{"id":637,"date":"2017-10-07T09:16:21","date_gmt":"2017-10-07T07:16:21","guid":{"rendered":"https:\/\/www.hsu-hh.de\/logistik\/?page_id=637"},"modified":"2017-11-25T12:56:20","modified_gmt":"2017-11-25T11:56:20","slug":"smtwtp","status":"publish","type":"page","link":"https:\/\/www.hsu-hh.de\/logistik\/research\/projects\/smtwtp","title":{"rendered":"SMTWTP"},"content":{"rendered":"

The single machine total weighted tardiness problem (SMTWTP) is a well-known planning problem from operations research, engineering and computer science.<\/p>\n

In the SMTWTP, a set of jobs\u00a0J<\/strong>\u00a0= {J1<\/sub>,…, Jn<\/sub>}\u00a0needs to be processed on a single machine. Each job\u00a0Jj<\/sub>\u00a0consists of a single operation only, involving a processing time\u00a0pj<\/sub>\u00a0> 0 \u2200 j = 1, …, n. The relative importance of the jobs is expressed via a nonnegative weight\u00a0wj<\/sub>\u00a0> 0 \u2200 j = 1, …, n. Processing on the machine is only possible for a single job at a time, excluding parallel processing of jobs. Each job\u00a0Jj<\/sub>\u00a0is supposed to be finished before its due date\u00a0Dj<\/sub>. If this is not the case, a tardiness\u00a0Tj<\/sub>\u00a0occurs, measured as\u00a0Tj<\/sub>\u00a0= max {sj<\/sub>+ pj<\/sub>\u00a0– Dj<\/sub>; 0}, where\u00a0sj<\/sub>\u00a0denotes the starting time of job\u00a0j. The overall objective of the problem is to find a feasible schedule\u00a0x\u00a0minimizing the total weighted tardiness\u00a0TWT, i. e.\u00a0min TWT = \u2211 wj<\/sub>\u00a0Tj<\/sub>.<\/p>\n

Proposition of new large benchmark instances<\/h3>\n

Looking at the scientific literature, it becomes clear, that the well-known benchmark instances (see the\u00a0OR Library<\/a>) do not pose a challenge to state-of-the-art algorithms any longer. Therefore, and on the basis of our previous research, novel and considerable larger instances have been proposed (n=1000).<\/p>\n