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The processing time of a batch is the greatest job processing time in that batch (parallel batching or p-batching). The scheduler wants to minimize a given objective function <jats:italic>f<\/jats:italic>, where <jats:italic>f<\/jats:italic> is the total rejection penalties of the rejected jobs (rejection cost) plus the makespan of the scheduled ones. We formulate the aforementioned problem as a 0\u20131 mixed integer programming model. We also apply an effective dynamic programming algorithm (DPA) to calculate a lower bound (LB) on the optimal cost of the problem. To tackle the problem, we propose a grouping algorithm, based on league championship algorithm (LCA), with new updating equations maintaining the major characteristics of the original updating equations of the LCA and well-suited to the structure of the problem. For small problems, performance of the proposed LCA is compared with GAMS\/CPLEX solver. For large-scale instances, a genetic algorithm is adopted as a basis for comparison. Simulated experiments confirm the performance of the proposed methods.<\/jats:p>","DOI":"10.1051\/ro\/2023050","type":"journal-article","created":{"date-parts":[[2023,4,7]],"date-time":"2023-04-07T08:07:25Z","timestamp":1680854845000},"page":"1453-1479","source":"Crossref","is-referenced-by-count":4,"title":["Effective league championship algorithm and lower bound procedure for scheduling a single batch-processing machine with non-identical job sizes and job rejection"],"prefix":"10.1051","volume":"57","author":[{"given":"Saeed","family":"Afkhami","sequence":"first","affiliation":[]},{"given":"Ali","family":"Husseinzadeh Kashan","sequence":"additional","affiliation":[]},{"given":"Bakhtiar","family":"Ostadi","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.cie.2017.08.007","volume":"112","author":"Abbasi-Pooya","year":"2017","journal-title":"Comput. 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