Question

Scheduling in the restaurant
Workforce management is central to efficient operations and good customer service. Proper scheduling
of employees can mean the difference between profitability and business failure.
After faithfully serving the OM profession for 40 years, you decide to retire and open a restaurant.
Among the hundreds of details with opening a restaurant, you need to hire and schedule employees.
Based on the foot traffic of other restaurants in the area, you expect that you will need the following
number of employees each day:
Day of the week Employees Needed
Monday 4
Tuesday 5
Wednesday 5
Thursday 10
Friday 12
Saturday 14
Sunday 2
Your employees will work four consecutive days and then have three days off. They will be paid $120 for
each day they work. In your rush to get the restaurant started, you haphazardly hire 19 employees. Five
will start on Monday, five will start on Thursday and nine will start on Friday. This schedule satisfies the
above work requirements, but you have no idea how optimal this is.
Question: How much money would you save each week from your current schedule if you optimized
your workforce?

Present the problem, present your approach, define variables, show excel model forumulation and solution using solver in excel.

Answer 1

The optimal workforce plan is determined by the following linear optimization model

Let M, T, W, Th, F, St, S be the number of employees who start on respective day

Minimize 120M+120T+120W+120Th+120F+120St+120S

s.t.

F+St+S+M >= 4

St+S+M+T >= 5

S+M+T+W >= 5

M+T+W+Th >= 10

T+W+Th+F >= 12

W+Th+F+St >= 14

Th+F+St+S >= 2

All variables integer

Solution using LINDO is following:

Optimal schedule:

Number of employees to start on Monday, M = 0

Number of employees to start on Tuesday, T = 2

Number of employees to start on Wednesday, W = 10

Number of employees to start on Thursday, Th = 0

Number of employees to start on Friday, F = 0

Number of employees to start on Saturday, St = 4

Number of employees to start on Sunday, S = 0

Total number of employees required = 0+2+10+0+0+4+0 = 16

Total weekly payroll = $ 1920

Total weekly payroll of 19 employees (original schedule) = 19*120 = $ 2280

Money saved by implementing optimal schedule = 2280 - 1920 = $ 360