Maximizing the number of mixed packages subject to variety constraints
We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The specific application is the allocation of excess of a population of various ty...
Uložené v:
| Vydané v: | Computers & operations research Ročník 26; číslo 13; s. 1323 - 1333 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Oxford
Elsevier Ltd
01.11.1999
Elsevier Science Pergamon Press Inc |
| Predmet: | |
| ISSN: | 0305-0548, 1873-765X, 0305-0548 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The specific application is the allocation of excess of a population of various types of cards (e.g., left over from a previous selling season) to fixed-sized “variety packs” which guarantee a given level of variety (i.e., no more than
k of any type of card). Some card types with large numbers (perhaps the most unpopular from the previous season) may have to be discarded to preserve the variety constraint. The method developed employs a test for feasibility of a given number of packs and includes a simple allocation procedure. A numerical example is provided along with (worst-case) complexity calculations. In addition, we solve a practical problem in which an organisation marketing Christmas cards sought to determine the impact of pack size and variety level on the level of unallocated cards.
Scope and purpose
Organisations involved in the stocking and sale of seasonal “style” items such as greeting cards, may periodically face excess stock of various items (e.g., from previous seasons), and may decide to market the items in packs guaranteed to contain a certain degree of variety. Our objective in this paper is to show how to maximise the number of card packs that can be formed from an assortment of excess stock, where there is a marketing-based variety constraint restricting the number of each type of card in each pack. The solution procedure developed is intuitively appealing and can be easily implemented on a spreadsheet. In addition to presenting a numerical example, we provide results from the application and implementation of the method in the card sales operations of a charitable organisation. The method could also have broader application in other settings where variety is sought – such as in groups or teams. |
|---|---|
| AbstractList | We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a pseudo-polynomial procedure to actually implement that optimal solution. The specific application is the allocation of excess of a population of various types of cards (e.g., left over from a previous selling season) to fixed-sized “variety packs” which guarantee a given level of variety (i.e., no more than
k of any type of card). Some card types with large numbers (perhaps the most unpopular from the previous season) may have to be discarded to preserve the variety constraint. The method developed employs a test for feasibility of a given number of packs and includes a simple allocation procedure. A numerical example is provided along with (worst-case) complexity calculations. In addition, we solve a practical problem in which an organisation marketing Christmas cards sought to determine the impact of pack size and variety level on the level of unallocated cards.
Scope and purpose
Organisations involved in the stocking and sale of seasonal “style” items such as greeting cards, may periodically face excess stock of various items (e.g., from previous seasons), and may decide to market the items in packs guaranteed to contain a certain degree of variety. Our objective in this paper is to show how to maximise the number of card packs that can be formed from an assortment of excess stock, where there is a marketing-based variety constraint restricting the number of each type of card in each pack. The solution procedure developed is intuitively appealing and can be easily implemented on a spreadsheet. In addition to presenting a numerical example, we provide results from the application and implementation of the method in the card sales operations of a charitable organisation. The method could also have broader application in other settings where variety is sought – such as in groups or teams. A polynomial-time algorithm is developed to optimize a variant of the one-dimensional bin-packing problem with side constraints. A pseudo-polynomial procedure is developed to actually implement that optimal solution. The specific application is the allocation of excess of a population of various types of cards to fixed-sized variety packs which guarantee a given level of variety. Some card types with large numbers (perhaps the most unpopular from the previous season) may have to be discarded to preserve the variety constraint. The method developed employs a test for feasibility of a given number of packs and includes a simple allocation procedure. A numerical example is provided along with (worst-case) complexity calculations. In addition, a practical problem is solved in which an organization marketing Christmas cards sought to determine the impact of pack size and variety level on the level of unallocated cards. |
| Author | Trietsch, Dan Robb, David J. |
| Author_xml | – sequence: 1 givenname: David J. surname: Robb fullname: Robb, David J. email: d.robb@auckland.ac.nz – sequence: 2 givenname: Dan surname: Trietsch fullname: Trietsch, Dan |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1957204$$DView record in Pascal Francis |
| BookMark | eNqFkM1KAzEURoNUsK0-ghDEhS5Gk8n8JCuRYlWouFDBXchkbmpqm6nJTGl9emfaokuzSQLn-y73DFDPVQ4QOqXkihKaXb8QRtKIpAm_EPySENr-6AHqU56zKM_S9x7q_yJHaBDCjLQnj2kfjZ_U2i7st3VTXH8Ads2iAI8rgxd2DSVeKv2pphBwaIoZ6BrXFV4pb6HeYF25UHtlXR2O0aFR8wAn-3uI3sZ3r6OHaPJ8_zi6nUSaUVpHNMlEIhKTkySPmSEF0JxkhjPBs0IRA3FhYkq0aF-pAJqV1HCTlUXMCDNZwobobNe79NVXA6GWs6rxrh0pqUg547FIW-h8D6mg1dx45bQNcuntQvlNB-Yx6brSHaZ9FYIH80cQ2YmVW7GysyYFl1uxkra5m10O2kVXFrwM2oLTUFrfGpJlZf9p-AHMtoCE |
| CODEN | CMORAP |
| ContentType | Journal Article |
| Copyright | 1999 Elsevier Science Ltd 1999 INIST-CNRS Copyright Pergamon Press Inc. Nov 1999 |
| Copyright_xml | – notice: 1999 Elsevier Science Ltd – notice: 1999 INIST-CNRS – notice: Copyright Pergamon Press Inc. Nov 1999 |
| DBID | AAYXX CITATION IQODW 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/S0305-0548(98)00105-1 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Business Applied Sciences |
| EISSN | 1873-765X 0305-0548 |
| EndPage | 1333 |
| ExternalDocumentID | 46777863 1957204 10_1016_S0305_0548_98_00105_1 S0305054898001051 |
| Genre | Feature |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 186 1B1 1OL 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 6J9 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAFJI AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO AAYFN AAYOK ABAOU ABBOA ABEFU ABFNM ABFRF ABJNI ABMAC ABMMH ABUCO ABXDB ABYKQ ACAZW ACDAQ ACGFO ACGFS ACNCT ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD AEBSH AEFWE AEHXG AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AI. AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV AKYCK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOMHK AOUOD APLSM ARUGR ASPBG AVARZ AVWKF AXJTR AZFZN BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q G8K GBLVA GBOLZ HAMUX HVGLF HZ~ H~9 IHE J1W KOM LY1 M41 MHUIS MO0 MS~ O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ PRBVW Q38 R2- RIG ROL RPZ RXW SDF SDG SDP SDS SES SEW SPC SPCBC SSB SSD SSO SSV SSW SSZ T5K TAE TN5 U5U UAO UPT VH1 WUQ XFK XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c311t-1469494f704723f0be1706f83986ba0fe2bf210c9fe259e16d1f8f6db2303f643 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000082714800005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0305-0548 |
| IngestDate | Tue Aug 12 03:57:11 EDT 2025 Mon Jul 21 09:17:45 EDT 2025 Sat Nov 29 03:23:25 EST 2025 Fri Feb 23 02:33:35 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 13 |
| Keywords | Seasonal products Bin packing Style goods Polynomial algorithm Pseudo-polynomial Integer programming Maximization Constraint Optimal solution Bin packing problem Variety Polynomial time |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c311t-1469494f704723f0be1706f83986ba0fe2bf210c9fe259e16d1f8f6db2303f643 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| PQID | 195838295 |
| PQPubID | 45870 |
| PageCount | 11 |
| ParticipantIDs | proquest_journals_195838295 pascalfrancis_primary_1957204 crossref_primary_10_1016_S0305_0548_98_00105_1 elsevier_sciencedirect_doi_10_1016_S0305_0548_98_00105_1 |
| PublicationCentury | 1900 |
| PublicationDate | 1999-11-01 |
| PublicationDateYYYYMMDD | 1999-11-01 |
| PublicationDate_xml | – month: 11 year: 1999 text: 1999-11-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationPlace | Oxford |
| PublicationPlace_xml | – name: Oxford – name: New York |
| PublicationTitle | Computers & operations research |
| PublicationYear | 1999 |
| Publisher | Elsevier Ltd Elsevier Science Pergamon Press Inc |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier Science – name: Pergamon Press Inc |
| SSID | ssj0000721 |
| Score | 1.5733691 |
| Snippet | We develop a polynomial-time algorithm to optimise a variant of the one-dimensional bin-packing problem with side constraints. We also develop a... A polynomial-time algorithm is developed to optimize a variant of the one-dimensional bin-packing problem with side constraints. A pseudo-polynomial procedure... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 1323 |
| SubjectTerms | Algorithms Applied sciences Bin packing Christmas Exact sciences and technology Greeting cards Mathematical programming Operational research and scientific management Operational research. Management science Operations research Packaging Polynomial algorithm Pseudo-polynomial Seasonal products Studies Style goods |
| Title | Maximizing the number of mixed packages subject to variety constraints |
| URI | https://dx.doi.org/10.1016/S0305-0548(98)00105-1 https://www.proquest.com/docview/195838295 |
| Volume | 26 |
| WOSCitedRecordID | wos000082714800005&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: ScienceDirect database customDbUrl: eissn: 1873-765X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000721 issn: 0305-0548 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLbKhtAQ4lKGKGPID0yCh4ykThr7cWKtAI0yQSf1zUpSG1VAEpquqvgH_GvOie2kFeP2wIsb2Wpi-Xw-_myfCyFP437CwtRXHvxwL2SDxEuzCG1dUx3j_iCamWQT8XjMp1Nx3ul8d74wq89xnvP1WpT_VdRQB8JG19l_EHfzUqiAZxA6lCB2KP9K8G-T9fzL_JtzgzIpP-pr9Pka2CXskT8lGNihukzxDAbJ5wo3zMDGMySLmDPChHdqIhjYzA9VjZOiVAtrP2cjBTUnyu8Lc71TG8q3F04TfHtlck6dWjTOrOedsB53DhrnavEREyAZ25BtM03UGh6QP6NJ1RV1Vtca73iHKbahOWFXzK5U6eZ04UPzOiDeAgpR5_b0gnYdc3f343dydHF2JifD6WS7tV62YWXAmHnsiI3Krx6mH8Nr-iN2aqBwjez240iAgtw9eT2cvmmX9bh24mv60bqDvWg790zw57ZjvyI6t8qkgumnTd6UnyhAzWsmd8ltuyGhJwZI90hH5V1yw_lDdMkdJ31ql4EuubkRxPI-GbWAowA4agBHC01rwFEHOGoBR5cFtYCjG4DbJxej4eTlK89m5_AyFgRLD5ZYEYpQxxhvlGk_VRiJSQPh5oM08bWC2d4P_EzAUyRUMJgFmmtMXwasSQMRfkB28iJXDwnNoJ6DwvD9VIQ8C3ismRaC-5kfa6XiHjl2QylLE4RFttaJMPYSx14KLuuxl0GPcDfg0jJJwxAloOpPfz3cElD7QRFhQqceOXACk3bWV9jGGe-L6NFvWw_IXjuxHpOd5eJSHZLr2Wo5rxZPLOB-AFa8oG8 |
| 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=Maximizing+the+number+of+mixed+packages+subject+to+variety+constraints&rft.jtitle=Computers+%26+operations+research&rft.au=Robb%2C+David+J&rft.au=Trietsch%2C+Dan&rft.date=1999-11-01&rft.pub=Pergamon+Press+Inc&rft.issn=0305-0548&rft.eissn=0305-0548&rft.volume=26&rft.issue=13&rft.spage=1323&rft_id=info:doi/10.1016%2FS0305-0548%2898%2900105-1&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=46777863 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0305-0548&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0305-0548&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0305-0548&client=summon |