Two-Stage Stochastic Inventory Optimization for the Assemble to Order System

doi:10.12068/j.issn.1005-3026.2024.06.020

Abstract

Abstract:

Based on the replenishment strategy for the basic inventory level of parts and components， a two?stage stochastic optimization model is constructed with multi‐period uncertain order product demands. In the first stage， the basic inventory level of components is the decision variable and needs to be determined at the condition of unknown demands， and the objective is to achieve the maximum system revenue. In the second stage， the order assignment variable is designed when the order due date constraint is required， and the objective of this stage is to maximize the expected order revenue by taking order revenue and tardiness penalty into account. Additionally， a single?stage deterministic model by transforming the uncertain demand to the determined expected demand is presented and the objective function value of this deterministic model is compared with that of the stochastic model. The numerical experiment results show the performance of the stochastic model is worse than that of the deterministic model， which indicates some value of the unknown information. Meanwhile， a sensitive analysis is implemented for the parameters in the model and a strategy is put forward to improve the system revenue in practice.

Key words: basic inventory level, two?stage stochastic optimization, assemble to order （ATO）system, uncertain demand, order assignment

CLC Number:

TP 205

Ke JING, Yu LIU, Le-hua LI. Two-Stage Stochastic Inventory Optimization for the Assemble to Order System[J]. Journal of Northeastern University(Natural Science), 2024, 45(6): 905-912.

Figures/Tables 4

References 16

1	李智.面向订单装配的生产管理系统研究［J］.中国制造业信息化（学术版），2005，34（9）：88-93.
	Li Zhi.Research on production management system for assemble to order［J］.Informatization of China’s Manufacturing Industry：Academic Edition，2005，34（9）：88-93.
2	金鑫，王正肖，叶建芳，等.非平稳需求面向订单装配系统库存稳定性研究［J］.计算机集成制造系统，2020，26（9）：2531-2540.
	Jin Xin， Wang Zheng‑xiao， Ye Jian‑fang，et al.Inventory stability of ATO system with non‑stationary demand［J］.Computer Integrated Manufacturing Systems，2020，26（9）：2531-2540.
3	Agrawal N， Cohen M A.Optimal material control in an assembly system with component commonality［J］.Naval Research Logistics，2001，48（5）：409-429.
4	Song J.A note on assemble‑to‑order systems with batch ordering［J］.Management Science，2000，46（5）：739-743.
5	Lu Y， Song J， Yao D D.Order fill rate，leadtime variability，and advance demand information in an assemble‑to‑order system［J］.Operations Research，2003，51（2）：292-308.
6	Hoen K M R， Güllü R， van Houtum G J，et al.A simple and accurate approximation for the order fill rates in lost‑sales assemble‑to‑order systems［J］.International Journal of Production Economics，2011，133（1）：95-104.
7	陈文博，董明.产能不确定时M型按订单装配产品（ATO）的多周期最优零部件补货策略［J］.工业工程与管理，2017，22（6）：63-70.
	Chen Wen‑bo， Dong Ming.Optimal component replenishment policy for a multi‐period M type assembly‐to‐order（ATO）with random supply capacity［J］.Industrial Engineering and Management，2017，22（6）：63-70.
8	ElHafsi M， Fang J X， Hamouda E.A novel decomposition‐based method for solving general‑product structure assemble‑to‑order systems［J］.European Journal of Operational Research，2020，286（1）：233-249.
9	Akçay Y， Xu S H.Joint inventory replenishment and component allocation optimization in an assemble‑to‑order system［J］.Management Science，2004，50（1）：99-116.
10	Huang K.Optimal FCFS allocation rules for periodic‐review assemble‑to‑order systems［J］.Naval Research Logistics，2015，62（2）：158-169.
11	Reiman M I， Wang Q.Asymptotically optimal inventory control for assemble‑to‑order systems with identical lead times［J］.Operations Research，2015，63（3）：716-732.
12	Sinha A K， Krishnamurthy A.Dual index production and subcontracting policies for assemble‑to‑order systems［J］.IIE Transactions，2016，48（5）：415-427.
13	Bortolini M， Faccio M， Gamberi M， al et，MTO/MTS policy optimization for sheet metal plate parts in an ATO environment［J］.Procedia CIRP，2019，81：1046-1051.
14	Chu J， Huang K.Integrating decisions with advance supply information in an assemble‑to‑order system［J］.Naval Research Logistics，2020，67（1）：34-44.
15	Feng J X， Zhang M， Yang J L.New necessary and sufficient condition for the irreducibility of joint inventory positions in an assemble‑to‑order system［J］.Operations Research Letters，2021，49（2）：171-175.
16	金鑫，王正肖，叶建芳，等.可拆分ATO系统的最优、渐进最优和次优库存控制策略［J］.计算机集成制造系统，2022，28（2）：426-441.
	Jin Xin， Wang Zheng‑xiao， Ye Jian‑fang，et al.Optimal，asymptotically optimal and suboptimal inventory control policies for detachable ATO systems［J］.Computer Integrated Manufacturing Systems，2022，28（2）：426-441.

i	1	2	3	4	5	L_i	c_i
1	2	0	3	4	1	20	6
2	3	2	0	5	1	30	10
3	0	3	2	2	2	10	1
4	5	0	0	1	4	10	9
5	0	3	1	0	3	40	5
W_j	1	1	2	3	1	—	—
r_j	80	70	80	100	50	—	—

i	1	2	3	4	5	L_i	c_i
1	2	0	3	4	1	20	6
2	3	2	0	5	1	30	10
3	0	3	2	2	2	10	1
4	5	0	0	1	4	10	9
5	0	3	1	0	3	40	5
W_j	1	1	2	3	1	—	—
r_j	80	70	80	100	50	—	—

T	B	SGB	GB1	GB2	V1/%	V2/%	运行时间/s
T	B	SGB	GB1	GB2	V1/%	V2/%	SGB	GB1	GB2
10	2 000	102 710.00	107 420.24	107 721.00	4.59	4.88	10.676	8.678	0.584
	2 500	104 914.00	113 000.71	113 385.00	7.71	8.07	11.227	6.981	0.566
	3 000	107 042.00	118 542.83	118 960.00	10.74	11.13	10.388	7.222	0.543
	3 500	109 149.00	124 047.51	124 491.00	13.65	14.06	11.844	7.053	0.868
15	2 000	135 067.00	164 608.05	165 393.00	21.87	22.45	20.972	17.319	0.588
	2 500	137 374.00	171 254.60	172 078.00	24.66	25.26	19.401	19.572	0.590
	3 000	139 566.00	177 809.30	178 697.00	27.40	28.04	20.021	16.573	0.696
	3 500	141 732.00	184 279.35	185 279.00	30.02	30.72	20.192	16.087	0.568

T	B	SGB	GB1	GB2	V1/%	V2/%	运行时间/s
T	B	SGB	GB1	GB2	V1/%	V2/%	SGB	GB1	GB2
10	2 000	102 710.00	107 420.24	107 721.00	4.59	4.88	10.676	8.678	0.584
	2 500	104 914.00	113 000.71	113 385.00	7.71	8.07	11.227	6.981	0.566
	3 000	107 042.00	118 542.83	118 960.00	10.74	11.13	10.388	7.222	0.543
	3 500	109 149.00	124 047.51	124 491.00	13.65	14.06	11.844	7.053	0.868
15	2 000	135 067.00	164 608.05	165 393.00	21.87	22.45	20.972	17.319	0.588
	2 500	137 374.00	171 254.60	172 078.00	24.66	25.26	19.401	19.572	0.590
	3 000	139 566.00	177 809.30	178 697.00	27.40	28.04	20.021	16.573	0.696
	3 500	141 732.00	184 279.35	185 279.00	30.02	30.72	20.192	16.087	0.568