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On the Meaningfulness of Optimal Solutions to Scheduling Problems: Can an Optimal Solution be Nonoptimal?
We consider the problem of finding an optimal schedule for jobs on a single machine when there are penalties for both tardy and early arrivals. We point out that if attention is paid to how these penalties are measured, then a change of scale of measurement might lead to the anomalous situation where a schedule is optimal if these parameters are measured in one way, but not if they are measured in a different way that seems equally acceptable. In particular, we note that if the penaltiesdoi:10.1287/opre.46.3.s120 fatcat:qa5ml2mmdfbh7gwh67q3mgcp6e