疫情爆发初期应急采购最优启动时间点选择

doi:10.16381/j.cnki.issn1003-207x.2021.2631

Abstract

Abstract:

Rational allocation of emergency medical resource is crucial for epidemic prevention and control. However， in the early stage of the epidemic， emergency departments are often difficult to accurately predict its spread trend in the first time， and need to update and revise the prediction results through continuous learning of new information in the later stage. Thus， early launch of emergency procurement plans may lead to idle resources due to the inaccurate prediction of epidemic evolution， and late launch may lead to the risk of resource shortage. In this context， optimal selection of the start time of resource procurement becomes an important decision problem faced by emergency departments.Since the 21st century， emergency procurement problems has been widely concerned and deeply studied by scholars. However， most of the existing studies only focus on supplier selection， order allocation， contract design problems under the background of natural disasters such as earthquake and hurricane， but little attention is paid to the start point selection of emergency procurement under the background of epidemic. In particular， compared with natural disasters， the evolution of the epidemic has dynamic and time-varying characteristics， which brings new challenges to the procurement optimization problem.In this context， a novel emergency procurement optimization problem is present under the epidemic situation. Firstly， in order to obtain the optimal start time of emergency procurement， an epidemic observation stopping time （or emergency start-up time） judgment rules is proposed， and the boundary characteristics and influencing factors of the optimal start-up time are analyzed. Secondly， in order to obtain an effective supplier selection and order allocation scheme after starting procurement， a novel mixed integer programming model is proposed after comprehensively considering the differences of each supplier in order quantity， supply capacity， procurement lead time and shortage risk. Thirdly， the above two problems are integrated and a data-driven framework model of emergency procurement is constructed based on the optimization process of “epidemic prediction， emergency response effect comparison， stop-judgment and parameter update”. Finally， the model is applied in a case study， and the simulation results show that the data-driven model not only ensures that procurement decisions are based on epidemic data， but also ensures that epidemic data are updated in real time.

Key words: epidemic, relief procurement, data-driven, optimal stopping

CLC Number:

O225

Yin Xiang. Optimal Selection of Relief Procurement Time in the Early Stage of Epidemics[J]. Chinese Journal of Management Science, 2024, 32(2): 210-220.

Figures/Tables 11

当前决策期 $τ 1$	未来决策期 $τ 2$
当前决策期 $τ 1$	$τ 2$ =2	$τ 2$ =3	$τ 2$ =4	$τ 2$ =5
$τ 1$ =1	$F (1 → 2)$	$F (1 → 3)$	$F (1 → 4)$	$F (1 → 5)$
$τ 1$ =2	×	$F (2 → 3)$	$F (2 → 4)$	$F (2 → 5)$
$τ 1$ =3	×	×	$F (3 → 4)$	$F (3 → 5)$
$τ 1$ =4	×	×	×	$F (4 → 5)$
$τ 1$ =5=\|T\|	×	×	×	×

求解算法

1. 初始化模型输入参数，令 $τ 1 = 1, τ 2 = 2, τ * = ?$

2. While $τ 1 < | T | - 1$

3. 预测后续 ${τ 1 + 1, …, | T |}$ 期的资源需求 $D F (τ 1)$ ，通过求解“模型1”并结合式(15)计算在 $τ 1$ 启动应急采购时整个疫情期的系统成本 $F (τ 1)$

4. While $τ 2 < | T |$

5. 依据资源预测需求 $D F (τ 1)$ ，通过求解“模型1”并结合式(15)计算在 $τ 2$ 启动应急采购时整个疫情期的系统成本 $F (τ 1 → τ 2)$

6. 令 $τ 2 = τ 2 + 1$

7. End

8. If $F (τ 1) ≤ F (τ 1 → τ 2)$ ，其中 $τ 2 ∈ {τ 1 + 1, …, | T | - 1}$

9. 停止疫情观测，记录最优的停止观测时间为 $τ * = τ 1$ ，退出while循环并转到第14行

10. Else

11. 令 $τ 1 = τ 1 + 1$ ，令 $τ 2 = τ 1 + 1$ ，继续观测疫情，更新传染病模型参数并继续迭代

12. End

13. End

14. If $τ * = | T | - 1$ 且 $I V τ * ≥ D F | T | (τ *) + Θ$

不启动应急采购

15 Else

16. 将最优采购启动时间 $τ *$ 带入模型，算出最优的供应商选择和订单分配方案 $x (τ) 、 y (τ)$

17.End

情境

特点

计算方法

参数说明

情境1

(预测偏小)

各期预测需求小于真实值，但偏差不断减少

D F t (τ 1) = α + (1 - α) ? τ 1 | T | ? D R t

$τ 1$ :决策期{1,2，…，|T|-1}; |T|:疫情初期时长

$D F t (τ 1)$ ： $τ 1$ 预测到 $t ∈ {τ + 1, …, | T |}$ 期的需求

$D R t$ ：各个时期t的真实需求

$α, β$ ：预测偏差系数， $α = 0.5, β = 1.5$

情境2

(预测偏大)

各期预测需求大于真实值，但偏差不断减少

D F t (τ 1) = β - (β - 1) ? τ 1 | T | ? D R t

需求	1	2	3	4	5	6	7	8	9	10
$D R t$	45	62	121	198	258	363	425	495	572	618
$D F t ∈ {2 . . . 10} (τ 1 = 1)$		34	67	109	142	200	234	272	315	340
$D F t ∈ {3 . . . 10} (τ 1 = 2)$			73	119	155	218	255	297	343	371
$D F t ∈ {4 . . . 10} (τ 1 = 3)$				129	168	236	276	322	372	402
$D F t ∈ {5 . . . 10} (τ 1 = 4)$					181	254	298	347	400	433
$D F t ∈ {6 . . . 10} (τ 1 = 5)$						272	319	371	429	464
$D F t ∈ {7 . . . 10} (τ 1 = 6)$							340	396	458	494
$D F t ∈ {8 . . . 10} (τ 1 = 7)$								421	486	525
$D F t ∈ {9,10 \|} (τ 1 = 8)$									515	556
$D F t ∈ {10} (τ 1 = 9)$										587

需求	1	2	3	4	5	6	7	8	9	10
$D R t$	45	62	121	198	258	363	425	495	572	618
$D F t ∈ {2 . . . 10} (τ 1 = 1)$		90	175	287	374	526	616	718	829	896
$D F t ∈ {3 . . . 10} (τ 1 = 2)$			169	277	361	508	595	693	801	865
$D F t ∈ {4 . . . 10} (τ 1 = 3)$				267	348	490	574	668	772	834
$D F t ∈ {5 . . . 10} (τ 1 = 4)$					335	472	553	644	744	803
$D F t ∈ {6 . . . 10} (τ 1 = 5)$						454	531	619	715	773
$D F t ∈ {7 . . . 10} (τ 1 = 6)$							510	594	686	742
$D F t ∈ {8 . . . 10} (τ 1 = 7)$								569	658	711
$D F t ∈ {9,10 \|} (τ 1 = 8)$									629	680
$D F t ∈ {10} (τ 1 = 9)$										649

s	*co_s*	*l_s*	*m_s*	*cp_s*	*up_s*	$η s$
1	0.8	1	50	14	30	3
2	0.9	2	40	13	40	1
3	1	4	50	11	70	1
4	0.5	4	60	11	60	5
5	0.9	3	40	12	55	2
6	0.8	5	60	11	50	3
7	0.8	1	70	10	55	2
8	0.9	1	30	14	25	1
9	0.8	2	40	12	40	2
10	0.7	2	20	15	35	4

$τ 1$	$F (τ 1)$	$τ 2$
		2	3	4	5	6	7	8	9
		$F (τ 1 → 2)$	$F (τ 1 → 3)$	$F (τ 1 → 4)$	$F (τ 1 → 5)$	$F (τ 1 → 6)$	$F (τ 1 → 7)$	$F (τ 1 → 8)$	$F (τ 1 → 9)$
1	4.198	4.194	4.191	4.188	4.185	4.181	4.178	4.175	4.172
2	4.405	0	4.402	4.398	4.395	4.391	4.388	4.385	11.011
3	4.612	0	0	4.609	4.605	4.601	4.598	4.594	27.481
4	5.306	0	0	0	5.303	5.299	5.547	6.113	44.980
5	5.558	0	0	0	0	5.554	5.847	20.233	61.880
6	5.760	0	0	0	0	0	6.091	34.023	78.550

$τ 1$	$F (τ 1)$	$τ 2$
		2	3	4	5	6	7	8	9
		$F (τ 1 → 2)$	$F (τ 1 → 3)$	$F (τ 1 → 4)$	$F (τ 1 → 5)$	$F (τ 1 → 6)$	$F (τ 1 → 7)$	$F (τ 1 → 8)$	$F (τ 1 → 9)$
1	7.898	7.892	7.886	7.879	7.873	7.867	68.976	139.787	221.710
2	7.689	0	7.683	7.678	7.672	7.666	59.280	127.614	206.769
3	7.477	0	0	7.471	7.466	7.460	48.086	114.044	190.327
4	7.216	0	0	0	7.211	7.205	35.868	99.470	172.985
5	6.955	0	0	0	0	6.950	24.072	85.200	155.843
6	6.744	0	0	0	0	0	12.750	71.427	138.559

IV₀	实验1	实验2		实验3		实验4
IV₀	最优采购启动时期	min(LT)	最优采购启动时期	$α$	最优采购启动时期	$β$	最优采购启动时期
500	4	1	6	0.5	6	1.5	4
1000	6	2	5	0.6	6	1.4	5
1500	6	3	4	0.7	6	1.3	5
2000	6	4	3	0.8	5	1.2	5
2500	8	5	2	0.9	5	1.1	5

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Optimal Selection of Relief Procurement Time in the Early Stage of Epidemics

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s	*co_s*	*l_s*	*m_s*	*cp_s*	*up_s*	$η s$
1	0.8	1	50	14	30	3
2	0.9	2	40	13	40	1
3	1	4	50	11	70	1
4	0.5	4	60	11	60	5
5	0.9	3	40	12	55	2
6	0.8	5	60	11	50	3
7	0.8	1	70	10	55	2
8	0.9	1	30	14	25	1
9	0.8	2	40	12	40	2
10	0.7	2	20	15	35	4

s	*co_s*	*l_s*	*m_s*	*cp_s*	*up_s*	$η s$
1	0.8	1	50	14	30	3
2	0.9	2	40	13	40	1
3	1	4	50	11	70	1
4	0.5	4	60	11	60	5
5	0.9	3	40	12	55	2
6	0.8	5	60	11	50	3
7	0.8	1	70	10	55	2
8	0.9	1	30	14	25	1
9	0.8	2	40	12	40	2
10	0.7	2	20	15	35	4

s	*co_s*	*l_s*	*m_s*	*cp_s*	*up_s*	$η s$
1	0.8	1	50	14	30	3
2	0.9	2	40	13	40	1
3	1	4	50	11	70	1
4	0.5	4	60	11	60	5
5	0.9	3	40	12	55	2
6	0.8	5	60	11	50	3
7	0.8	1	70	10	55	2
8	0.9	1	30	14	25	1
9	0.8	2	40	12	40	2
10	0.7	2	20	15	35	4