A STUDY ON HUMAN CONTROL IN STOCK-ADJUSTMENT TASKS
Ernst W, Diehl
System Dynamics Group
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT. Results of an ongoing study investigating the effect of
different task feedback characteristics on human performance are
reported. In a computer-assisted experiment, subjects were asked to
perform a dynamic stock-adjustment control, A subject's control action
enters the system in two ways: it effects the stock to be adjusted and
it feeds back on the disturbance that impinges on the system. The latter
effect is varied with respect to its strength and its delay. The major
finding that emerges from the experiment is that increasing strength in
the feedback link (in either a positive or negative direction) worsens
performance. An effect of delay length on performance could not be
shown.
INTRODUCTION
Developing a theory that relates complexity of decision situations to
the likelihood of dysfunction in human decision strategies is a major
research challenge in behavioral decision theory (Hogarth 1981,
Kleinmuntz 1985). One obstacle in meeting the challenge is to find a
framework that permits the comparison of different decision tasks with
respect to their complexity. I believe that feedback theory can provide
such a framework (Mackinnon and Wearing 1985). Following this approach
the challenge can then be reformulated as to determine what particular
characteristics in feedback structures lead people to perform poorly or
well.
The feedback structure of dynamic decision situations can be
characterized along various dimensions: number of feedback links, number
of states present, degree of non-linearity, degree of uncertainty,
strength of feedback, delay of feedback, system stability, eigenvalues
and eigenvectors of the system, etc, Each of these dimensions could
conceivably have an influence on how people perceive the consequences of
the feedback structure and on what decision strategies they employ. what
is ultimately needed is a systematic effort to determine how the
The suggestions of Bent Bakken,, Don Kleinmuntz, and John Sterman and the
research assistance of Chris Sonne are gratefully acknowledged.
206
various dimensions of the feedback structure interact and influence
peoples behavior.
A possible starting point for such a systematic effort is to investigate
decision making in basic feedback structures. Once behavior in simple
systems is understood, the groundwork is laid to investigate how people
perform in more complex feedback structures that are composed of several
basic systems. One structure that is of particular interest is the class
of stock-adjustment tasks. A vast number of human activities can be
characterized as attempts to adjust the actual state of a variable to a
desired value, How is stock-adjustment control effected by changes in
the characteristics of the underlying feedback structure? Finding an
answer to this question is the motivation behind the experiment reported
in this study.
PRIOR EXPERIMENTAL WORK IN BEHAVIORAL DECISION THEORY
Stimulated by papers by Edwards (1962) and Toda(1962) a literature known
as dynamic decision theory developed in the 60's and early 70's. See
Rapoport and Wallsten(1972) and Rapoport (1975) for an overview. Of
particular interest: for the current study are the experiments on
multistage control problems. Rapoport (1966a,1966b) examines how people
perform control on an unstable process of the kind x(k+1)=a*x(k) where
a>1. Rapoport (1967) and Ebert (1972) report on experiments on stock-
adjustment problems. Most of the studies focus on the effects of varying
time horizons and uncertainty on performance.
Although interest in dynamic decision theory has continued through the
70's until today (Broadbent and Aston 1978, Mackinnon andd Wearing 1980
Hogarth and Makridakis 1981, Kleinmuntz and Thomas 1987; Brehmer 1987
for an overview), dynamic decision theory has not been a very active
research area. Slovich et al (1977) suggest that the mathematical
sophistication of dynamic decision problems and the need for time
consuming computer programs might be some of the reasons behind the
decline in interest among psychologists
System dynamics practitioners have only recently begun to conduct
studies into how people solve dynamic decision tasks (Bakken 1988, Diehl
1988, Sterman 1987). Sterman's work (Sterman 1989a, 1989b) strongly
207
dynamic decision-making. It is not clear, however, if these
misperceptions are due to a lack of information about the environment,
due to a lack of understanding of the basic task or due to a lack of
understanding of the connections between decision and outcomes.
EXPERIMENTAL DESIGN
The stock-adjustment task is formulated as an inventory-production
system with a quadratic cost function. Over a 30-step decision period,
subjects are charged with adjusting production in the presence of
varying sales. Figure 1 displays the stock-flow diagram of the system.
The subjects’ objective is to minimize total accumulated cost. Changes
in production are twice as costly as a deviation of inventory from its
setting point (=0) .
Figure 1: Stock-flow diagram of the task
Cost of Production” Total sales
inventory 3, 3
gap
Inventory gap
Delay (4 periods,
2 periods, no delay)
Cost of
change in
production
Sales (random walk) Sales ( dent
on production)
Production
Change in Production Strength of
(= subject's decision) production >sales
link (-0.6, -0.3,
0, +0.3, +0.6)
Sales consist of two parts: sales independent from a subject's
production decision and sales directly influenced by a subject's
decision. Independent sales follow a random path. Subjects are informed
that their best bet is to expect that independent sales next round will
be the same as independent sales in the current round, but that the
actual value can differ anywhere between +20 and -20. The link between
production and dependent sales varies from trial to trial along two
dimensions: strength of the link and delay length of the link. The
subjects are informed about the conditons for each trial.
A two-factorial, within-subject design is chosen for the experiment.
Strength of the production-sales link can take on five values (+0.6,
+0.3, 0, -0.3, -0.6), delay of the link can take on three values (4
periods, 2 periods, no delay). Since length of delay is undefined for a
link strength of 0, the conditions can be combined in 13 different ways
(5*3-2). Each subject received the thirteen treatments in a different,
randomized order. The overall sequence order was balanced.
Thirteen subjects participated in the experiment. Ten of the subjects
are undergraduates at M.I.T., three of the subjects are enrolled in a
masters program at M.I.T. The subjects performed the 13 trials in 4
sessions (2-3-4-4). It took about 25 min. to complete a trial. Subjects
received detailed instructions at the beginning of the first session and
a short reminder of the rules at the beginning of each of the following
sessions. Each subject received a base payment of $20 and additional
payments based on performance. Subjects were informed that the expected
average pay would be $40 and that performance would be computed on base
of their ten best trials. Four subjects did not complete all four
sessions. There did not appear to be a difference in performance of
subjects who dropped out of the experiment and of subjects who completed
the experiment. The results presented below are based solely on the nine
subjects who completed the experiment.
EXPERIMENTAL RESULTS
To evaluate the subjects’ performance, accumulated cost at the end of
each trial is compared to the cost that would have resulted if the
optimum control rule had been used. Figure 2 shows the performance
ratios for the nine subjects. For each subject, performance in the
median game is indicated by the black square. In addition, performance
for the third best game and for the third worst game is shown. In 48 of
the total 117 trials (41.0%), the actual cost did not deviate by more
than %50 from the optimum cost. In 4 trials (3.4%) actual cost was more
than 100 times higher than optimum cost.
209
Figure 2: Subjects' score (3rd, median, and 11th best)
rs er
Subject # (ranked by med. performance)
Figure 3 displays the average performance ratio achieved in the thirteen
consecutive trials. The practice effect is statistically significant
(F12/96=2.63; Prob.>0.99). For the statistical analysis presented below
the practice effect was removed.
Practice effect
Figure
00
Average performance
(optimum/score)
a
Na
4
2
of
i 3 5 7 5 ii 3
Trial #
Figure 4 shows the influence of the feedback characteristics on
performance. Each of the 13 cells contains the average score that the
subjects achieved under that cell condition. The cell values are
adjusted for the practice effect. Scores are computed as optimum cost
divided by actual cost. The average score for all 13 conditions combined
210
is 0.558. Cell values above 0.558 indicate that performance is improved
with respect to the cell condition. Cell values below 0.558 indicate
that performance is worsened.
Figure 4: Average score for each of the 13 conditions
Strength of feedback link
-0.6 -0.3 0 +0.3 +0.6
0 0.558 0.571 0.703 0.640 0.435,
se
Bg 2 0.450 0.666 0.566 0.529
As
4 0.438 0.546 0.662 0.493
For a statistical analysis of the effects, positive and negative
feedback conditions were separated. Performance worsens both with
increasing negative feedback and with increasing positive feedback, as
Figure 5 shows. Delay length does not influence performance.
Figure 5: Statistical analysis of the main effects
F Prob.
Increasing positive feedback 3.440 > 0.90
Increasing negative feedback 4.889 > 0.95
Increasing delay length 0.046 ng.
effect
CONCLUSIONS AND FURTHER RESEARCH
The results seem to indicate that decision makers insufficiently adjust
their decision rules to increasing feedback strength in stock-adjustment
tasks. To corroborate this conclusion, a detailed statistical analysis
of the decision rules used is indicated. The research task ahead can be
illustrated with help of Figure 6.
ant
Figure 6: Feedback structure of the stockK-adjustment task
Change
in
Production
The bold links between variables represent the physical structure of the
Independent
Sales " Production
system, the other links represent the assumed information structure that
is used in the decision process. The research task ahead can then be
formulated as: What information structure is used by the decision maker
to accomplish a task, given a specific physical structure and a specific’
objective? In the experiment reported in this study, the physical link
between production and sales was varied systematically along the two
dimensions link strength and link delay. An analysis of the decision
rules used should reveal how decision makers adjust the information
links in response. The adjustment used by the decision makers can then
be compared to the adjustment suggested by the normative model.
REFERENCES
Bakken, Bent E.
games. Mimeo, System Dynamics Group, MIT. Cambridge (1988).
Brehmer, Berndt. Systems design and the psychology of complex systems.
Empirical foundations of
In: Rasmussen, Jens and Zunde, Pranas. (eds.) rical
information and software science III. Plenum Publishing Company. (1975)
21-32.
Broadbent, Donald E. and Aston, Ben. Human control of a simulated
economic system. Ergonomics 21(1978) 1035-1043.
Diehl, Ernst W. Participatory simulations as training tools ~ a study
based on the market growth model. In:
i . La Jolla, CA
(1988) 52-65.
Ebert, Ronald J, Human control of a two-variable decision system.
P. 7(1972) 237-264.
212
Edwards, Ward. Dynamic decision theory and probabilistic information
processing. Human Factors 4(1962) 59-73.
Hogarth, Robin M. Beyond discrete biases: functional and dysfunctional
aspects of judgmental heuristics. Psychological Bulletin 90(1981) 197-
217.
Hogarth, Robin M. and Makridakis, Spyros. The value of decision making
in a complex environment: an experimental approach. Management Science
27(1981) 93-107.
Kleinmuntz, Don N. Cognitive heuristics and feedback in a dynamic
decision environment. Management Science 31(1985) 680-702.
Kleinmuntz, Don N. and Thomas, James B. The value of action and
inference in dynamic decision making.
Decision Processes (1987).
Mackinnon, Andrew J. and Wearing, Alexander J. Complexity and decision
making. Behavioral Science 25(1980) 285-296.
Mackinnon, Andrew J. and Wearing, Alexander J. Systems analysis and
dynamic decision making. Acta Psychologica 58(1985) 159-172.
Rapoport, Amnon, A study of human control in a stochastic multistage
decision task. Behavioral Science 11(1966a) 18-32.
Rapoport, Amnon. A study of a multistage decision task with an unknown
duration. Human Factors 8(1966b) 54-61.
Rapoport, Amnon. Variables affecting decisions in a multistage inventory
task. Behavioral Science 12(1967) 194-204.
Rapoport, Amnon, Research paradigms for studying dynamic decision
behavior. In: Wendt, D. and Vlek, C. (eds.)
. D, Reidel Publishing Company. Dordrect-Holland
(1975) 349-369.
Rapoport, Amnon and Wallsten, Thomas S. Individual decision behavior.
23(1972) 131-176.
Slovic, P., Fischhoff, B. and Lichtenstein, S. Behavioral decision
theory. Annual Review of Psychology 28(1977) 1-39.
Sterman, John D, Testing behavioral simulation models by direct
experiment. Management Science 33(1987) 1572-1592.
Sterman, John D. Modeling managerial behavior: Misperceptions of
feedback in a dynamic decision-making experiment. Management Science.
Forthcoming March 35(1989a)
Sterman, John D. Misperceptions of feedback in dynamic decision making.
Organizational Behavior and Human Decision Processes. Forthcoming June
43(1989b).
Toda, M. The design of a fungus-eater: a model of human behavior in an
unsophisticated environment. Behavioral Science 7(1962) 164-183.
