考虑居民聚集居住的家庭医疗护理调度研究

doi:10.16381/j.cnki.issn1003-207x.2024.2240

Abstract

Abstract:

With the rapid economic growth and accelerated urbanization in China， there is an increasing demand for health management and long-term disease treatment. Home health care （HHC） is a type of medical service where professional caregivers， such as nurses， therapists， or doctors， provide in-home care for patients. It mainly serves the elderly， people with chronic illnesses， or those recovering from surgery. It focuses on a novel home health care routing and scheduling problem for clustered residents in this paper. Unlike residents in Western countries who often live dispersedly， urban residents in China typically cluster together in communities， inevitably leading to a large number of requests for home healthcare services in the same area during the same period. The traditional “one caregiver per vehicle” service model， where each caregiver travels alone to visit patients， is simple to schedule but incurs high operational costs when patient locations are spatially clustered. To address this challenge， a novel team-based “multiple caregivers per vehicle” service model is proposed. In this model， multiple medical staff travel together on a bus， disembark at designated stops simultaneously， and individually provide personalized care to patients in the surrounding area. To minimize the total cost of home healthcare centers， a mixed-integer programming model is established， which simultaneously determines team composition， vehicle routes， and the sequence of patient visits for nurses. Given the NP-hardness of the studied problem， an improved adaptive large neighborhood search algorithm （IALNS） is developed to generate solutions. Considering the two-echelon routing structure arising from the team-based mode， a total of seven destroy operators and seven repair operators are specifically designed. To further improve the solution quality， a penalizing strategy is applied to handling infeasible solutions. Computational results on small-sized and large-sized test instances are conducted. For small-sized instances， IALNS performs better than CPLEX in terms of both solution quality and computation time. For large-sized instances， IALNS outperforms the simulated annealing （SA）， variable neighborhood search （VNS）， and ALNS allowing infeasible solutions. In addition， sensitivity analysis of key parameters is conducted to provide managerial insights to home healthcare centers. Most importantly， the team-based service model provides greater cost advantages compared to the traditional individual-caregiver model.

Key words: home health care, medical team, vehicle routing, scheduling, adaptive large neighborhood search

CLC Number:

TP301

Jie Zhou,Kai Wang. Home Health Care Scheduling for Clustered Residents[J]. Chinese Journal of Management Science, 2026, 34(9): 197-208.

Figures/Tables 15

符号	定义
参数
$V$	点的集合， $V = H C ⋃ P = 0,1, ⋯, p + 1$
$A$	弧的集合， $A = i, j i, j ∈ V, i ≠ j$
$H C$	医疗护理中心， $H C = 0, p + 1$
$P$	患者集合， $P = 1,2, ⋯, p$
$s i$	患者 $i ∈ P$ 的服务持续时间
$K v$	医疗护理中心可用的巴士集合， $K v = 1,2, ⋯, k v$
$K n$	医疗护理中心可用的医护人员集合， $K n = 1,2, ⋯, k n$
$k c$	每辆医疗巴士最多可搭载的医护人员数量， $k c ≤ k n$
$V T$	每辆医疗巴士的最大运行时长，包括行驶时长、停靠后的等待时长
$S T$	医护人员每次下车的最大工作时长，包括步行时长、等待患者时间窗开启时间、服务时长
$d i j$	点 $i ∈ V \ p + 1 与点 j ∈ V \ 0$ 之间的距离
$v k$	医疗巴士的平均行驶速度
$v n$	医护人员平均步行速度， $v n < v k$
$F$	每辆医疗巴士的固定成本
$c d$	每辆医疗巴士的单位距离行驶成本
$c h$	每辆医疗巴士的单位行驶时间成本
$c o$	每位医护人员的固定成本
$c t$	每位医护人员的单位时间工作成本
$e i, l i$	节点 $i ∈ V$ 的时间窗
$M$	一个足够大的正数
决策变量
$x i j k$	0-1变量，为1时表示医疗巴士 $k ∈ K v$ 经过弧 $i, j ∈ A$ ，否则为0
$y k n$	0-1变量，为1时表示医疗巴士 $k ∈ K v$ 搭载医护人员 $n ∈ K n$ ，否则为0
$y r k n$	0-1变量，为1时表示医疗巴士 $k ∈ K v$ 搭载的医护人员 $n ∈ K n$ 在停靠点 $r ∈ P$ 下车，否则为0
$f r i j k n$	0-1变量，为1时表示巴士 $k ∈ K v$ 搭载的医护人员 $n ∈ K n$ 在停靠点 $r ∈ P$ 步行出发，经过弧 $i, j ∈ A$ ，否则为0
$a i k$	医疗巴士 $k ∈ K v$ 到达停靠点 $i ∈ V \ 0$ 的时刻
$d i k$	医疗巴士 $k ∈ K v$ 从停靠点 $i ∈ P$ 出发的时刻
$d 0 k$	医疗巴士 $k ∈ K v$ 从医疗护理中心0出发的时刻
$w i k$	医疗巴士 $k ∈ K v$ 等待患者 $i ∈ P$ 服务时间窗开启的时长
$a j k n$	医疗巴士 $k ∈ K v$ 上下车的医护人员 $n ∈ K n$ 步行到达点 $j ∈ P$ 的时刻
$w j k n$	医疗巴士 $k ∈ K v$ 上下车的医护人员 $n ∈ K n$ 等待患者 $j ∈ P$ 服务时间窗开启的时长
$a r k - m a x$	在停靠点 $r ∈ P$ 从医疗巴士 $k ∈ K v$ 上下车的所有医护人员返回点 $r$ 的最晚时刻

参数名称	值
患者 $i$ 的服务时长 $s i$	20
每辆巴士最多可搭载的医护数量 $k c$	4
每辆巴士的最长工作时长 $V T$	300
医护人员每次下车最长工作时长 $S T$	120
巴士的平均时速 $v k$	60千米/小时
护理人员的平均步行速度 $v n$	6千米/小时
每辆巴士的固定成本 $F$	50
每辆巴士的单位距离行驶成本 $c d$	1
每辆巴士的单位时间行驶成本 $c h$	0.1
每位医护人员的操作成本 $c o$	10
每位医护人员单位时间工作成本 $c t$	0.01
随机生成的患者所占比例 $m$	$0,0.25,0.5,0.75$

算例 (p-m)	$o b j C p l e x$	$G A P 0$ /%	$o b j I A L N S$	$G A P 1$ /%	$T C p l e x$	$T I A L N S$
6-0	269.57	0	269.57	0	0.12	0.55
6-0.25	262.42	0	262.42	0	0.40	0.53
6-0.5	164.58	0	164.58	0	11.74	0.67
6-0.75	157.30	0	157.30	0	18.64	1.32
8-0	376.50	0	376.50	0	665.62	0.68
8-0.25	317.50	0	317.50	0	947.53	0.58
8-0.5	275.48	0	275.48	0	332.81	0.59
8-0.75	207.34	0	207.34	0	2891.87	1.73
10-0	497.95	0	497.95	0	1317.94	1.38
10-0.25	560.30	0	560.30	0	6078.95	0.83
10-0.5	521.58	0	521.58	0	1454.56	0.75
10-0.75	372.58	0	372.58	0	4186.31	2.16
12-0	734.82	0	734.82	0	1728.80	1.90
12-0.25	835.42	12.74	835.42	0	10800.00	0.79
12-0.5	605.95	0	605.95	0	5371.20	1.70
12-0.75	472.11	0	472.11	0	4495.60	1.70
14-0	890.72	33.60	891.89	0.13	10800.00	2.86
14-0.25	871.91	18.32	871.91	0	10800.00	1.45
14-0.5	807.08	66.55	789.47	-2.23	10800.00	1.48
14-0.75	837.84	85.64	673.76	-24.35	10800.00	3.16

算例 (p-m)	SA		VNS		ALNS		IALNS
算例 (p-m)	$B R P D$	$A R P D$	$B R P D$	$A R P D$	$B R P D$	$A R P D$	$B R P D$	$A R P D$
20-0	0.52	3.85	0.39	2.05	0.02	1.32	0.00	0.88
20-0.25	0.11	1.93	0.15	1.68	0.00	1.39	0.00	0.70
20-0.5	0.04	1.25	0.19	1.42	0.29	1.53	0.00	0.75
20-0.75	1.35	4.53	1.38	3.23	0.97	2.39	0.00	0.87
40-0	0.44	3.58	0.18	2.36	0.24	0.96	0.00	0.62
40-0.25	1.12	4.27	1.33	4.05	2.13	3.89	0.00	1.99
40-0.5	0.49	4.41	0.41	2.94	0.71	2.61	0.00	1.07
40-0.75	1.60	4.84	1.04	4.97	2.15	4.53	0.00	1.30
60-0	3.22	5.51	1.69	4.44	1.00	2.36	0.00	1.57
60-0.25	1.09	5.58	1.13	5.81	0.19	1.85	0.00	0.88
60-0.5	1.10	4.12	0.59	3.95	1.22	4.34	0.00	1.18
60-0.75	2.21	5.56	1.56	5.22	2.40	5.07	0.00	2.19
80-0	2.98	6.84	0.99	4.53	0.09	3.04	0.00	2.79
80-0.25	1.88	6.58	2.06	5.91	0.54	3.68	0.00	2.81
80-0.5	1.57	6.12	1.51	4.75	1.09	4.69	0.00	3.49
80-0.75	2.02	5.09	1.24	4.88	0.61	6.06	0.00	3.60
100-0	2.48	5.76	1.21	3.62	0.08	2.39	0.00	1.91
100-0.25	1.26	5.91	0.86	4.61	1.59	3.07	0.00	2.08
100-0.5	1.30	5.35	1.10	4.03	1.00	3.39	0.00	2.26
100-0.75	1.81	4.74	1.83	6.13	1.90	6.71	0.00	5.13
120-0	1.54	4.29	1.43	4.59	0.83	4.09	0.00	3.16
120-0.25	1.75	4.10	1.01	5.49	1.29	4.49	0.00	3.13
120-0.5	2.07	6.73	1.72	6.03	0.96	5.41	0.00	3.63
120-0.75	1.68	4.10	1.82	4.18	1.46	5.20	0.00	2.86
均值	1.48	4.79	1.12	4.20	0.95	3.52	0.00	2.12

算例 (p-m)	“一车多人”服务模式				“一人一车”服务模式
算例 (p-m)	巴士数	医护人员数	行驶距离	运营总成本	$∆$ 巴士数	$∆$ 医护人员数	$∆$ 行驶距离(%)	$∆$ 运营总成本(%)
20-0.75	5	8	432.16	804.11	1 $↑$	-2 $↓$	34.14 $↑$	21.73 $↑$
40-0.75	7	11	546.17	1046.59	1 $↑$	-3 $↓$	19.86 $↑$	11.14 $↑$
60-0.75	10	15	946.31	1645.12	2 $↑$	-3 $↓$	13.49 $↑$	8.49 $↑$
80-0.75	12	17	1209.50	2197.80	3 $↑$	-2 $↓$	12.26 $↑$	9.77 $↑$
100-0.75	15	23	1520.76	2834.30	5 $↑$	-3 $↓$	15.90 $↑$	11.25 $↑$
120-0.75	18	27	1731.02	3359.88	5 $↑$	-4 $↓$	14.17 $↑$	11.20 $↑$
平均值	11.17	16.83	1064.32	1981.30	2.83 $↑$	-2.83 $↓$	18.30 $↑$	12.27 $↑$

算例 (p-m)	$v k = 60 → v k = 30$
算例 (p-m)	$∆$ 巴士数量	$∆$ 医护数	$∆$ 行驶距离(%)	$∆$ 运营总成本(%)
20-0.75	-	4 $↑$	-0.89 $↓$	10.33 $↑$
40-0.75	1 $↑$	8 $↑$	-14.55 $↓$	8.27 $↑$
60-0.75	2 $↑$	7 $↑$	-3.50 $↓$	29.24 $↑$
80-0.75	3 $↑$	11 $↑$	-8.48 $↓$	21.75 $↑$
100-0.75	8 $↑$	15 $↑$	-4.92 $↓$	26.92 $↑$
120-0.75	3 $↑$	20 $↑$	-5.18 $↓$	10.72 $↑$
平均值	2.83 $↑$	10.83 $↑$	-6.25 $↓$	17.87 $↑$

算例 (p-m)	$S T = 120 → S T = 60$
算例 (p-m)	$∆$ 巴士数	$∆$ 医护数	$∆$ 行驶距离(%)	$∆$ 运营总成本(%)
20-0.75	-	1 $↑$	-0.44 $↓$	1.47 $↑$
40-0.75	-	-	1.18 $↑$	0.86 $↑$
60-0.75	1 $↑$	-	3.13 $↑$	6.61 $↑$
80-0.75	-	2 $↑$	-2.57 $↓$	2.70 $↑$
100-0.75	-	5 $↑$	-2.17 $↓$	3.09 $↑$
120-0.75	-	4 $↑$	-1.73 $↓$	2.26 $↑$
平均值	0.17 $↑$	2.00 $↑$	-0.43 $↓$	2.83 $↑$

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