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 h ierarchical categories of employees on four-day or three-day workweeks. Emp loyees work four days (three days in the case of three-day workweek) each w eek, have at least a fraction A out of every B weekends off, work no more t han four (three in the case of three-day workweek) consecutive days in a wo rkstretch and have at least some prescribed number of hours off when changi ng shifts. Such contexts exist in many seven-days-week manufacturing and se rvice organizations such as paper mills, steel plants and hospitals. We det ermine the most economical mix of categories of employees satisfying schedu ling constraints under a pattern of demand for employees. The pattern is su ch that the weekday demand is greater than or equal to the weekend demand f or each category and each shift. We then present an algorithm to construct feasible work schedules by assigning offdays and shifts to employees. We es tablish that the work schedules satisfy all the scheduling constraints and meet the pattern of demand. This paper extends the frontiers of research cl oser to real world contexts by considering the simultaneous prevalence of m ultiple shifts and hierarchical workforce.