Question

Cara Ryder managers a ski school in a large resort and is trying to develop a schedule for instructors. The instructors receive little salary and work just enough to earn room and board. The receive free skiing and spend most of their free time tackling the resort’s notorious double black-diamond slopes. Hence, the instructors work only 4 days a week. One of the lesson packages offered at the resort is a 4-day beginner package. Ryder likes to keep the same instructor with a group over the 4-day period, so she schedules the instructors for 4 consecutive days and then 3 days off. Ryder uses years of experience with demand forecasts provided by management to formulate her instructor requirements for the upcoming month.

Day	M	T	W	Th	F	S	Su
Requirements	7	5	4	5	6	9	8

a) Determine how many instructors Ryder needs to employ. Give preference to Saturday and Sunday off. (Hint: Look for the group of 3 days with the lowest requirements.)

b) Specify the work schedule for each employee. How much slack does your schedule generate for each day?

Answer 1

a)

Let M, T, W, Th, F, S, Su be the number of employees to start work on respective day of the week.

The LP model is following:

Min M+T+W+Th+F+S+Su

s.t.

F+S+Su+M >= 7

S+Su+M+T >= 5

Su+M+T+W >= 4

M+T+W+Th >= 5

T+W+Th+F >= 6

W+Th+F+S >= 9

Th+F+S+Su >= 8

Solution using LINGO is following:

Optimal solution:

M = 1

T = 0

W = 2

Th = 2

F = 2

S = 3

Su = 1

Objective Value = 11 (total employed)

b)

Work schedule:

1 employee starts on Monday and works through Thursday.

2 employees start on Wednesday and work through Saturday

2 employees start on Thursday and work through Sunday

2 employees start on Friday and work through Monday

3 employees start on Saturday and work through Tuesday

1 employees start on Sunday and work through Wednesday

Refer LINGO Solution Report, Slack for each day (Row 2 through 8) is 0