Mystery Shoppers Problem
A well-known cosmetic company wants to evaluate the performance of her
saleladies, who station at the company's counters at various department
stores in different geographical locations. For this purpose, the
company has hired some secret agents to disguise as shoppers to visit
the salesladies. The visits must be scheduled in such a way that each
saleslady must be visited by shoppers of different varieties and that
the visits should be spaced out roughly evenly. Also, shoppers should
visit salesladies in different geographic locations. The exact constraints,
which ensure the statistical soundness of the project, follow.
1. There are totally 19 outlets to be visited. They are located in 4
geographical regions:
- 5 outlets in Area 1: Outlet 1
Outlet 2
Outlet 3
Outlet 4
Outlet 5
- 5 outlets in Area 2: Outlet 6
Outlet 7
Outlet 8
Outlet 9
Outlet 10
- 5 outlets in Area 3: Outlet 11
Outlet 12
Outlet 13
Outlet 14
Outlet 15
- 4 outlets in Area 4: Outlet 16
Outlet 17
Outlet 18
Outlet 19
2. There will be 1 to 4 salesladies in each outlet. Each saleslady will
be visited by 4 different shoppers. The frequency of visits to a
particular outlet will be the number of salesladies times 4. There are
totally 35 salesladies working in all outlets everyday. Therefore,
the total number of visits is 140.
3. The shoppers are divided into 4 groups according to age, professions,
and etc. Each group has 10 shoppers. Therefore, the total number
of shoppers is 40. Therefore, in each group of shoppers, 5 shoppers
will perform 3 visits and the other 5 shoppers will perform 4 visits.
4. Each shopper should only visit 1 outlet in each of the 4 areas.
5. 4 of the outlets are boutiques, namely Outlet 1, Outlet 10, Outlet 14
and Outlet 15. They are not to be visited by shoppers in Group 2.
6. All salesladies should be visited 2 times in the first 2 weeks of
fieldwork.
7. The total fieldwork period will be 4 weeks. Theoretically, each
shopper has to pay 1 visit each week. However, shoppers making 4 visits
must have done 2 visits by the end of the second week. Shoppers making
3 visits should have done 1 or 2 visits by the end of the second week.
The data of the first 50% visits will be analysed and put in an interim
report.
8. Listed below are locations of the 19 outlets and the number of
salesladies in that particular outlet. (Outlets with * are boutiques)
Outlet Number of Salesladies
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*Outlet 1 2
Outlet 2 4
Outlet 3 1
Outlet 4 2
Outlet 5 1
Outlet 6 2
Outlet 7 1
Outlet 8 1
Outlet 9 1
*Outlet 10 2
Outlet 11 2
Outlet 12 2
Outlet 13 1
*Outlet 14 2
*Outlet 15 1
Outlet 16 2
Outlet 17 2
Outlet 18 4
Outlet 19 2