The decision variables for a staff scheduling optimization problem are as follows:

• X = one shift consisting of three hours or one hour
• h = employee type

Where, h = 1 Full-time employee

h = 2 Part-time employee

h = 3 Casual employee

• i = employee number

Where, 6 employees available for full-time work

12 employees available for part-time work

2 employees available for casual work

• j = shift

Where, j = 1 8 am - 11 am

j = 2 11 am - 2 pm

j = 3 2 pm - 5 pm

j = 4 5 pm - 6 pm

• k = day of week

Where k = 1 Monday

k = 2 Tuesday

k = 3 Wednesday

k = 4 Thursday

k = 5 Friday

k = 6 Saturday

k = 7 Sunday

i.e.)

X₁₃₄₄ = 1, if full-time employee 3 is assigned to shift 4 on Thursday

X₃₁₂₇ = 1, if casual employee 1 is assigned to shift 2 on Sunday

How to write the following constraints for Integer Linear Programming:

1) All employees may not work more than 6 consecutive days

2) All employees will not work more than 5 consecutive hours without a meal break