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JOk i

FACULTY WORKING

PAPER NO. 998

JTHE UBRARY OF THK

•JAN 1

UNIVER.

An Application of Computerized Decision
Tree Models In Management-Union Bargaining

Frederick W. Winter

College Of Comrnerce and Business Administration
Bureau cf Economic an:J B^sr-ans ftesearcti
University ©1 Illinois, Mr^anB-Charripaign

BEBR

FACULTY WORKING PAPER NO. 998
College of Commerce and Business Administration
University of Illinois at Urbana- Champaign
December 1983

An Application of Computerized Decision
Tree Models in Management-Union Bargaining

Frederick W. Winter, Professor
Department of Business Administration

A computerized model to assist in management-union negotiations
is presented. Results indicate that benefits extend beyond improved
decision-making .

Digitized by the Internet Archive

in 2011 with funding from

University of Illinois Urbana-Champaign

http://www.archive.org/details/applicationofcom998wint

For a management team assigned to negotiate a labor contract with a
union, often the only perceived certainty is that the outcome will be
viewed as no win: either they will give away more than absolutely
necessary or they could cause a costly strike that the company can ill-
afford. To add to this burden, team members often must debate upper
management prior to engaging the union in verbal combat. The team's
recommendations are generally difficult to defend since they are based
on members' intuition. Thus if management has different intuition, a
pre-bargaining stalemate is reached. Whatever the outcome, both the
bargaining team and management are vulnerable to swings of emotion
during the bargaining process.

This paper will show how a decision tree approach was used to
develop reasonable bargaining positions that helped reduce the no win
atmosphere of bargaining. In general, the model and its computer
application offered the following benefits:

1. The model helped- the bargaining team to select preferred
positions/strategies from a large set of possible bargaining
posit ions/ strategies.

2. The model can improve communication between upper management
and the bargaining team by focussing the application of
intuition on only those model components that are uncertain.
Therefore, rather than debate the preferred position, it is
more productive to debate the inputs to the model that lead to
the preferred position.

3. The model easily demonstrated the risks of alternative bar-
gaining positions/strategies.

-2-

4. The model increased the confidence of bargaining team members
and made them less vulnerable to union tactics.

Decision Modelling of the Bargaining Process
By most standards, the decision process and outcomes of management-
union bargaining is simple. Management decides on the package it is
prepared to offer and the union decides whether it will settle for the
package or strike. What complicates the game slightly is that the game
is played over multiple periods because each party believes that some-
times a strike may dislodge the opponent from an unfavorable position.
Thus any bargaining position must consider subsequent moves in the
event a settlement is not reached.

Figure 1 details how complex a decision tree of just 3 settlement
packages can look after 3 strike periods (plus one period prior to
strike). In spite of the apparent complexity, the structure is really
quite simple. As shown in Figure 1, management can decide at time
period 0 (prior to strike) to offer either package 1, 2 or 3. In the
same time period, the union can agree to settle or strike. If a strike
results, management can, during the first period of strike, offer
settlement packages 1, 2 or 3. In the accompanying computer applica-
tion, a simplifying assumption was made that management cannot offer a
package of less attractiveness to the union which earlier rejected a
package. In this way, subsequent expansion of the tree is greatly
duced. Therefore, if packages are ordered in increasing attraction

n, management cannot offer package 1 to a union which struck
on an offer of package 2.

-3-

tri^

Figure 1. Decision Tree for Four Period-
3 Package Model

-4-

Al though the management team may believe the negotiation process
to be loaded with uncertainty, decision structuring indicates that
there are a number of components to the decision that are known: the
cost of the strike and the cost of the settlement package (discounted
over the life of the contract) are generally calculable. The only
uncertainty is whether the union will settle or strike for each of the
packages during the various time periods.

Although modeling of settlement probabilities based on either sta-
tistical data or preposterior analysis would be possible, the approach
that is generally most simple and acceptable to management is to use
simple subjective probability judgments (that may be based on histori-
cal data) . The general feeling is "each bargaining situation is dif-
ferent." These probabilities are simply anticipated union settlement
probabilities for the alternative packages at different strike inter-
vals. (See Figure 2 for the inputs in the computer program to be
described in the next section.)

Computational Procedures
The decision facing management here and now is "what settlement
package should 1 next be prepared to offer the union?" Because the
choice of a package at time 0. can constrain choices later on, it is
necessary to determine the optimal path through the multi-stage deci-
sion tree of Figure 1.

A method of solution is to use a dynamic programming type of back-
sgration to determine optimal offers at period n and work back-
•terraine the optimal offer at time period 0. "Best decisions'
on minimum expected loss (or in today's bargaining climate

PROGRAM BARGAIN

HOW MANY PACKAGES I'O CONSIDER?

? 3

A PERIOD IS HOW LONG? ( E *G* J WEEK»?.WEEKS )

? 1 w e e k

HOW MANY STRIKE PERIODS MAXIMUM? (UP (0 P ALLOWED)

? 3

IE HOT SETTLED BY THIS Tl ME t IT IS ASSUMED TO BE SETTLED

AFTER 6 STRIKF PERIODS WITH PACKAGE 3 AS THE RE SUM

WHAT'S T H E C 0 S T 0 F S T R I K h. F 0 R f H t. NU M B E R 1 P E R 1 0 1 1 ( I W I... E K ) 1

? 20000

WHAT'S THE COST OF STRIKF FOR THE NUMBER ? PERIOD CI WEEK)?

? 24000

W H A T ' S T HE: COST OF' S T R I K E I- ( ) R T H E N U M H E R 3 F1 E R 1 0 D ( 1 W I • h. K ) ?

? 35000

WHAT'S THE COST OF STRIKE FOR THE NUMBER A PERIODd WEEK)?

? 38000

WH A T / S I H E COST OF STR I K E F 0 R I H I N UM H F" R 5 P F R 1 0 D ( 1 W EF K ) ?

? 40000

WHAT'S THE COST OF STRIKE FOR TFIF NUMBER 6 PERIOD <1 WEEK)?

? 40000

ORDER PACKAGES BY INCREASING ATTRACTION TO UNION

WHAT IS THE COST PER PACKAGE?

PACKAGE 1 'jI

? 1 0000

PACKAGE 2 ?

"? 40000

PACKAGE 3 ?

? 95000

WHAT' S ! It E P R 0 B A B 1 1 . I T V 0 F S E T T I. I N G F 0 R

PACKAGE 1 AFTER 0 PERIODS OF STRIKE?

? ♦!

PACKAGE 1 AFTER 1 PERIODS OF STRIKE?

? .15

PACKAGE 1 AFTER ? PERIODS OF STRIKE?

? ,10

PACKAGE 1 AFTER 3 PERIODS OF STRIKE?

? 1 2

PACKAGE 2 AFTER 0 PERIODS OF STRIKE?

? ,3

PACKAGE 2 AFTER 1 PERIODS OF STRIKE?

? ,33

PACKAGE 2 AFTER 2 PERIODS OF STRIKE?

? .4

PACKAGE 2 AFTER 3 PERIODS OF STRIKE?

? ,5

PACKAGE 3 AFTER 0 PERIODS OF STRIKE?

? ,8

PACKAGE 3 AFTER 1 PERIODS OF STRIKE?

■■: .,'?

PACKAGE 3 AFTER 2 PERIODS 01 STRIKF?

? our

PACKAGE 3 AFTER 3 PERIODS OF STRIKE?
'i:- ,99

Figure 2. Sample Inputs to Computer Model

-6-

maybe even maximum expected gain) . More complicated algorithms based
on risk-return tradeoffs are possible but require more demands of man-
agement. However, because risk concerns are important, the program
deliberately avoids the choice of a "best position." Instead the
expected loss of each option as well as a probability distribution of
outcomes (see Figure 3) is shown. Traditional variance measures are
avoided since a graphic display is more meaningful to management. In
addition, the best moves following the initial position choice are
output (see Figure 4).

The program to process this has been written in BASIC language and
has been run on a Control Data mainframe and IBM and Radio Shack per-
sonal computers. BASIC allows a simple questioning interaction between
negotiator and computer and allows the program to be run on most micro-
computers.

Results
The initial objective of the program was to develop a tool whereby
the negotiator could realize more favorable bargaining outcome through
improved decision-making. This, as it turns out, was realized, but by
products of this application turned out to be much more significant
than the mere determination of the optimal bargaining position.

For example, the first use of the model convinced the users that
good data Inputs would be important. In response, the firm developed
:rocoraputer program that could calculate the package costs.

sly, calculations had been no trivial task given complicated cost
allowance factors. Secondly the negotiating team felt that
them more confident in establishing a meaningful dialog

THIS PERTAINS TO INITIAL. OH-ER 01' HACK, 2 WITH SUBSEQ MOVES
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OABCDEFG H I J K L. M r
PACKAGE 2 EXPECTED I.OSS=

o p

89812

♦ 1

Note: left column of numbers represents probability of dollar outcome
represented by letters. A key as to letter outcomes is printed
but not shown; for example here: $-66,400 < outcome Q < $-52,300.

Figure 3. Sample Output for Offer of Package 2

GIVEN r

01-

FER

I N

PERT on

PACK

;agf

■->

(STRIKE PER I 0)D THE BEST NEXT

OFFER IS PACKAGI
n

3
3
'?
2

3
3
3
3
3
3

Figure 4. Output Indicating Best Moves Following Initial Offer

-9-

with upper management prior to actual bargaining. In the bargaining
team there was the pervasive feeling that management was often unaware
of the risks of alternative bargaining strategies. Now a tool was
available to demonstrate those risks. To further demonstrate the out-
come of strategies of particular interest to upper management, a
feature was added that allowed the expected value and risk of manage-
ment's preferred strategies to be seen (see Figure 5).

Although different use strategies of the model are still being
tested, the first actual application did result in a solution which
increased the confidence of all members of the bargaining strategy
group. The process which was used and the results produced were the
following:

1. Five committee members decided on six diverse packages to
be offered to the union

2. Consensus was developed on the cost of the packages (using
the previously described microcomputer estimation package)
as well as the cost of each period of strike

3. Each member of the committee interacted with the computer
by inputting his probabilities of union settlement over
the time horizons considered.

4. One of two "adjacent" settlement packages (Packages 2 and 3)
were favored by all group members. It was interesting to
note that even though diverse probabilities produced quite
different levels, often the rank order of packages was
similar across team members. Of the two packages the one
not favored was the second choice of each group member.

5. Variations around and between the two settlement packages
(i.e., 2A, 2B, 2C, 2D, 2E) were considered and again the
analysis was done. Two alternatives were selected although ■
the bargaining committee prepared to enter negotiations
with all five as options.

6. Discussions with upper management produced an authority for
bargaining which went beyond the computer model-assisted
settlement point which gave the bargaining team some latitude
during negotiations.

WOULD YOU LIKE TO SEE k

THE RESULTS OF ANY MORE
3TRATEGIF.STTYPF ( FOR YES AND N K«H NO

? H

WHAT PACKAGE WOULD YOU LIKE TO OFFER,,

AFTER 0 PERIODS OF SIR I KE ( O'-Bf- 1- ORE SIR IKE)

W H A T P A C K AGE W 0 U !... D Y 0 U L I K E T 0 0 F 1 F R ♦ .

A F T E E 1 P E R 1 0 D S 0 F S T R I K E ( 0 - B E I- 0 R E S T E I K b )

WHAT PACKAGE WOULD YOU LIKE 10 OFFER.*

E E 2 P F R 1 0 D S 0 F S T R I K I" < 0 ■■ h YS 0 R t S T R I K E )

44
43
42

31
30
2?
23

27
26
25

20
13
16

WHAT PACKAGE WOULD YOU LIKE
AFTER 3 PERIODS OF STRIKE (0'

TO OI-FER* •>
'BEFORE SIR

!' 6

IES TO REQUESTED STRATEGY 1 1
I

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Figure 5.

Solicitation and Provision of Management's Preferred
Strategy With Subsequent Output

D I OSS-

<-;

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11. 1162.

-11-

During the strategy session, the ease with which results could be
seen without time consuming calculations contributed to an atmosphere
of looking at a large number of options.

Although a sample of one observation, the settlement agreed to by
management and the union was similar to those considered by the bar-
gaining team; three weeks of negotiation produced some fine tuning and
a settlement (without a strike) that was agreeable to both parties.
The bargaining strategy session was conducted by the members of one
division of the client firm along with two members of the corporate
industrial relations department. Other than the head of the affected
division being involved, no upper management from corporate or other
divisions are aware of the model. It is believed that the approach of
using subjective probabilities along with computer assistance may be
a little revolutionary until some success stories are build up. The
model is planned for future usage, and since approximately six con-
tracts are negotiated by various divisions each year, quick familiarity
and documentation of effectiveness is expected.

Variations
Although the example of Figures 1-5 show typical manufacturing
inputs, the actual bargaining unit where the model was applied was a
parts order processing facility which has a strike cost per period
which decreases with time (initially orders are lost, but eventually
other warehouses take up the slack reducing the cost. In fact some-
time the strike cost can become negative — therefore representing posi-
tive cash flow). In contrast, most manufacturing plants will experience

-12-

a strike cost that increases with time. The model is equally adaptable
to either circumstance. It will also handle concessions where the cost
of packages is negative thereby resulting in positive cash flow. (This
is especially important in today's concessionary environment.)

In one trial circumstance, the model was applied to the situation
where the company could either force a contract or let the union con-
tinue to work for another year without a contract. The union favored
working without a contract because it believed its bargaining leverage
to be better a year later. The model was used in conjunction with a
decision tree that specified alternative economic environments for its
firm one year in the future. The three expected results were then
weighted by the probability of the economic environments to yield an
overall expectation associated with delaying contract talks one year
( see Figure 6) .

Although a natural future extension to the model might be to pool
probabilities from the different members of the bargaining strategy
team (perhaps even weighting them based on confidence and/or past
historical accuracy), a different approach is favored. Because the
number of potential packages is almost infinite, conjoint analysis
will be used to vary alternative package features. Resultant esti-
mates as to team members' perceptions of union settlement — together
with the cost program previously mentioned — will help develop a set of
Initial packages which seem to offer the maximum probability of
settlement to cost ratio.

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Full text of "An application of computerized decision tree models in management-union bargaining"

See other formats