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Moreover, four heuristics have been proposed in order to optimize our algorithm. Then, we present a Polynomial Time Approximation Scheme (PTAS) to generate an approximate Pareto Frontier. In this scheme, we use a simplification technique based on the merging of jobs. Furthermore, we present a Fully Polynomial Time Approximation Scheme (FPTAS) to generate an approximate Pareto Frontier, based on the conversion of the dynamic programming algorithm. The proposed FPTAS is strongly polynomial. Finally, some numerical experiments are provided in order to compare the proposed approaches.<\/jats:p>","DOI":"10.1051\/ro\/2024029","type":"journal-article","created":{"date-parts":[[2024,2,1]],"date-time":"2024-02-01T09:05:54Z","timestamp":1706778354000},"page":"2393-2419","source":"Crossref","is-referenced-by-count":0,"title":["Approximation schemes for scheduling jobs on identical parallel machines to minimize the maximum lateness and makespan"],"prefix":"10.1051","volume":"58","author":[{"given":"Gais","family":"Alhadi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6649-7257","authenticated-orcid":false,"given":"Imed","family":"Kacem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2191-1335","authenticated-orcid":false,"given":"Pierre","family":"Laroche","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Izzeldin M.","family":"Osman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s10479-019-03250-x","volume":"285","author":"Alhadi","year":"2019","journal-title":"Ann. 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