Scientific References

ULSAlgorithms treats scientific provenance as part of the public strategy contract. A strategy named after a publication is not merely a label: its source documentation, applicability conditions, complexity statement and implementation note must remain consistent with the literature basis and with the code that is actually shipped.

v0.29.0 pre-1.0 provenance audit

Before freezing the 1.x compatibility baseline, all 42 public strategy IDs were reviewed against the runtime catalog, source-level documentation and, where durable publisher metadata is available, the publication record.

The audit deliberately distinguishes three things:

1. publication metadata — author/year and DOI or other durable publication record when one can be asserted confidently;
2. implementation metadata — what this C# implementation actually does;
3. complexity/applicability metadata — claims about the implementation, not an automatic copy of an abstract or historical program listing.

A blank DOI is intentional and means ULSAlgorithms does not assert a DOI for that catalog entry. It must not be interpreted as a claim that no DOI exists.

The v0.29.0 audit made three concrete metadata corrections/clarifications:

• Evans (1985) now records DOI 10.1016/0272-6963(85)90009-9, already present in the source-level documentation but previously absent from the runtime catalog.
• DeMatteis (1968), the early primary Part-Period Algorithm reference, now records DOI 10.1147/sj.71.0030.
• The Lyu-Lee parallel strategy now states the complexity of the library implementation explicitly: O(T²) total work with ideal O(T²/p) parallel candidate-evaluation span. The implementation remains documented as a modern shared-memory reconstruction rather than a transliteration of the historical PVM code.

No solver mathematics or public solver identifier is changed by this audit.

Audited strategy matrix

Foundational exact methods

• H. M. Wagner and T. M. Whitin (1958), Dynamic Version of the Economic Lot Size Model, Management Science 5(1), 89-96. DOI: https://doi.org/10.1287/mnsc.5.1.89
• J. R. Evans (1985), An Efficient Implementation of the Wagner-Whitin Algorithm for Dynamic Lot-Sizing, Journal of Operations Management 5(2), 229-235. DOI: https://doi.org/10.1016/0272-6963(85)90009-9
• W. I. Zangwill (1969), A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System–A Network Approach, Management Science 15(9), 506-527. DOI: https://doi.org/10.1287/mnsc.15.9.506
• A. Federgruen and M. Tzur (1991), A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in O(n log n) or O(n) Time, Management Science 37(8), 909-925. DOI: https://doi.org/10.1287/mnsc.37.8.909
• A. Wagelmans, S. van Hoesel and A. Kolen (1992), Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case, Operations Research 40(1 supplement), S145-S156. DOI: https://doi.org/10.1287/opre.40.1.S145
• A. Aggarwal and J. K. Park (1993), Improved Algorithms for Economic Lot Size Problems, Operations Research 41(3), 549-571. DOI: https://doi.org/10.1287/opre.41.3.549

Data-dependent, implementation-oriented and parallel exact methods

• H. C. Bahl and S. Taj (1991), A data-dependent efficient implementation of the Wagner-Whitin algorithm for lot-sizing, Computers & Industrial Engineering 20(2), 289-291. DOI: https://doi.org/10.1016/0360-8352(91)90033-3
• R. B. Heady and Z. Zhu (1994), An Improved Implementation of the Wagner-Whitin Algorithm, Production and Operations Management 3(1), 55-63. DOI: https://doi.org/10.1111/j.1937-5956.1994.tb00109.x
• N. T. Chowdhury, M. F. Baki and A. Azab (2018), Dynamic Economic Lot-Sizing Problem: A new O(T) Algorithm for the Wagner-Whitin Model, Computers & Industrial Engineering 117, 6-18. DOI: https://doi.org/10.1016/j.cie.2018.01.010
• S. J. Sadjadi, M. B. Gh. Aryanezhad and H. A. Sadeghi (2009), An Improved WAGNER-WHITIN Algorithm, International Journal of Industrial Engineering & Production Research 20(3), 117-123. No DOI is asserted by the runtime catalog.
• J.-J. Lyu and M.-C. Lee (2001), A parallel algorithm for the dynamic lot-sizing problem, Computers & Industrial Engineering 41(2), 127-134. DOI: https://doi.org/10.1016/S0360-8352(01)00047-X
• C. Saydam and M. McKnew (1987), A Fast Microcomputer Program for Ordering Using the Wagner-Whitin Algorithm, Production and Inventory Management Journal 28(4), 15-19. No DOI is asserted by the runtime catalog.
• F. R. Jacobs and B. M. Khumawala (1987), A Simplified Procedure for Optimal Single-Level Lot Sizing, Production and Inventory Management 28(3), 39-43. No DOI is asserted by the runtime catalog.

Mathematical formulations and cutting planes

• J. Krarup and O. Bilde (1977), Plant location, Set Covering and Economic Lot Size: An O(mn)-Algorithm for Structured Problems, in Numerische Methoden bei Optimierungsaufgaben Band 3, pp. 155-180. DOI: https://doi.org/10.1007/978-3-0348-5936-3_10
• N. Brahimi, S. Dauzere-Peres, N. M. Najid and A. Nordli (2006), Single item lot sizing problems, European Journal of Operational Research 168(1), 1-16. DOI: https://doi.org/10.1016/j.ejor.2004.01.054
• I. Barany, T. Van Roy and L. A. Wolsey (1984), Uncapacitated lot-sizing: The convex hull of solutions, Mathematical Programming Study 22, 32-43. DOI: https://doi.org/10.1007/BFb0121006
• Y. Pochet and L. A. Wolsey (1994), Polyhedra for lot-sizing with Wagner-Whitin costs, Mathematical Programming 67, 297-323. DOI: https://doi.org/10.1007/BF01582225

For solver-backed formulations, the catalog may cite the publication that most directly identifies the represented formulation, while the implementation documentation can additionally cite the Brahimi et al. survey used to cross-check formulation families.

Classical and modern heuristics

• E. A. Silver and H. C. Meal (1973), A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment, Production and Inventory Management 14(2), 64-74. No DOI is asserted by the runtime catalog.
• J. J. DeMatteis (1968), An Economic Lot-Sizing Technique I: The Part-Period Algorithm, IBM Systems Journal 7(1), 30-38. DOI: https://doi.org/10.1147/sj.71.0030
• G. K. Groff (1979), A Lot-Sizing Rule for Time-Phased Component Demand, Production and Inventory Management 20(1), 47-53. No DOI is asserted by the runtime catalog.
• J. R. Freeland and J. L. Colley Jr. (1982), A Simple Heuristic Method for Lot-Sizing in a Time-Phased Reorder System, Production and Inventory Management 23(1), 15-22. No DOI is asserted by the runtime catalog.
• J. W. Patterson and R. L. LaForge (1985), The Incremental Part-Period Algorithm: An Alternative to EOQ, Journal of Purchasing and Materials Management 21(2), 28-33. DOI: https://doi.org/10.1111/j.1745-493X.1985.tb00132.x
• U. Wemmerlov (1983), The Part-Period Balancing Algorithm and Its Look Ahead-Look Back Feature, Journal of Operations Management 4(1), 23-39. DOI: https://doi.org/10.1016/0272-6963(83)90023-2
• L. Baciarello, M. D'Avino, R. Onori and M. M. Schiraldi (2013), Lot Sizing Heuristics Performance, International Journal of Engineering Business Management 5. DOI: https://doi.org/10.5772/56004
• A. Segerstedt, B. Abdul-Jalbar and B. Samuelsson (2023), Reformulated Silver-Meal and Similar Lot Sizing Techniques, Axioms 12(7), 661. DOI: https://doi.org/10.3390/axioms12070661
• Y. P. Chiu (2004), A modification of the least unit cost lot-sizing heuristic, Journal of Statistics and Management Systems 7(1), 197-207. DOI: https://doi.org/10.1080/09720510.2004.10701115
• S. W. Chiu, C.-K. Ting and Y.-S. P. Chiu (2005), A modified version of the part period lot-sizing heuristic, International Journal for Engineering Modelling 18(1-2), 59-64. No DOI is asserted by the runtime catalog.
• J. C. Ho, Y.-L. Chang and A. O. Solis (2006), Two modifications of the least cost per period heuristic for dynamic lot-sizing, Journal of the Operational Research Society 57(8), 1005-1013. DOI: https://doi.org/10.1057/palgrave.jors.2602076

Lot-for-Lot, classical Least Unit Cost and Periodic Order Quantity are cataloged as classical rules rather than being assigned a single paper DOI.

Provenance policy

A publication name on a public class or catalog entry is treated as a provenance claim.

When the original program listing is unavailable and the implementation reconstructs the published architecture, the documentation says modern reconstruction (or equivalent wording) rather than implying line-by-line transcription.

The audited unit-test baseline now locks, for every public strategy ID:

• scientific/historical reference;
• normalized DOI value, including intentional blanks;
• documented time and space complexity;
• applicability conditions;
• implementation characterization.

Any future change to one of these fields is therefore deliberate and must update both the runtime catalog and the scientific audit baseline.