In recent years, labour negotiations for seven-day-week organizations such as hospitals, mining companies and chemical industries have seen an increased emphasis on improving shift schedules. This paper gives an exact lower bound on the number of workers required to satisfy such primary contractual commitments as ensuring that each employee receives at least A out of every B weekends off, everyone works exactly five days per week, and no one works more than six consecutive days. The model addressed is general in that it allows the number of workers required each day to vary. The proof that the bound is the best possible is constructive. A linear time algorithm is presented that generates schedules satisfying all the primary objectives. Extensions discuss means of incorporating secondary objectives such as giving pairs of adjacent days off.
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