Solving multi-choice linear programming problems by interpolating polynomials
Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right h...
Saved in:
| Published in: | Mathematical and computer modelling Vol. 54; no. 5; pp. 1405 - 1412 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Kidlington
Elsevier Ltd
01.09.2011
Elsevier |
| Subjects: | |
| ISSN: | 0895-7177, 1872-9479 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a parameter are considered as functional values of an affine function at some non-negative integer nodes. An interpolating polynomial is formulated using functional values at non-negative integer nodes to take care of any multi-choice parameter. After establishing interpolating polynomials of all multi-choice parameters, a mathematical programming problem is formulated. The formulated problem is treated as a nonlinear programming problem involving mixed integer type variables. It can be solved by using standard nonlinear programming software. Finally, a numerical example is presented to illustrate the solution procedure. |
|---|---|
| AbstractList | Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi-choice in nature. In this paper, the multiple choices of a parameter are considered as functional values of an affine function at some non-negative integer nodes. An interpolating polynomial is formulated using functional values at non-negative integer nodes to take care of any multi-choice parameter. After establishing interpolating polynomials of all multi-choice parameters, a mathematical programming problem is formulated. The formulated problem is treated as a nonlinear programming problem involving mixed integer type variables. It can be solved by using standard nonlinear programming software. Finally, a numerical example is presented to illustrate the solution procedure. |
| Author | Acharya, S. Biswal, M.P. |
| Author_xml | – sequence: 1 givenname: M.P. surname: Biswal fullname: Biswal, M.P. email: mpbiswal@maths.iitkgp.ernet.in – sequence: 2 givenname: S. surname: Acharya fullname: Acharya, S. email: srikumarc@iitkgp.ac.in |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24266326$$DView record in Pascal Francis |
| BookMark | eNp9kE1v1DAQhq2qSGwLP4BbLkhcko4_YifihCoKSEUcCmfLcSatV_5Y7Gyl_ff1suXSQ08z0rzPaOa5IOcxRSTkA4WOApVX2y7Y0DGgtAPRAYxnZEMHxdpRqPGcbGAY-1ZRpd6Si1K2ANCPMGzIz7vkH128b8Ler661D8lZbLyLaHKzy-k-mxCO89pPHkNppkPj4op5l7xZ_02SP8QUnPHlHXmz1ILvn-sl-XPz9ff19_b217cf119uW8slrK0Y52FYaqtgmgUbkUkUph-UlXThk52EsFQKyflAp94oMcJsFMyKIeWMCX5JPp321qv-7rGsOrhi0XsTMe2Lporzngomhhr9-Bw1xRq_ZBOtK3qXXTD5oJlgUnIma06dcjanUjIu2rq1Ppjimo3zmoI-itZbXUXro2gNQlfRlaQvyP_LX2M-nxislh4dZl2sw2hxdhntqufkXqGfADFWl_4 |
| CitedBy_id | crossref_primary_10_1109_ACCESS_2024_3450280 crossref_primary_10_1007_s40819_022_01483_2 crossref_primary_10_1002_int_22663 crossref_primary_10_1016_j_amc_2015_09_030 crossref_primary_10_3390_a12070143 crossref_primary_10_1080_00949655_2021_1980880 crossref_primary_10_1007_s12597_016_0272_7 crossref_primary_10_3846_transport_2021_15649 crossref_primary_10_1080_02522667_2017_1400743 crossref_primary_10_3390_app10196937 crossref_primary_10_1080_00207721_2012_669862 crossref_primary_10_3390_app13126882 crossref_primary_10_3390_axioms11110659 crossref_primary_10_31272_jae_i148_1334 crossref_primary_10_1016_j_amc_2014_03_036 crossref_primary_10_1080_02522667_2015_1132579 crossref_primary_10_1007_s41066_018_0129_y crossref_primary_10_1007_s40819_015_0041_y crossref_primary_10_1007_s12597_018_0330_4 crossref_primary_10_1080_02331934_2017_1339704 crossref_primary_10_1080_09720510_2018_1437943 crossref_primary_10_1007_s10479_018_2825_z crossref_primary_10_1007_s40305_016_0125_3 |
| Cites_doi | 10.1016/j.cie.2008.04.007 10.1057/jors.1984.8 10.1016/j.omega.2005.07.009 10.1016/0969-6016(94)90004-3 10.1016/j.cie.2009.12.004 10.1016/j.apm.2010.03.008 10.1016/j.amc.2008.12.080 10.1016/j.apm.2007.09.008 10.1016/j.eswa.2008.08.044 |
| ContentType | Journal Article |
| Copyright | 2011 Elsevier Ltd 2015 INIST-CNRS |
| Copyright_xml | – notice: 2011 Elsevier Ltd – notice: 2015 INIST-CNRS |
| DBID | 6I. AAFTH AAYXX CITATION IQODW 7S9 L.6 |
| DOI | 10.1016/j.mcm.2011.04.009 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis AGRICOLA AGRICOLA - Academic |
| DatabaseTitle | CrossRef AGRICOLA AGRICOLA - Academic |
| DatabaseTitleList | AGRICOLA |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1872-9479 |
| EndPage | 1412 |
| ExternalDocumentID | 24266326 10_1016_j_mcm_2011_04_009 S0895717711002111 |
| GroupedDBID | --K --M -DZ -~X .DC .~1 0R~ 0SF 186 1B1 1RT 1~. 1~5 29M 4.4 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN 9JO AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABAOU ABFNM ABMAC ABUCO ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADMUD ADTZH AEBSH AECPX AEKER AEXQZ AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q HAMUX HVGLF HZ~ IHE IXB J1W JJJVA KOM LG9 M26 M41 MHUIS MO0 MVM N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SES SEW SPC SSB SSD SST SSW SSZ T5K T9H TN5 VOH WUQ XPP XSW YNT YQT ZMT 9DU AATTM AAXKI AAYWO AAYXX ABJNI ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU CITATION EFKBS ~HD AFXIZ AGCQF AGRNS IQODW SSH 7S9 L.6 |
| ID | FETCH-LOGICAL-c360t-49d88f36070bd429e26e4a587c61f3bcb44c16463381b5a7490da70d72e132243 |
| ISICitedReferencesCount | 29 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000291243300016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0895-7177 |
| IngestDate | Sun Nov 09 11:04:12 EST 2025 Mon Jul 21 09:13:45 EDT 2025 Sat Nov 29 06:30:26 EST 2025 Tue Nov 18 21:33:09 EST 2025 Fri Feb 23 02:22:47 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Multi-choice programming Linear programming Mixed integer programming Nonlinear programming Interpolating polynomial Polynomial Optimization method Nonlinear problems Non linear programming Integer Integer programming Numerical analysis Applied mathematics Software Mixed problem Mathematical model Computer aided analysis Mathematical programming |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c360t-49d88f36070bd429e26e4a587c61f3bcb44c16463381b5a7490da70d72e132243 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.mcm.2011.04.009 |
| PQID | 1733514248 |
| PQPubID | 24069 |
| PageCount | 8 |
| ParticipantIDs | proquest_miscellaneous_1733514248 pascalfrancis_primary_24266326 crossref_citationtrail_10_1016_j_mcm_2011_04_009 crossref_primary_10_1016_j_mcm_2011_04_009 elsevier_sciencedirect_doi_10_1016_j_mcm_2011_04_009 |
| PublicationCentury | 2000 |
| PublicationDate | 2011-09-01 |
| PublicationDateYYYYMMDD | 2011-09-01 |
| PublicationDate_xml | – month: 09 year: 2011 text: 2011-09-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Mathematical and computer modelling |
| PublicationYear | 2011 |
| Publisher | Elsevier Ltd Elsevier |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier |
| References | Lee, Kang, Chang (br000050) 2009; 36 Biswal, Acharya (br000045) 2009; 210 L. Schrage, LINGO release 11.0, LINDO System, Inc, 2008. Snyder (br000010) 1984; 35 Chang (br000035) 2008; 32 Ravindran, Phillips Don, Solberg James (br000020) 1987 Hiller, Lieberman (br000025) 1990 Healey (br000005) 1964; 12 Liao, Kao (br000055) 2010; 58 Atkinson (br000065) 2009 Chang (br000030) 2007; 35 Paksoy, Chang (br000060) 2010; 34 Lin (br000015) 2008; 1 Liao (br000040) 2009; 56 Paksoy (10.1016/j.mcm.2011.04.009_br000060) 2010; 34 Lin (10.1016/j.mcm.2011.04.009_br000015) 2008; 1 Ravindran (10.1016/j.mcm.2011.04.009_br000020) 1987 Liao (10.1016/j.mcm.2011.04.009_br000055) 2010; 58 Biswal (10.1016/j.mcm.2011.04.009_br000045) 2009; 210 Atkinson (10.1016/j.mcm.2011.04.009_br000065) 2009 Hiller (10.1016/j.mcm.2011.04.009_br000025) 1990 10.1016/j.mcm.2011.04.009_br000070 Chang (10.1016/j.mcm.2011.04.009_br000030) 2007; 35 Healey (10.1016/j.mcm.2011.04.009_br000005) 1964; 12 Liao (10.1016/j.mcm.2011.04.009_br000040) 2009; 56 Snyder (10.1016/j.mcm.2011.04.009_br000010) 1984; 35 Chang (10.1016/j.mcm.2011.04.009_br000035) 2008; 32 Lee (10.1016/j.mcm.2011.04.009_br000050) 2009; 36 |
| References_xml | – year: 2009 ident: br000065 article-title: An Introduction to Numerical Analysis – volume: 32 start-page: 2587 year: 2008 end-page: 2595 ident: br000035 article-title: Revised multi-choice goal programming publication-title: Applied Mathematical Modelling – year: 1987 ident: br000020 article-title: Operations Research Principles & Practice – volume: 34 start-page: 3586 year: 2010 end-page: 3598 ident: br000060 article-title: Revised multi-choice goal programming for multi-period, multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing publication-title: Applied Mathematical Modelling – volume: 35 start-page: 389 year: 2007 end-page: 396 ident: br000030 article-title: Multi-choice goal programming problem publication-title: Omega-The International Journal of Management Science – reference: L. Schrage, LINGO release 11.0, LINDO System, Inc, 2008. – year: 1990 ident: br000025 article-title: Introduction to Operations Research – volume: 36 start-page: 6318 year: 2009 end-page: 6325 ident: br000050 article-title: Fuzzy multiple goal programming applied to TFT-LCD supplier selection by downstream manufacturers publication-title: Expert Systems with Applications – volume: 58 start-page: 571 year: 2010 end-page: 577 ident: br000055 article-title: Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming publication-title: Computers & Industrial Engineering – volume: 1 start-page: 409 year: 2008 end-page: 421 ident: br000015 article-title: Multiple choice programming: a state-of-the-art review publication-title: International Transactions in Operational Research – volume: 12 start-page: 122 year: 1964 end-page: 138 ident: br000005 article-title: Multiple choice programming publication-title: Operations Research – volume: 210 start-page: 182 year: 2009 end-page: 188 ident: br000045 article-title: Transformation of multi-choice linear programming problem publication-title: Applied Mathematics and Computation – volume: 56 start-page: 138 year: 2009 end-page: 141 ident: br000040 article-title: Formulating the multi-segment goal programming publication-title: Computers & Industrial Engineering – volume: 35 start-page: 69 year: 1984 end-page: 74 ident: br000010 article-title: Linear programming with special ordered sets publication-title: Journal of the Operational Research Society – volume: 12 start-page: 122 year: 1964 ident: 10.1016/j.mcm.2011.04.009_br000005 article-title: Multiple choice programming publication-title: Operations Research – year: 1990 ident: 10.1016/j.mcm.2011.04.009_br000025 – volume: 56 start-page: 138 year: 2009 ident: 10.1016/j.mcm.2011.04.009_br000040 article-title: Formulating the multi-segment goal programming publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2008.04.007 – volume: 35 start-page: 69 year: 1984 ident: 10.1016/j.mcm.2011.04.009_br000010 article-title: Linear programming with special ordered sets publication-title: Journal of the Operational Research Society doi: 10.1057/jors.1984.8 – year: 2009 ident: 10.1016/j.mcm.2011.04.009_br000065 – volume: 35 start-page: 389 year: 2007 ident: 10.1016/j.mcm.2011.04.009_br000030 article-title: Multi-choice goal programming problem publication-title: Omega-The International Journal of Management Science doi: 10.1016/j.omega.2005.07.009 – ident: 10.1016/j.mcm.2011.04.009_br000070 – volume: 1 start-page: 409 year: 2008 ident: 10.1016/j.mcm.2011.04.009_br000015 article-title: Multiple choice programming: a state-of-the-art review publication-title: International Transactions in Operational Research doi: 10.1016/0969-6016(94)90004-3 – volume: 58 start-page: 571 issue: 4 year: 2010 ident: 10.1016/j.mcm.2011.04.009_br000055 article-title: Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2009.12.004 – volume: 34 start-page: 3586 year: 2010 ident: 10.1016/j.mcm.2011.04.009_br000060 article-title: Revised multi-choice goal programming for multi-period, multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing publication-title: Applied Mathematical Modelling doi: 10.1016/j.apm.2010.03.008 – volume: 210 start-page: 182 year: 2009 ident: 10.1016/j.mcm.2011.04.009_br000045 article-title: Transformation of multi-choice linear programming problem publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2008.12.080 – volume: 32 start-page: 2587 year: 2008 ident: 10.1016/j.mcm.2011.04.009_br000035 article-title: Revised multi-choice goal programming publication-title: Applied Mathematical Modelling doi: 10.1016/j.apm.2007.09.008 – volume: 36 start-page: 6318 issue: 3 year: 2009 ident: 10.1016/j.mcm.2011.04.009_br000050 article-title: Fuzzy multiple goal programming applied to TFT-LCD supplier selection by downstream manufacturers publication-title: Expert Systems with Applications doi: 10.1016/j.eswa.2008.08.044 – year: 1987 ident: 10.1016/j.mcm.2011.04.009_br000020 |
| SSID | ssj0005908 |
| Score | 2.1615856 |
| Snippet | Multi-choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1405 |
| SubjectTerms | computer software Exact sciences and technology Interpolating polynomial Linear programming Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Mixed integer programming Multi-choice programming Nonlinear programming Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming Numerical methods in mathematical programming, optimization and calculus of variations Sciences and techniques of general use |
| Title | Solving multi-choice linear programming problems by interpolating polynomials |
| URI | https://dx.doi.org/10.1016/j.mcm.2011.04.009 https://www.proquest.com/docview/1733514248 |
| Volume | 54 |
| WOSCitedRecordID | wos000291243300016&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-9479 dateEnd: 20131231 omitProxy: false ssIdentifier: ssj0005908 issn: 0895-7177 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3da9swEBcj3cPGGPtk2UfxYE8rDv6QLOmxjI5tLKWQDvImbFmGFscJdbo1__3uJPmjKyvbYC_GcWLL0f18ujvf_Y6Qd7FmLCuTIoypLkOaw5MuE01DxqoijiLDmLaU-V_58bFYLuWJf9He2nYCvGnE1ZXc_FdRwzEQNpbO_oW4-4vCAdgHocMWxA7bPxL8Yl3bIIFNFQxBu4EqOEBjEkmtXTbWypWg21YyLRqgZ67bFubF4TfreofVynndjm3Xec_w6vkFtO8I4drp1N0iaEPu7Q_bSeBgPjuZ9aDCEq-dtVYXs3G4AeOnchxu6OtghqQjq6okC8ExdEuncapU8CSU1LWK6XStI4z2mGIjxQl-HhstwjF1ydU3FLyLNZzPVnrl-VeR_VwOq1mfY7jAm8J7QlI8cHPBRd5LOJNiQvYOPx8tvwyZQNI2Luz_RPfy26YB_jLQ78yXB5u8hdmvXDeUGwu7tVZOH5GH3s0IDh08HpM7pnlC7o_IJ-HTIM_2KZl72ARj2AQONsEINkEHm6DYBddgE4xg84x8-3h0-uFT6FtthDrNom1IZSlEBbs8KkowUUySGZozwXUWV2mhC0o1MtGlYOAVLOdURmXOo5InBsMZNH1OJs26MS9IkEqdCYHsFjylUqC9m8RFlVZcxjSPzJRE3Qwq7XnosR1KrbqEw3MFk65w0lVEFUz6lLzvT9k4Epbbfkw7sShvRTrrUAGGbjtt_5oI-4GsDQtOzpS87WSqQAXje7W8MevLVsU8xXqYhIqX_zb2K3JveNRek8n24tK8IXf19-1Ze7Hv4foT_K6sLQ |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Solving+multi-choice+linear+programming+problems+by+interpolating+polynomials&rft.jtitle=Mathematical+and+computer+modelling&rft.au=Biswal%2C+M.P.&rft.au=Acharya%2C+S.&rft.date=2011-09-01&rft.pub=Elsevier+Ltd&rft.issn=0895-7177&rft.eissn=1872-9479&rft.volume=54&rft.issue=5&rft.spage=1405&rft.epage=1412&rft_id=info:doi/10.1016%2Fj.mcm.2011.04.009&rft.externalDocID=S0895717711002111 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0895-7177&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0895-7177&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0895-7177&client=summon |