Question

Workforce management is central to efficient operations and good customer service. Proper scheduling of employees can mean the difference between profitability and business failure.

As the manager of a Popsicle stand, you are required to hire and set the weekly work schedule for your employees. The required staffing levels for the week are as follows:
Total employees required Monday = 5, Tuesday = 7, Wednesday = 7, Thursday = 10, Friday = 16, Saturday = 18, Sunday = 12. Assume the same staffing requirements continue week after week.

Full time employees work 5 consecutive days and earn $120 per day.

Question: Provide any feasible schedule so you can start first week of work. What is the minimal weekly staffing cost you can achieve while meeting the required staffing levels? How much savings do you have compared to your first week schedule?

Excel would also be great(:

Answer 1

A feasible first week schedule is following:

Number of employees starting their work on Monday = 5

Number of employees starting their work on Tuesday = 2

Number of employees starting their work on Wednesday = 0

Number of employees starting their work on Thursday = 3

Number of employees starting their work on Friday = 6

Number of employees starting their work on Saturday = 7

Number of employees starting their work on Sunday = 0

Total number of employees scheduled in the first week = 5+2+0+3+6+7+0 = 23

Total payroll cost based on first week schedule = 23*120*5 = $ 13800

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Stable weekly schedule (except for first week) is determined using the following linear program

Let M, T, W, Th, F, St, S be the number of employees scheduled to start their work week from respective day of the week, i.e. M for Monday, T for Tuesday, W for Wednesday, Th for Thursday, F for Friday, St for Saturday and S for Sunday.

Minimize 120*5*(M+T+W+Th+F+St+S)

s.t.

Th+F+St+S+M >= 5

F+St+S+M+T >= 7

St+S+M+T+W >= 7

S+M+T+W+Th >= 10

M+T+W+Th+F >= 16

T+W+Th+F+St >= 18

W+Th+F+St+S >= 12

All variables >= 0

Solution of the LP model using LINDO is following:

Optimal schedule:

M = 0

T = 6

W = 7

Th = 4

F = 1

St = 0

S = 0

Weekly payroll = $ 10800

Savings compared to the first week schedule = 13800 - 10800 = $ 3000