Abstract: In recent years, the blood shortage in mainland China has become increasingly serious, endangering people’s lives and health safety. In order to increase the blood collection volume and alleviate the blood shortage, it is necessary to improve the layout system of blood collection facilities, optimize the allocation of blood collection resources, and construct an efficient and reliable blood collection network. There are two types of blood collection facilities, fixed blood collection houses and mobile blood donation vehicles. Blood collection houses are permanent facilities that, once established, are difficult to change in the short term. Blood donation vehicles are mobile facilities whose location decisions are variable from one period to the next. Therefore, the problem is defined as a dynamic optimization problem of location-resource allocation integration for two types of heterogeneous blood collection points. Therefore, this study proposes a heterogeneous blood collection point location-resource allocation integrated decision optimization problem under uncertain environments. The problem addresses the following decisions. Where should fixed blood collection houses be located? How to dynamically locate blood collection points for mobile blood donation vehicles? How to dynamically allocate resources such as blood collection personnel and equipment to blood collection facilities?
   China’s blood collection practice shows that the number of volunteers and blood supply at blood collection points cannot be obtained directly. Comprehensive assessment of candidate locations for blood collection vehicles and blood collection houses by means of key indicators and then determining the coverage weights will make the decision of optimizing the location of blood collection points more reasonable and operational. These key indicators include: the flow of people in the target area, the accessibility of people, the level of blood collection service, the activity of blood donation, and the interval between blood collection periods. A comprehensive multi-attribute evaluation of the above key indicators can obtain their coverage values. In this study, the generalized maximum coverage model is introduced to establish an integrated decision-making model of blood collection point location-resource allocation with the goal of maximizing the coverage weight. Subject to the constraints of realistic factors, the number of available blood donation vehicles, personnel and equipment available for allocation in each period are uncertain. Robust optimization techniques are used to deal with the uncertainties in the parameters of available blood donation vehicles, personnel and equipment. The corresponding robust optimization model is developed based on linear programming dyadic theory.
   Aiming at the characteristics of the model, an improved grey wolf optimization algorithm (IGWO) is designed to solve the model. The improvement strategies are as follows. Firstly, the dynamic weighting factor is introduced to accelerate the convergence speed of the algorithm and improve the optimization performance. Secondly, the simulated annealing Metropolis criterion is introduced to prevent the algorithm from falling into premature maturity. Thirdly, the 3-opt local optimization strategy is introduced. The above improvements better balance the exploration and exploitation capabilities of the algorithm.
   Different cases with different sizes are set up to test the performance of IGWO and compare it with the traditional grey wolf optimization algorithm (GWO) and particle swarm optimization algorithm (PSO). The results show that IGWO has obvious advantages in convergence speed, solution accuracy, and stability of solution compared with traditional GWO and PSO, which proves the effectiveness of the proposed algorithm.
   The results also show that although the robust optimization makes the total coverage of the localization points decrease, the decrease ratio is small, in which the optimal value gap is only 0.19%. Thus, robust optimization reduces the risk caused by uncertainty. In a realistic decision-making environment, the uncertainty of the parameters should be fully considered for robust optimization of the positioning and resource allocation decisions of blood collection points to reduce the risk of uncertainty.

Key words: facility location, resource allocation, robust optimization, GWO, blood supply chain

摘要： 为提高血液采集量、缓解血液短缺现状,研究不确定环境下两类采血点定位-资源配置集成决策优化问题。首先,考虑区域人流量、献血活跃度等因素对采血点权重的影响,基于广义最大覆盖模型,建立以覆盖权重最大为目标的采血点定位-资源配置集成决策模型。在此基础上,采用鲁棒优化技术处理可用献血车、人员和设备等参数的不确定性,建立相应的鲁棒优化模型。针对模型特点,设计改进的灰狼优化算法对模型进行求解。数值结果表明,改进的灰狼优化算法优于传统灰狼优化算法与粒子群算法。

关键词: 设施选址, 资源配置, 鲁棒优化, 灰狼优化算法, 血液供应链