Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916092756099072 |
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| author | van Jaarsveld, Willem Arts, Joachim |
| author_facet | van Jaarsveld, Willem Arts, Joachim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_07519 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes van Jaarsveld, Willem Arts, Joachim Probability Optimization and Control 60, 90 G.3 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. |
| title | Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes |
| topic | Probability Optimization and Control 60, 90 G.3 |
| url | https://arxiv.org/abs/2101.07519 |