Mathematical Programming and Service Scheduling

There are many business situations where it might be necessary to keep the potential service level (preparedness) above requirements at least in some of the time intervals. For instance, a fleet of trucks (or cabs) or group of production machines, cannot be easily adjusted month by month and, therefore, during slack periods the potential service level may exceed requirements. In a manufacturing firm, there are certain functions to be performed, such as maintenance or clerical work (often overhead type functions), where again the potential service level is expensive to change. In fact, even in the case of production workers, the expense of hiring, training, firing, or the contractual obligations of guaranteed wage agreements may make it undesirable to change the level of employment during slack periods. The reader will readily find further illustrations of the type of planning problems we are describing here.