Shift Planning in a Department Store

The sales staff in a department store are working in a shift system. During a business reorganization the management are planning to re-engineer the shift system. According to the new regulations, every shift has to include seven or eight working hours. For eight-hours-shifts, one or two hours of rest time have to be granted after four hours of
working. For seven-hours-shifts, one hour of rest time has to be granted after three or four hours of working.

The gross costs per working hour are determined as follows:

  • for an eight-hours-shift with one hour rest – 60 francs;
  • for an eight-hours-shift with two hours rest – 70 francs;
  • for a seven-hours-shift – 65 francs.

The opening hours of the department store are from 8:00 till 21:00. The demand for sales staff (number of persons per one hour interval) has been determined basing on customer numbers depending on time and can be found in the following table:

Demand for sales staff per one hour intervals

Our task is to find a shift plan covering staff demand with minimal costs.