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Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

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Willem van Jaarsveld, Joachim Arts

Probability · Submitted 19 Jan 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions.

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arXiv ID2101.07519 (version 4)
Pith IDVW6ZLDUZ, Pith's permanent record of this paper and its review
CitationJoachim Arts, Willem van Jaarsveld. "Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes." arXiv:2101.07519 (2021). https://pith.science/paper/VW6ZLDUZ
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,344 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.61 · human participants 0.01 · controlled comparison 0.79 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. background 1.00 0.20 0.02 asserted 0.70
s1 We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. contribution 0.71 0.94 0.07 asserted 0.99
s2 We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. result 0.96 0.96 0.60 asserted 1.00
s3 We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. result 0.97 0.96 0.19 asserted 1.00
s4 Numerical results show this policy also performs superior relative to other policies. result 1.00 0.94 0.11 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.73 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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