A Personnel Allocation Problem in a JapaneseElectrical Manufacturer: A Brief NoteQuestions
1. Can a personnel allocation planned with researcher-proposing DA algorithmbe, in theory, an eﬀective way to solve a personnel problem this electricalmanufacturer is currently faced with?
2. What are pros and cons of a personnel allocation planned with researcherproposing DA algorithm?
3. Consider whether a personnel allocation planned with researcher-proposing
DA algorithm can be an eﬀective way to solve a personnel problem for thismanufacturer, referring to data described in this case.
4. A clinical training system reform made in 2004 is a precedent of applicationof the DA algorithm to real practices in Japanese society. Consider pros
and cons of introducing DA algorithm to the Japanese firms which havediﬀerent employment systems and practices.
5. To what industries can we apply the DA algorithm to personnel allocation
problems?

1

1

A situation

1.1

Allocation of in-house researchers to R&D teams

In a Japanese electrical manufacturer, there are some departments which arecovered with inter-departmental divisions. The R&D division is one of those divisions, which functions as a control oﬃce of technical things for each department.
There are 113 researchers in the R&D division and department, each belonging
to one of 13 R&D teams.
• The configuration of the R&D teams and the allocation of in-house researchers placed in each team may be fine-tuned as necessary, but in mostcases, those are reviewed in the budget formulation period (in January orFebruary) for the next fiscal year.
• It is the group manager (GM) who is responsible for senior managementin the R&D division to examine the allocation of researchers to each R&Dteam; For each team, GM one-sidedly determines a team manager (TM)
who manages the team and assigns some researchers to the team.
• Researchers’ requests are rarely reflected on their personnel assignment, because of their placement history, past evaluation, the in-house qualifications
and positions, and their future career development planned by the company.
• The tendency to be fixed is rigid in their allocation to each division; Since
each researcher has a technical expertise area, it is diﬃcult to replace researchers even when it is desired according to the amounts or types ofvarious tasks required by the company.
• Problem: Further innovation in R&D is constantly being sought within
this company, and there is concern that the rigid assignment of researchers
in R&D teams may be a factor that hampers this.
• In addition, This company well recognizes that, in order to promote R&D
activities, it is necessary to motivate researchers and induce themto invest for further skill acquisition.

2• This electrical manufacturer has several R&D themes and priority diﬀers according to each theme. In addition, complementarity among themes shouldalso be considered.
There are many evaluation criteria on personnel assignment of in-house researchers to R&D teams; The company must take into consideration variousfactors, as noted above.

1.2

Researcher-proposing DA algorithm

In late 2016, before the time of budget formulation for the next fiscal year, thiselectrical manufacturer examined a test with researcher-proposing DA algorithm,
which has the following nice properties.
• Stability: When a personnel allocation is proposed, if, for any objections
that are claimed by any groups consisting of researchers and a R&D team,(1) no researcher in such a group is not matched with the team within
the group which is at a higher rank in his or her preferences and (2) noresearcher who is at a higher rank in the evaluation of the team is not
assigned to the team, then the matching is called a stable matching.
• Strategy-proofness for researchers: For each researcher, whatever otherresearchers report their preferences over R&D teams, it is never assigned
to the more preferable R&D team for him- or her-self by misrepresenting
their true preference.
• Optimality for researchers: Every researcher is matched with the teamhe or she most prefers among among R&D teams with which he or she canbe matched with in all stable matchings.
Any (pair-wise) objections to stable matchings do not make sense from its
definition, if they exist. In other words, unless there is no change in the company’s
R&D policy and there is no unexpected shock in the external environment, for
any researches and any R&D teams, any replacements of human resources due totheir dissatisfaction at the current assignment do not occur.
On the other hand, the following property is not guaranteed for researcherproposing DA algorithm.
3• Pareto eﬃciency among researchers: In order for a researcher to bematched with an R&D team which is at a higher rank than a team currently
assigned to in his or her own preference, someone(s) else must be transferred
to a team which is at a lower rank in their preferences.

2

Personnel Allocation Plan

The examiner asked researchers to represent their preferences and solicited TMs
to state their evaluation via emails. All data were put IDs in order to secure
their privacy. GM was asked to submit the quotas of teams, where quota A is thecurrent one while quota B was the one planned for the next fiscal year. There
are two types of questionnaire to researchers.
(1) Simply asked to represent their preferences over R&D teams(2) After suggesting the directions of R&D in the division, asked to state theirpreferences in order to make further innovation in this electrical manufacturer.
In practice, people in the department other than the personnel department do
not recognize all researchers. As for questionnaires to 13 TMs, the examiner thus
asked to refer to the department of human resources with evaluation items such as
skills, knowledge, job qualifications and carriers that each division emphasizes inthe execution of tasks, as evaluation items, if TMs do not know some researchersother than particular ones.
In practice, the department other than the Personnel Department does notrecognize all employees, it is diﬃcult to rank accurately and it is inconvenience.
10 researchers who could not reply to questionnaires by the due date arededuced from the quota of teams. Thus, the number of researchers in this examination is 103.

4

Table 1: Questionnaire (1) to researchers
resercher ID

rank 1

rank 2

rank 3···rank 12rank 131142···

1213211112···

323..
.

3..
.

13..
.

4..
.

···

1..
.

2..
.

102

2129···

18103

2117···

13Table 2: Questionnaire (2) to researchers
rank 3 · · ·researcher ID

rank 1

rank 2

rank 12rank 131365···

21221112···

313..
.

3..
.

7..
.

5..
.

···

2..
.

1..
.

102

2116···

15103

2117···

13Table 3: Questionnaire to teams
rank 3 · · ·team IDrank 1

rank 2

rank 102

rank 103111412···1314275

102

92···

97

98

375

102

92···

97

98

475

102

99···

98

100

574

102

27···

97

101

674

102

24···

97

101

7..
.

102..
.

103..
.

81..
.

···

100..
.

101..
.

1391514···145

Table 4: Quota of teams
team ID

quota Aquota B

1882121238841095111066671312845988101010115512331357total1031036

Excel for Two-Sided Matching ver.1 (sample1.xlsm) was used for computing
matchings. (1) and (2) in Tables 5-7 correspond to Questinnaires (1) and (2). Forresearchers, the eﬃciency of allocations is measured with the total sum of ranks ofteams matched with researchers in their preferences divided by 103. For teams,
similarly, the eﬃciency is measured with the total sum of ranks of researchers
matched with teams in their evaluation divided by 103. In Table 7, values of theeﬃciency index is shown also for researchers and for teams, separately.
Table 5: Teams with which researchers are matched
123···

102103111···

1212(1)+quota A 1

13···

211(1)+quota B

113···

26(2)+quota A 323···211(2)+quota B

23···

211current

3Table 6: Ranks of teams to which researchers are assigned
123···

102103113···

11(1)+quota A 1

11···12(1)+quota B

111···

12(2)+quota A 1

11···12(2)+quota B

11···12current

17

Table 7: eﬃciency for assignments
current (1)+quota A(1)+quota B(2)+quota A(2)+quota B

eﬃciency

12.9

39.4

40.0

29.4

33.4

teams

10.4

37.6

38.2

27.1

31.1

researchers

2.5

1.8

1.8

2.3

2.38