An algorithm for multiple shift scheduling of hierarchical workforce on four-day or three-day workweeks

This paper presents an optimal algorithm for multiple shift scheduling of hierarchical categories of employees on four-day or three-day workweeks. Employees work four days (three days in the case of three-day workweek) each week, have at least a fraction A out of every B weekends off, work no more than four (three in the case of three-day workweek) consecutive days in a workstretch and have at least some prescribed number of hours off when changing shifts. Such contexts exist in many seven-day-a-week manufacturing and service organizations such as paper mills, steel plants and hospitals. We determine the most economical mix of categories of employees satisfying scheduling constraints under a pattern of demand for employees. The pattern is such that the weekday demand is greater than or equal to the weekend demand for each category and each shift. We then present an algorithm to construct feasible work schedules by assigning offdays and shifts to employees. We establish that the work schedules satisfy all the scheduling constraints and meet the pattern of demand. This paper extends the frontiers of research closer to real world contexts by considering the simultaneous prevalence of multiple shifts and hierarchical workforce.