逼近理想解法,给出基于专家主观权重一次性求解专家综合权重的方法,避免将主观和客观权重合成综合权重时无法有效确定加权系数的难题;将TOPSIS法扩展到序数偏好,避免逆序的产生。最小化序数偏好距离法,定义两种序数偏好距离,并证明其中一种满足Cook等从社会选择角度提出的几个条件,将Cook-Seiford社会选择函数扩展到多属性决策且考虑权重的情形,可较好地避免排序结果的非唯一性。
然后,研究特定契约下多供应商多时间段订单分配优化。针对多对一的两层供应链,每个供应商对采购方各时段采购量有最小、最大约束,对总采购量有最小约束的情形,先假设需求确定、不允许缺货,以采购方多时段货物、库存、运输成本总和最小为目标建立优化模型,给出多维动态规划与启发式算法相结合的两阶段解法。进而假设各时段需求随机且独立、允许缺货,以采购方多时段货物、库存、缺货成本总和与期末库存残值的差的期望值最小为目标,先考虑阶段采购量区间约束及多供应商,扩展基本报童模型得出单时段的最优采购策略,再以此为基础建立多时段启发式算法,然后通过仿真分析多个参数对最优采购策略及其总成本的影响。从而将最小总量承诺契约扩展到多供应商及时变需求情形,也是对传统报童模型向多供应商、多时间段、资源有限与特定契约四个方向的同时扩展。
最后,讨论需求随机与资源有限的多周期安全库存配置。针对一对一的两层供应链,假设需求随机、供应商有订货批量约束、采购方库容有限,采用粒子群算法求得使采购方相邻两次订货时点之间单位时间的订购、货物、库存及缺货成本总和期望值最小的(R,Q)库存控制策略,并对相关参数进行敏感性分析,结果表明最优再订货点和最优订货批量均与产品价格有关,有时不持有安全库存可能更优。而后进一步考虑累进制数量折扣,给出基于粒子群算法的求解方法,通过算例和仿真讨论了供应商选择问题。从而纠正了(R,Q)策略研究的一些不妥之处,将安全库存研究扩展到资源有限与特定契约情形;可为采购方选择具有不同固定订货费、产品价格、订货批量约束以及数量折扣菜单的供应商提供依据。
Supplier selection in supply chains plays a more and more important strategic role in reducing cost, increasing efficiency and improving service. In view of resource constraints and uncertainties of demand and supply, large enterprises and project construction units usually select several suppliers according to multiple objectives or attributes at first, and then allocate orders among them. In order to reduce the impact of supply chain uncertainties and promote cooperation relationship, suppliers and demanders usually sign some bilateral contracts with each other. As an effective method for disposing the uncertainties in supply chains, setting up safety stock plays an important role in reducing cost and improving customer service. So developing some methods supporting supplier selection, order allocation and safety stock placement is of important academic and practical significance to enrich and perfect supply chain management and decision analysis theories and promote effective operation of supply chains.
This paper summarized and analyzed the situation and development trend of researches on supplier selection, order allocation and safety stock placement, and then did some research on supplier selection group decision-making modeling, and multi-period and multi-supplier order allocation and safety stock placement in the presence of stochastic demands, resource constraints and supply chain contracts.
Firstly, several new multi-attribute group decision-making models were developed for supplier selection. The method based on group's ideal solutions which extended the technique for order preference by similarity to ideal solution (TOPSIS) to group decision-making, substituted group's ideal solution for group utility and was beneficial to differentiate the alternatives. The TOPSIS with experts' synthetic weights under ordinal preferences in which a new expert's synthetic weights setting method was proposed and this methodology can avoid the conundrum of set the weighting coefficient when synthesizing subjective expert' weights with objective ones to synthetic weights, generalizes TOPSIS to ordinal preferences and eliminates rank reversal. The method minimizing the distances of ordinal preferences in which two distance functions for ranking vectors were defined and one of which was been proved to satisfy the conditions proposed by Cook and Seiford in social selection theory and the methodology extends Cook-Seiford social selection function to multi-attribute decision-making with weights and may avoid non-uniqueness of the solutions for the same decision-making problem.
Secondly, multi-supplier and multi-period order allocation optimization under some supply chain contracts was investigated. The order allocation problems in multi-supplier and one-buyer scenario where every supplier specified the minimum and maximum of the quantity purchased each period and the total minimum purchased over the predetermined plan horizon were researched as follows. Under the conditions of certain demands and no short a model minimizing the sum of purchase cost, inventory cost and transportation cost of the buyer over the plan horizon was developed and for which a solution integrating multi-dimensional dynamic programming and heuristic algorithm was proposed. For the scenario where demands in every period are stochastic and independent and the stockout is permitted, an optimization model was developed and which minimized the expected value of the total cost including purchase, inventory, stockout cost and salvage value of the ending inventory for the buyer over the plan horizon. At first, the optimal procurement policy in single period was obtained according to the newsboy model after the order constraints and multiple suppliers were considered. Then the heuristic policy for multi-period procurement was derived from the one in single period. Some simulations were made to show the effect of the parameters on the optimal policy and the minimum cost. This work extends the total minimum contract to the stochastic and non-stationary demands and multiple suppliers setting, and extends newsboy model to the setting with multi-supplier, multi-period, resource constraints and supply chain contracts.
Finally, multi-period safety stock placement with stochastic demands and resource constraints was dealt with. For a one-supplier and one-buyer supply chain with stochastic demands, order lot size constraints from the supplier and the buyer's storage capacity constrains, an optimization model was developed and which minimized the expected value of the sum of order, purchase, inventory, and stockout cost in unit time between two successive order when the buyer used (R, Q) policy. A solution based on particle swarm optimization (PSO) was proposed and some case study and simulations were made. The results showed that the optimal reorder point and the optimal order quantity is dependent on the product price and that holding no safety stock may be optimal in some cases. Then the incremental quantity discounts was taken into account and a PSO-based algorithm was developed to obtain the optimal (R, Q) policy and selection supplier for the buyer. The works correct some mistakes in published literatures on (R, Q) optimization and extend safety stock research to the settings with resource constraints and supply chain contracts. These results can provide a theoretic basis for the buyer to select the suppliers with different ordering cost, product price, order quantity constraints and quantity discount menu.
引文
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