Optimal Policies for a Finite-Horizon Production Inventory Model
This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule...
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| Published in: | Advances in Operations Research Vol. 2012; no. 2012; pp. 360 - 375 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cairo, Egypt
Hindawi Limiteds
01.01.2012
Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc |
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| ISSN: | 1687-9147, 1687-9155 |
| Online Access: | Get full text |
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| Abstract | This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan. |
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| AbstractList | This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan. |
| Author | Benkherouf, Lakdere Boushehri, Dalal |
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| CitedBy_id | crossref_primary_10_1080_23302674_2020_1803435 crossref_primary_10_1080_23270012_2020_1811787 crossref_primary_10_1002_qre_2408 crossref_primary_10_1080_23302674_2023_2235268 |
| Cites_doi | 10.1016/j.apm.2005.02.002 10.1016/S0377-2217(03)00222-4 10.1016/S0360-8352(01)00068-7 10.1137/070683945 10.1016/j.cie.2007.03.001 10.1016/S0377-2217(00)00133-8 10.2307/3009379 10.1016/S0377-2217(02)00296-5 10.1057/jors.1996.17 10.1057/jors.1977.142 10.1016/j.camwa.2010.07.047 10.1016/0925-5273(96)00033-3 |
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| Contributor | Boushehri, Dalal |
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| Copyright | Copyright © 2012 Lakdere Benkherouf and Dalal Boushehri. Copyright © 2012 Lakdere Benkherouf and Dalal Boushehri. Lakdere Benkherouf et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Copyright_xml | – notice: Copyright © 2012 Lakdere Benkherouf and Dalal Boushehri. – notice: Copyright © 2012 Lakdere Benkherouf and Dalal Boushehri. Lakdere Benkherouf et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| References | (1) 2005; 29 (5) 1977; 28 (9) 1996; 43 (12) 2001; 132 (4) 2009; 48 (6) 1979; 30 (10) 2002; 42 (11) 2007; 52 (7) 1996; 47 (2) 2003; 147 (3) 2004; 157 (8) 2010; 60 11 1 2 (9) 2002; 42 4 (12) 2005; 29 6 7 (3) 1996; 47 (10) 2007; 52 (8) 1996; 43 |
| References_xml | – volume: 42 start-page: 35 year: 2002 end-page: 42 ident: 10 article-title: An optimal batch size for a production system under linearly increasing-time varying demand process – volume: 28 start-page: 663 year: 1977 end-page: 670 ident: 5 article-title: Inventory replenishment policy for a linear trend in demand—an analytical solution – volume: 60 start-page: 2066 issue: 7 year: 2010 end-page: 2077 ident: 8 article-title: Optimal integrated policies for a single-vendor single-buyer time-varying demand model – volume: 132 start-page: 210 issue: 1 year: 2001 end-page: 223 ident: 12 article-title: On a finite horizon production lot size inventory model for deteriorating items: an optimal solution – volume: 29 start-page: 987 year: 2005 end-page: 1003 ident: 1 article-title: Deterministic economic production quantity models with time-varying demand cost – volume: 147 start-page: 549 issue: 3 year: 2003 end-page: 557 ident: 2 article-title: The production-inventory problem of a product with time varying demand, production and deterioration rates – volume: 157 start-page: 357 issue: 2 year: 2004 end-page: 371 ident: 3 article-title: A production-inventory model for a deteriorating item with trended demand and shortages – volume: 30 start-page: 611 issue: 7 year: 1979 end-page: 617 ident: 6 article-title: Inventory replenishment policy for increasing demand – volume: 48 start-page: 993 issue: 2 year: 2009 end-page: 1030 ident: 4 article-title: On a class of optimization problems for finite time horizon inventory models – volume: 52 start-page: 521 year: 2007 end-page: 532 ident: 11 article-title: A general and optimal approach for three inventory models with a linear trend in demand – volume: 47 start-page: 188 year: 1996 end-page: 200 ident: 7 article-title: On an inventory model for deteriorating items with increasing time-varying demand and shortages – volume: 43 start-page: 149 year: 1996 end-page: 154 ident: 9 article-title: Batching policies for linearly increasing demand with finite input rate – volume: 29 start-page: 987 year: 2005 ident: 12 publication-title: Applied Mathematical Modelling doi: 10.1016/j.apm.2005.02.002 – ident: 11 doi: 10.1016/S0377-2217(03)00222-4 – volume: 42 start-page: 35 year: 2002 ident: 9 publication-title: Computers and Industrial Engineering doi: 10.1016/S0360-8352(01)00068-7 – ident: 2 doi: 10.1137/070683945 – volume: 52 start-page: 521 year: 2007 ident: 10 publication-title: Computers and Industrial Engineering doi: 10.1016/j.cie.2007.03.001 – ident: 1 doi: 10.1016/S0377-2217(00)00133-8 – ident: 7 doi: 10.2307/3009379 – ident: 6 doi: 10.1016/S0377-2217(02)00296-5 – volume: 47 start-page: 188 year: 1996 ident: 3 publication-title: Journal of the Operational Research Society doi: 10.1057/jors.1996.17 – volume: 28 start-page: 663 year: 1977 ident: 5 publication-title: Operational Research Quarterly doi: 10.1057/jors.1977.142 – ident: 4 doi: 10.1016/j.camwa.2010.07.047 – volume: 43 start-page: 149 year: 1996 ident: 8 publication-title: International Journal of Production Economics doi: 10.1016/0925-5273(96)00033-3 |
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| SubjectTerms | Algorithms Costs Deterioration Economic models Economic theory Hypotheses Integer programming Integers Inventories Mathematical models Nonlinearity Operations research Optimization Schedules Stockpiling Studies |
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| Title | Optimal Policies for a Finite-Horizon Production Inventory Model |
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