Table 3 Summary of model components

There is a single objective function to be maximized

Maximize number of personnel work performed per week measured by number of employees included in the plan

One objective function equation is included

Shift sequence restrictions

No worker is to be assigned more than one shift out of three consecutive shifts

For each employee there are 21 inequality constraints

Personnel requirement per shift

At least 1 personnel is required in each shift

There are 21 inequality constraints, the same as the number of shifts in a week

Night shifts per employee

Limits the number of night shifts an employee should serve relative to other shifts the employee is at work. The weekly number of night shifts an employee is on duty should not exceed the number of morning shifts as well as the number of afternoon shifts.

There are 10 constraints in total, 2 per employee.

Weekly total number of shifts per worker

The number of shifts an employee should work in a week is specified by personnel department policy to be exactly 6shifts. If an employee can’t be assigned to 6 shifts per week the employee is excluded from the assignment plan.

There are equations indicating that each personnel should work exactly 6 shifts per week, or none otherwise.

Employee-shift matching variables

The yes or no response variables that indicate whether an employee is assigned to a given shift Xij=1 if shift i assigned to employee j.

There are 21 variables per worker, and a total of 105variables

Variables indicating inclusion in weekly schedule

y _j =1 if employee j is included to work in the weekly shifts, 0 otherwise

There are 5 variables, one per employee