A new approach to two-location joint inventory and transshipment control via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>♮</mml:mi></mml:mrow></mml:msup></mml:math>-convexity

Chen, Xin; Gao, Xiangyu; Hu, Zhenyu

doi:10.1016/j.orl.2014.11.007

Cited by 32 publications

(14 citation statements)

References 8 publications

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“…Their model differ significantly from Yang and Qin (2007)'s model in that the capacity T i is random and is realized after making the production decision y i , and thus the effective inventory level is Hu et al (2008) use a complicated induction argument to prove the preservation property of supermodularity and diagonal dominance of the cost-to-go function f k ðx 1 ; x 2 Þ (Hu et al 2008 actually consider the profit-to-go function, which can be regarded as the negative of f k ) and obtain the optimal polices. Later, Chen et al (2015) provide a new and simpler proof of this preservation result by showing L \ -convexity of a modified cost-to-go function f k ðx 1 ; Àx 2 Þ (i.e., changing one variable to its negative). Interestingly, since by Proposition 3.19…”

Section: Production Control Problems With Twomentioning

confidence: 99%

Discrete Convex Analysis and Its Applications in Operations: A Survey

Chen

2021

Production and Operations Management

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D iscrete convexity, in particular, L \ -convexity and M \ -convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, L \ -convexity and M \ -convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much more simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.

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Section: Production Control Problems With Twomentioning

confidence: 99%

Discrete Convex Analysis and Its Applications in Operations: A Survey

Chen

2021

Production and Operations Management

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“…Lateral transshipment is an effective approach to virtual inventory pooling and has a variety of applications as showcased in Yang and Qin (2007), Hu et al (2008), Abouee‐Mehrizi et al (2015) and Chen et al (2015). Most papers assume a negligible transshipment time (e.g., Zhao et al, 2008) or a deterministic transshipment time (e.g., Olsson, 2015) while our models allow a positive random transshipment time which is more compatible with our study in the global operations settings.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal and heuristic policies for production and inventory controls in dual supply chains with fluctuating demands

Lin

Chen

Bhatnagar

2023

Naval Research Logistics

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In the context of fast‐fashion business, we study the joint control of production, inventory, and unilateral transshipment in dual supply chains in which one supply chain is a responsive supply chain for fashion products and the other is an efficient supply chain for basic products in a fluctuating demand environment (FDE). Our research focuses on: (1) formulating an appropriate model for this complex problem; (2) characterizing the structured optimal policy, which can be used to develop effective heuristic policies; and (3) generalizing our studies for more applications. To address these issues, we formulate a discrete‐time finite‐horizon stochastic dynamic program model in which FDE is represented by a world state evolving in accordance with the discrete‐time Markov chain. The supply chain for the fashion product is modeled by a two‐stage tandem production system with a make‐to‐stock (MTS) stage for the fabric and a subsequent MTS stage for finished fashions. In parallel, the supply chain for the basic products is also modeled by a two‐stage tandem production system with a MTS stage for the fabric and a subsequent make‐to‐order (MTO) stage for finished basics. Further, the two supply chains are coupled via the unilateral transshipment of fabric with random transshipment time. By value iteration, we characterize the optimal policy for the single‐product problem with a set of monotone switching surfaces. The results are extended to the multi‐product multi‐supplier case. Further, based on the structure of the optimal policy, we develop a heuristic policy for the multi‐dimensional dynamic program model. From a practice perspective, we demonstrate the value of transshipment and controlled transshipment, analytically and numerically, and therefore justify the establishment of two separate local manufacturing bases in dual supply chains. Additionally, to achieve both quick response and efficiency, we show that the total cost can be reduced significantly if sufficient fabric is prepared just in time (JIT) for in‐season production at the beginning of a season.

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“…We compare our work with closely related research in Table 1. Note Chen et al (2015) and Li and Yu (2014) used methods similar to those we employ. However, our work is different from both in a number ways, which we detail next.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis in this paper employs a structural property called L ♮ ‐convexity, which has been used in the analysis of inventory models previously (Chen et al, 2015; Feng et al, 2019; Gong & Chao, 2013; Huh and Janakiraman, 2010; Pang et al, 2012; Zipkin, 2008); see Chen (2017) for a recent survey of L ♮ ‐convexity applications and Chen and Li (2021) for a comprehensive review of L ♮ ‐convexity, M ♮ ‐convexity and variants. Furthermore, two of the aforementioned papers studied a transshipment problem or a similar substitution problem using L ♮ ‐convexity.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, two of the aforementioned papers studied a transshipment problem or a similar substitution problem using L ♮ ‐convexity. More specifically, Chen et al (2015) investigated a lost‐sales version of Hu et al (2008) in which virtual transshipment is allowed, and established that the optimal cost functions are L ♮ ‐convex. Feng et al (2019) considered a periodic‐review inventory system of two substitutable products with positive replenishment lead times.…”

Section: Introductionmentioning

confidence: 99%

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Optimal replenishment and transshipment management with two locations

Keblis

Feng

et al. 2023

Naval Research Logistics

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We study the problem of optimally managing an inventory system with backorders over a finite time horizon where the objective is minimization of expected total discounted costs. The system consists of two locations each stocking the same product. At the beginning of each time period decisions are made about replenishment at each location and about any quantity to transship between the locations before demand is observed. Leveraging the L ♮ -convexity of the problem's cost function; we characterize the optimal replenishment and transshipment policy for this system. More specifically, we show the optimal policy can be described using switching curves monotone in the system state. We also discuss two extensions. For a lost-sales model, we establish L ♮ -convexity and apply it to characterize the optimal policy, simplifying the analysis found in previous work. In the other extension, we investigate the optimal policy for a partial transshipment problem where only one location orders from the external supply source and then transships to the other location.

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A new approach to two-location joint inventory and transshipment control via L♮-convexity

Cited by 32 publications

References 8 publications

Discrete Convex Analysis and Its Applications in Operations: A Survey

Discrete Convex Analysis and Its Applications in Operations: A Survey

Optimal and heuristic policies for production and inventory controls in dual supply chains with fluctuating demands

Optimal replenishment and transshipment management with two locations

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