Achieving High Individual Service-Levels without Safety Stock? Optimal Rationing Policy of Pooled Resources

Jiashuo, Jiang,; Wang, Shixin; Zhang, Jiawei

doi:10.2139/ssrn.3385089

Cited by 6 publications

(10 citation statements)

References 49 publications

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“…\end{equation}$$We refer interested readers to Jiang et al. (2022) for more examples of the feasible set

\mathcal {S}(x,d)

.…”

Section: Modelmentioning

confidence: 99%

“…Recently, Jiang et al. (2022) considered a framework for a very general resource pooling problem with service‐level constraints. The main difference between our paper and Jiang et al.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Recently, resource pooling problems focusing on improving service levels have received considerable attention from both academics and practitioners (Jiang et al., 2022; Zhong et al., 2018). Different types of service‐level constraints have been proposed in the operations management literature.…”

Section: Introductionmentioning

confidence: 99%

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Target‐based resource pooling problem

Cui

Ding

Xie

et al. 2023

Production and Operations Management

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We study a two-stage resource pooling problem with multiple resources and customers. The central decision-maker decides the capacity level of the resources within a total budget before the realization of uncertain demand. Then, the fulfillment policy is determined by individual service-level requirements. We use a robust satisficing framework to formulate the problem and allow ambiguity in the distribution of demand. Moreover, we introduce a new utility-based probability distance allowing the model to be solved exactly using a column and constraint generation algorithm. We also provide a more efficient solution method for some special cases. Finally, we conduct experiments for a process flexibility problem, which is an example of the resource pooling problem. We show the advantage of our model over some benchmark approaches, and show the impact of the flexibility structure and correlation between demands.

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“…\end{equation}$$We refer interested readers to Jiang et al. (2022) for more examples of the feasible set

\mathcal {S}(x,d)

.…”

Section: Modelmentioning

confidence: 99%

“…Recently, Jiang et al. (2022) considered a framework for a very general resource pooling problem with service‐level constraints. The main difference between our paper and Jiang et al.…”

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Target‐based resource pooling problem

Cui

Ding

Xie

et al. 2023

Production and Operations Management

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“…Our Long-run vs. Shortrun Fairness objectives distinguish between "fairness in expectation" vs. "fairness on every realization", which correspond to the "Type-II" vs. "Type-III" service rates studied in Operations Management. A comprehensive discussion of these different ways to measure service (from which our fairness metrics are defined) can be found in the stream of work which studies inventory pooling and supply chain rationing to meet service targets [Zhong et al, 2018, Lyu et al, 2019a, Jiang et al, 2019. However, to our knowledge, this literature has focused on service in an offline setting, with the exception of , who incorporate these service definitions into the constraints instead of a max-min objective like we do.…”

Section: Related Workmentioning

confidence: 99%

Group-level Fairness Maximization in Online Bipartite Matching

Ma,

Xu,

2020

Preprint

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In typical online matching problems, the goal is to maximize the number of matches. This paper studies online bipartite matching from the perspective of group-level fairness, and the goal is to balance the number of matches made across different groups of online nodes. We assume that an online node's group belongings are revealed upon arrival, and measure performance based on the group with the smallest fraction of its nodes matched at the end. We distinguish between two different objectives: long-run fairness, where the algorithm is audited for its fairness over many realizations from the same instance; and short-run fairness, where the algorithm is audited for its fairness on a single realization.We focus on the known-IID model of online arrivals and analyze, under both objectives, the competitive ratio for two classes of algorithms: non-rejecting algorithms, which must match an online node as long as a neighbor is available; and general online algorithms, which are allowed to reject online nodes to improve fairness. For long-run fairness, we analyze two online algorithms (sampling and pooling) which establish asymptotic optimality across many different regimes (no specialized supplies, no rare demand types, or imbalanced supply/demand). By contrast, outside all of these regimes, we show that the competitive ratio for online algorithms is between 0.632 and 0.732. For short-run fairness, we focus on the case of a complete bipartite graph and show that the competitive ratio for online algorithms is between 0.863 and 0.942; we also derive a probabilistic rejection algorithm which is asymptotically optimal as total demand increases.

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“…As explained in detail inLien et al (2014), even though the daily demand for food donations from different agencies are not temporally scattered, they will only be observed by the operators upon their arrival at the sites.4 Other recent papers have focused on fairness in the contexts of pricing(Cohen et al 2019), information acquisition(Cai et al 2020), targeted interventions(Levi et al 2019), service levels(Jiang et al 2019), and online learning(Gupta and Kamble 2019). See also the work ofCayci et al (2020) that considers fair resource allocation with online learning.…”

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confidence: 99%

Fair Dynamic Rationing

Manshadi¹,

Niazadeh²,

Rodilitz³

2021

Preprint

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We study the allocative challenges that governmental and nonprofit organizations face when tasked with equitable and efficient rationing of a social good among agents whose needs (demands) realize sequentially and are possibly correlated. As one example, early in the COVID-19 pandemic, the Federal Emergency Management Agency faced overwhelming, temporally scattered, a priori uncertain, and correlated demands for medical supplies from different states. To better achieve their dual aims of equity and efficiency in such contexts, social planners intend to maximize the minimum fill rate across agents, where each agent's fill rate must be irrevocably decided upon its arrival. For an arbitrarily correlated sequence of demands, we establish upper bounds on both the expected minimum fill rate (ex-post fairness) and the minimum expected fill rate (ex-ante fairness) achievable by any policy. Our bounds are parameterized by the number of agents and the expected demand-to-supply ratio, and they shed light on the limits of attaining equity in dynamic rationing.Further, we show that for any set of parameters, a simple adaptive policy of projected proportional allocation achieves the best possible fairness guarantee, ex post as well as ex ante. Our policy is transparent and easy to implement, as it does not rely on distributional information beyond the first conditional moments.Despite its simplicity, we demonstrate that this policy provides significant improvement over the class of non-adaptive target-fill-rate policies by characterizing the performance of the optimal such policy, which relies on full distributional knowledge. We obtain the performance guarantees of (i) our proposed adaptive policy by inductively designing lower-bound functions on its corresponding value-to-go, and (ii) the optimal target-fill-rate policy by establishing an intriguing connection to a monopoly-pricing optimization problem.Further, we extend our results to considering alternative objective functions and to rationing multiple types of resources. We complement our theoretical developments with a numerical study motivated by the rationing of COVID-19 medical supplies based on a projected-demand model used by the White House. In such a setting, our simple adaptive policy significantly outperforms its theoretical guarantee as well as the optimal target-fill-rate policy.

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Achieving High Individual Service-Levels without Safety Stock? Optimal Rationing Policy of Pooled Resources

Cited by 6 publications

References 49 publications

Target‐based resource pooling problem

Target‐based resource pooling problem

Group-level Fairness Maximization in Online Bipartite Matching

Fair Dynamic Rationing

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