Employee Scheduling long Problem QMB612

Jake operates a small business that requires di↵erent numbers of full-time employees on di↵erent days of the week. The number of full-time employees required each day is given in Table 2. The employees are part of an employee union whose rules state that each full-time employee must work five consecutive days and then receive two days o↵. For example, an employee who works Monday to Friday must be o↵ on Saturday and Sunday. The company wants to meet its daily requirements using only full-time employees. Its objective is to minimize the number of full-time employees on its payroll. a) Develop an optimization model that relates five day shift schedules to daily numbers of employees available and to use solver on this model to find a schedule that uses the fewest number of employees a nd meet all daily workforce requirements b) Suppose the employees want more flexibility in their schedules. They want to be allowed to work five consecutive days followed by two days o↵ or to . Modify the original model (with integer constraints) to allow this flexibility. That is, reformulate the problem above and solve it. Please show your formulation go get credit. Might this be a good deal for management as well as labor? Explain c)In the original employee scheduling problem, suppose Jake has 28 full-time employees and is not allowed to fire any of them or hire more. Reformulate this problem to determine a schedule that maximizes the number of weekend days o↵ received by these employees.