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Optimal structure of joint inventory-pricing management with dual suppliers and different lead times

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We consider a joint inventory-pricing control problem in a single-product, periodic-re-view, dual-supplier inventory system. The two suppliers have different lead times. One expedited supplier offers instantaneous replenishment, and one regular supplier requires an L-period lead time for delivery. The supply quantity is stochastic and the demand is price-dependent. For the expedited inventory replenishment, we characterize the optimal policy as a state-dependent almost-threshold policy by extending the stochastically linear in mid-point to a multidimensional setting. To investigate the optimal regular inventory replenishment and pricing policy, we propose the notions of partially stochastic translation (PST) and increasing partially stochastic translation (IPST), which help in obtaining the antimultimodularity preservation in dynamic programming problems. We provide prop-erties, sufficient conditions, and examples for PST and IPST functions. By applying PST and IPST, we obtain the antimultimodularity of the profit functions. The antimultimodular profit functions ensure that the optimal regular ordering quantity and the optimal price are monotone in the current inventory level and outstanding order quantities. Moreover, we reveal that as the time interval increases, the effects of previous outstanding orders on the optimal regular ordering and pricing decisions are decreasing and increasing, respectively. PST and IPST also enable us to further characterize the optimal expedited ordering quantity as decreasing in the inventory level. However, the optimal expedited ordering quantity can be non-monotone with respect to the outstanding order quantities, as shown in the example.

Inventory-pricing controlDual supplyLead timeAntimultimodularity

Xiaoyi Feng、Yangyang Xie、Shouyang Wang、Houmin Yan

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Department of Risk Strategy,The Hongkong and Shanghai Banking Corporation Limited,Hong Kong,China

International Institute of Finance,School of Management,University of Science and Technology of China,Hefei,Anhui,230026,China

University of the Chinese Academy of Sciences,Beijing,100049,China

Department of Management Sciences,College of Business,City University of Hong Kong,Hong Kong,China

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This research is supported in part by NSFCThis research is supported in part by NSFCThis research is supported in part by NSFCThis research is supported in part by NSFCThis research is supported in part by NSFCNational Key&nbsp,R&D Program of ChinaFundamental Research Funds for the Central Universities&nbspUSTC Research Funds of the Double First-Class InitiativeUSTC Research Funds of the Double First-Class InitiativeUSTC Research Funds of the Double First-Class Initiative

72001198717310107198810171991464/719914602020AAA0103804/2020AAA0103800WK2040000027YD2040002004GRF Grant 115080/17

2021

管理科学学报(英文)

管理科学学报(英文)

ISSN：2096-2320
年,卷(期)：2021.6(1)
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