Lot sizing with piecewise concave production costs

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dc.citation.epage779en_US
dc.citation.issueNumber4en_US
dc.citation.spage767en_US
dc.citation.volumeNumber26en_US
dc.contributor.authorKoca, E.en_US
dc.contributor.authorYaman, H.en_US
dc.contributor.authorAktürk, M. S.en_US
dc.date.accessioned2016-02-08T10:59:14Z
dc.date.available2016-02-08T10:59:14Z
dc.date.issued2014en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractWe study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.en_US
dc.identifier.doi10.1287/ijoc.2014.0597en_US
dc.identifier.eissn1526-5528
dc.identifier.issn1091-9856
dc.identifier.urihttp://hdl.handle.net/11693/26398
dc.language.isoEnglishen_US
dc.publisherInstitute for Operations Research and the Management Sciences (I N F O R M S)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1287/ijoc.2014.0597en_US
dc.source.titleINFORMS Journal on Computingen_US
dc.subjectLot sizingen_US
dc.subjectPiecewise concave production costen_US
dc.subjectQuantity discountsen_US
dc.subjectSubcontractingen_US
dc.subjectPiece-wiseen_US
dc.subjectProduction costen_US
dc.subjectDynamic programmingen_US
dc.titleLot sizing with piecewise concave production costsen_US
dc.typeArticleen_US
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