One-processor scheduling with symmetric earliness and tardiness penalties
Mathematics of Operations Research
Art and Theory of Dynamic Programming
Art and Theory of Dynamic Programming
Bicriterion scheduling with equal processing times on a batch processing machine
Computers and Operations Research
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Given a set of simultaneously available jobs, each assigned a due-date, to be processed on a single machine, the problem is to find an optimal order to process the jobs that minimizes a penalty function. Since the effectiveness of a schedule is primarily evaluated on the basis of its effects on the WIP inventory and order delivery performance, we employ a bicriterion penalty function defined as the weighted sum of the flowtime and earliness and tardiness values of each job. This sequencing problem is shown to be NP-complete, so it is doubtful that a polynomial bound solution algorithm exists. In this paper, a dynamic programming (DP) formulation of the problem is presented and the optimal job sequence is determined by implicit enumeration in accordance with the DP optimality principle.