A presentation given at ISAGA 2016

1. A Serious Game for
Eliciting Tacit Strategies
for Dynamic Table
Assignment in a
Restaurant
Hajime Mizuyama, Ayano Yoshida,
Tomomi Nonaka
Aoyama Gakuin University, Japan
28/Sep/2016 @ Melbourne, Australia
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 1 / 27

2. Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 2 / 27

3. Research Background and Objective
Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 3 / 27

4. Research Background and Objective
Research Background
In a restaurant, customers often need to wait until they can be seated
at a table, and this waiting time can lower their satisfaction level.
The waiting time is affected by:
Amount of resources, i.e. seats and tables
Configurations of the seats and tables
How the tables are allocated to customers on the fly
→ Dynamic table assignment task
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 4 / 27

5. Research Background and Objective
Research Objective
Table assignment task is usually not automated, and handled by an
individual due to the task’s dynamic as well as subjective aspects.
Accordingly, the task’s performance depends largely on who is in
charge.
The objective of this research is to provide a means for:
Eliciting effective tacit strategies from those who are good at
performing the task
Experientially learn the strategies
→ A serious game
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 5 / 27

6. Description of Table Assignment Problem
Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 6 / 27

7. Description of Table Assignment Problem
Some Notations and Assumptions
There are N tables Tn (n = 1, . . . , N), and whose capacity is Pn.
Some tables can be combined into a unit, and whose capacity is
equivalent to the sum of the composing tables’ capacities.
The table configurations are expressed by a graph G = (V, E),
where V = {T1, T2, . . . , TN} and any edge in E represents that the
pair of tables connected by the edge can be combined.
There are M customer groups Cm (m = 1, . . . , M) of size Sm.
Each customer group Cm should be assigned a table or a
combined unit whose capacity is equivalent to or greater than Sm.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 7 / 27

8. Description of Table Assignment Problem
Basic Problem Structure
Decision variables: xmn (m = 1, . . . , M; n = 1, . . . , N)
A variable whose value is 1 if table Tn is assigned to customer group
Cm, and 0 otherwise
Constraints:
M
m=1
xnm ≤ 1 (n = 1, . . . , N)
(Vm, E|Vm) = a connected subgraph of G
Vm = {Tn|xnm = 1} (m = 1, . . . , M)
Tn∈Vn
Pn ≥ Sm (m = 1, . . . , M)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 8 / 27

9. Description of Table Assignment Problem
Dynamic Aspect of the Problem
Customer groups may arrive at the restaurant without
reservations.
Each customer group assigned to certain tables will at some time
finish the meal and leave the restaurant.
Some customer groups may leave the queue without being
assigned to tables due to, for instance, a long waiting time.
→ The table assignment problem should be handled in a dynamic
manner, where the assignment should be kept updated according to
the changing conditions.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 9 / 27

10. Description of Table Assignment Problem
Subjective Aspect of the Problem
The level of dissatisfaction of customers may depend not only on
the length of their wait time but also that of other customers as
well as how they are treated while waiting.
It may also depend on which table they are assigned to, etc.
Further, as this is subjective, how those factors affect the level of
dissatisfaction will differ among individual customers.
→ It is difficult to define a formal objective function, and the task’s
performance should be evaluated in the field through the interpretation
of customer behavior.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 10 / 27

11. Development of a Serious Game
Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 11 / 27

12. Development of a Serious Game
Outline of Single Player Simulation Game
Customers randomly arrive at the restaurant in groups of different
sizes, and wait in a room to be seated.
The player can at any time assign a set of tables to any of the
customer groups, if all the tables are vacant and combinable.
When the player successfully assigns tables to a customer group,
a certain number of points are added to the score.
If the level of dissatisfaction due to waiting reaches a specified
limit, a customer group will leave before being assigned to tables,
and this results in a deduction of points from the score.
When some conditions are satisfied, points are added to or
deducted from the score according to the customers’ preference.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 12 / 27

13. Development of a Serious Game
Table Configurations
Capacities of tables and their combinability
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 13 / 27

14. Development of a Serious Game
Game Screens
Waiting room Dining room
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 14 / 27

15. Application Experiments
Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 15 / 27

16. Application Experiments
Case1: Experienced and Inexperienced Players
Experienced Inexperienced
AverageScore
02004006008001000
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 16 / 27

17. Application Experiments
Case2: Characterization of Strategies of Players
In Case2, players were instructed to play the game twice.
1st trial: according to their own strategies
2nd trial: following specified standard rules
The standard rules used were a simple First-Come-First-Served
(FCFS) dispatching rule with small modifications.
→ The scores of their 1st trials are significantly higher than those of
the 2nd.
→ The difference between the trials are analyzed.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 17 / 27

18. Application Experiments
Characteristic Variables #1
x1 : the difference between the trials (1st minus 2nd) in the
number of customers assigned tables
x2 : the difference between the trials in the number of groups
assigned tables
x3 : the difference between the trials in the average size of the
groups assigned tables
x4 : the difference between the trials in the number of customers
who left without having a meal
x5 : the difference between the trials in the number of groups who
left without having a meal
x6 : the difference between the trials in the average size of the
groups who left without having a meal
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 18 / 27

19. Application Experiments
Characteristic Variables #2
x7 : the difference between the trials in the number of times bonus
points were received
x8 : the difference between the trials in the number of times
penalty points were deducted
x9 : the difference between the trials in the average level of
dissatisfaction of the customer groups
x10 : the difference between the trials in the number of times
players changed the sequence of customer groups from the
one specified by the standard rules
x11 : the difference between the trials in the number of times that
players assigned bar seats to customer groups when other
tables were available as well
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 19 / 27

20. Application Experiments
Clustering Players into Groups
16
2
8
17
20
14
1
15
5
11
10
7
18
4
19
3
13
9
6
12
012345
Distance
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 20 / 27

21. Application Experiments
Characteristics of Gourp 1
y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
-2-1012
More customers led to dining
room (x1, x2)
More customers left (x4, x5)
Lower dissatisfaction level (x9)
Frequent sequence changes
(x10)
Score improved only a little (y)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 21 / 27

22. Application Experiments
Characteristics of Gourp 2
y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
-2-1012
More customers led to dining
room (x1, x2)
Small groups prioritized (x3)
Not increasing customers left
(x4, x5)
Lower dissatisfaction level (x9)
Infrequent sequence changes
(x10)
Tables rather than bar seats
(x11)
Best performance (y)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 22 / 27

23. Application Experiments
Characteristics of Gourp 3
y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
-2-1012
Fewer customers led to dining
room (x1)
Smaller groups prioritized (x3)
Larger groups left (x6)
Slightly higher dissatisfaction
level (x9)
Bar seats rather than tables
(x11)
Worst performance (y)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 23 / 27

24. Application Experiments
Characteristics of Gourp 4
y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
-2-1012
More customers led to dining
room (x1)
Larger groups prioritized (x3)
Fewer customers left (x4)
Quite high dissatisfaction level
(x9)
Infrequent sequence changes
(x10)
Moderate performance (y)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 24 / 27

25. Application Experiments
Characteristics of Gourp 5
y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11
-2-1012
Fewer customers led to dining
room (x1)
Larger groups prioritized (x3)
Fewer customers left (x4)
Fewest bonus points (x7)
Bar seats rather than tables
(x11)
Score improved only a little (y)
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 25 / 27

26. Conclusions
Table of Contents
1 Research Background and Objective
2 Description of Table Assignment Problem
3 Development of a Serious Game
4 Application Experiments
5 Conclusions
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 26 / 27

27. Conclusions
Conclusions
A serious game approach was proposed for eliciting effective tacit
strategies to handle the dynamic table assignment task.
A prototype of the game was developed and laboratory
experiments were conducted using the prototype.
It was confirmed that the proposed game and the actual table
assignment task have at least some characteristics in common.
Further, the strategies taken by the players can be characterized
through the data obtained by the game.
Mizuyama, Yoshida, Nonaka (AGU) Serious Game for Table Assignment ISAGA 2016 27 / 27