IMPULSE CONTROL WITH DISCONTINUOUS SETUP COSTS: DISCOUNTED COST CRITERION

doi:10.1137/19M1299244

CSpace > 应用数学研究所

	IMPULSE CONTROL WITH DISCONTINUOUS SETUP COSTS: DISCOUNTED COST CRITERION
	Xu, Fen 1,2; Yao, Dacheng3 ; Zhang, Hanqin 4
	2021
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	59 期号:1 页码:267-295
摘要	This paper studies a continuous-review backlogged inventory model considered by [K. L. Helmes, R. H. Stockbridge, and C. Zhu, SIAM J. Control. Optim., 53 (2015), pp. 2100-2140] but with discontinuous quantity-dependent setup cost for each order. In particular, the setup cost is characterized by a two-step function and a higher cost would be charged once the order quantity exceeds a threshold Q. Unlike the optimality of the (s, S)-type policy obtained by Helmes, Stockbridge, and Zhu for continuous setup cost with the discounted cost criterion, we find that, in our model, although some (s, S)-type policy is indeed optimal in some cases, the (s, S)-type policy cannot always be optimal. In particular, we show that there exist cases in which an (s, S) policy is optimal for some initial levels but it is strictly worse than a generalized (s, {S(x) : x <= s}) policy for the other initial levels. Under (s, {S(x) : x <= s}) policy, it orders nothing for x > s and orders up to level S(x) for x <= s, where S(x) is a nonconstant function of x. We further prove the optimality of such (s, {S(x) : x <= s}) policy in a large subset of admissible policies for those initial levels. Moreover, the optimality is obtained through establishing a more general lower bound theorem which will also be applicable in solving some other optimization problems by the lower bound approach.
关键词	inventory impulse control quantity-dependent setup cost (s, S) policy (s, S(x) : x <= s) policy
DOI	10.1137/19M1299244
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11771432] ; National Natural Science Foundation of China[11871461] ; National Natural Science Foundation of China[11401566]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000623931700011
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58294
专题	应用数学研究所
通讯作者	Yao, Dacheng
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, MADIS, CEMS, Beijing 100190, Peoples R China 4.Natl Univ Singapore, Dept Analyt & Operat, Singapore 119245, Singapore
推荐引用方式 GB/T 7714	Xu, Fen,Yao, Dacheng,Zhang, Hanqin. IMPULSE CONTROL WITH DISCONTINUOUS SETUP COSTS: DISCOUNTED COST CRITERION[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2021,59(1):267-295.
APA	Xu, Fen,Yao, Dacheng,&Zhang, Hanqin.(2021).IMPULSE CONTROL WITH DISCONTINUOUS SETUP COSTS: DISCOUNTED COST CRITERION.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,59(1),267-295.
MLA	Xu, Fen,et al."IMPULSE CONTROL WITH DISCONTINUOUS SETUP COSTS: DISCOUNTED COST CRITERION".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 59.1(2021):267-295.