{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:07Z","timestamp":1760149027679,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T00:00:00Z","timestamp":1688342400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Literature and most textbooks around the world describe Silver-Meal in such a way that periods with zero demand make Silver-Meal suggest a higher frequency of order replenishments than necessary and therefore higher total costs than necessary. Silver-Meal, still the best-known technique, is therefore inferior to other lesser-known techniques when the time interval in the calculations presently is days and not months. The purpose of this article is to show that another mathematical formulation of Silver-Meal avoids this trouble. We also point to characteristics such as Silver-Meal, Least Unit Cost, Part-Period Balancing, and lot-sizing techniques that are available in many textbooks for operations and supply chain management. We illustrate the techniques with different examples of periods without demand, declining demand, and varying demand. We point out possible problems with the different techniques. Literature mostly does not consider periods of zero demand, which was not so important before. Lot-sizing methods must cope with the important performance indicator \u201cDays of inventory\u201d. Numerous practical situations with zero demand periods exist where a lot of sizing techniques help for efficient operations. It is necessary knowledge and a tool for students (future users, performers, and managers). \u201cL\u00e4gsta periodkostnad\u201d is a restored and reformulated Silver-Meal, with Silver-Meal\u2019s characteristics already presented in literature, except those difficulties with zero demand periods disappear.<\/jats:p>","DOI":"10.3390\/axioms12070661","type":"journal-article","created":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T01:42:47Z","timestamp":1688434967000},"page":"661","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reformulated Silver-Meal and Similar Lot Sizing Techniques"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1173-6713","authenticated-orcid":false,"given":"Anders","family":"Segerstedt","sequence":"first","affiliation":[{"name":"Department of Business Administration, Technology and Social Sciences (ETS), Lule\u00e5 University of Technology, HB Segerstedts Konsultbyr\u00e5, 97432 Lule\u00e5, Sweden"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0321-7662","authenticated-orcid":false,"given":"Beatriz","family":"Abdul-Jalbar","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de La Laguna, 38200 La Laguna, Spain"}]},{"given":"Bj\u00f6rn","family":"Samuelsson","sequence":"additional","affiliation":[{"name":"Department of Civil and Industrial Engineering, Quality Science, Uppsala University, Campus Gotland, 62167 Visby, Sweden"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1287\/mnsc.30.9.1121","article-title":"Approximation Methods for the Uncapacitated Dynamic Lot Size Problem","volume":"30","author":"Bitran","year":"1984","journal-title":"Manag. Sci."},{"key":"ref_2","unstructured":"Peterson, R., and Silver, E.A. (1979). Decision System for Inventory Management and Production Planning, John Wiley."},{"key":"ref_3","unstructured":"Orlicky, J. (1975). Material Requirements Planning, McGraw-Hill."},{"key":"ref_4","unstructured":"Hax, A.C. (1978). Studies in Operations Management, North-Holland."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1111\/j.1540-5915.1980.tb01170.x","article-title":"Heuristic lot-sizing performance in a rolling-schedule environment","volume":"11","author":"Blackburn","year":"1980","journal-title":"Decis. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0360-8352(90)90044-M","article-title":"A comparative performance analysis of the Wagner-Whitin algorithm and lot-sizing heuristics","volume":"18","author":"Saydam","year":"1990","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1108\/eb054746","article-title":"Two lot-sizing heuristics for the case of deterministic time-varying demands","volume":"5","author":"Bookbinder","year":"1985","journal-title":"Int. J. Oper. Prod. Manag."},{"key":"ref_8","first-page":"56","article-title":"Two modifications of the Silver Meal Lot Sizing Heuristic","volume":"22","author":"Silver","year":"1984","journal-title":"INFOR Inf. Syst. Oper. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1016\/S0377-2217(03)00419-3","article-title":"The effect of lot sizing rules on order variability","volume":"159","author":"Pujawan","year":"2004","journal-title":"Eur. J. Oper. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.ejor.2014.09.045","article-title":"The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory","volume":"242","author":"Govindan","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1057\/palgrave.jors.2602076","article-title":"Two Modifications of the Least Cost per Period Heuristic for Dynamic Lot-Sizing","volume":"57","author":"Ho","year":"2006","journal-title":"J. Oper. Res. Soc."},{"key":"ref_12","unstructured":"Segerstedt, A. (1999). Logistik Med Fokus p\u00e5 Material-Och Produktionsstyrning, Liber. (In Swedish)."},{"key":"ref_13","first-page":"210","article-title":"A heuristic for selecting lot size requirements for the case of deterministic time-varying demand rate and discrete opportunities for replenishment","volume":"14","author":"Silver","year":"1973","journal-title":"Prod. Inventory Manag."},{"key":"ref_14","unstructured":"Silver, E.A., Pyke, D.F., and Peterson, R. (1998). Inventory Management and Production Planning and Scheduling, John Wiley & Sons. [3rd ed.]."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Axs\u00e4ter, S. (2015). Inventory Control, Springer International Publishing. [3rd ed.].","DOI":"10.1007\/978-3-319-15729-0"},{"key":"ref_16","unstructured":"Nahmias, S. (2013). Production and Operations Analysis, McGraw-Hill\/Irwin. [6th ed.]."},{"key":"ref_17","unstructured":"Olhager, J. (2013). Produktionsekonomi, Studentlitteratur. (In Swedish)."},{"key":"ref_18","unstructured":"G\u00fcnter, H.-O., and Tempelmeier, H. (2007). Produktion und Logistik, Springer. [7th ed.]. (In German)."},{"key":"ref_19","unstructured":"Dom\u00ednguez-Machuca, J.A., Garc\u00eda, S., Dom\u00ednguez, M.A., Ruiz, A., and \u00c1lvarez, M.J. (1995). Direcci\u00f3n de Operaciones. Aspectos T\u00e1cticos y Operativos en la Producci\u00f3n y Los Servicios, McGraw-Hill. (In Spanish)."},{"key":"ref_20","first-page":"75","article-title":"Dynamic order quantities","volume":"9","author":"Gorham","year":"1968","journal-title":"Prod. Inventory Manag. J."},{"key":"ref_21","unstructured":"Segerstedt, A. (2008). Logistik Med Fokus p\u00e5 Material-Och Produktionsstyrning, Liber. [2nd ed.]. (In Swedish)."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1147\/sj.71.0030","article-title":"An economic lot-sizing technique, I: The part-period algorithm","volume":"7","author":"DeMatteis","year":"1968","journal-title":"IBM Syst. J."},{"key":"ref_23","first-page":"135","article-title":"How many parts to make at once","volume":"10","author":"Harris","year":"1913","journal-title":"Fact. Mag. Manag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.ijpe.2014.03.024","article-title":"Economic Order Quantities in Production: From Harris to Economic Lot Scheduling Problems","volume":"155","author":"Holmbom","year":"2014","journal-title":"Int. J. Prod. Econ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/j.ijpe.2006.12.022","article-title":"A new iterative heuristic to solve the Joint Replenishment Problem using a spread-sheet technique","volume":"108","author":"Nilsson","year":"2007","journal-title":"Int. J. Prod. Econ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.cor.2009.04.012","article-title":"A new heuristic to solve the One-warehouse N-retailer problem","volume":"37","author":"Segerstedt","year":"2010","journal-title":"Comput. Oper. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1287\/mnsc.5.1.89","article-title":"Dynamic version of the economic lot size model","volume":"5","author":"Wagner","year":"1958","journal-title":"Manag. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/0377-2217(82)90176-X","article-title":"Worst case performance for lot sizing heuristics","volume":"9","year":"1982","journal-title":"Eur. J. Oper. Res."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/661\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:05:05Z","timestamp":1760126705000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/7\/661"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,3]]},"references-count":28,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["axioms12070661"],"URL":"https:\/\/doi.org\/10.3390\/axioms12070661","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2023,7,3]]}}}