Empirical Studies in Decision Rule-Based Flexibility Analysis for Complex Systems Design and Management

Abstract

This paper presents the results of human subject experiments focusing on the role of decision rules in the study of flexibility and real options analysis (ROA) in design and management of complex engineering systems. Decision rules are heuristics-based triggering mechanisms that help determine the ideal conditions for exercising flexibility in system operations. In contrast to standard ROA based on dynamic programming, decision rules can be parameterized as decision variables, and therefore capture the decision-making process based on specific realizations of the main uncertainty drivers affecting system performance. Similar to standard ROA, a decision rule approach can be used to quantify the benefits of flexibility in early conceptual design studies, and help identifying the best flexible systems design concepts before a more detailed design phase. While many studies demonstrate expected lifecycle performance improvement stemming from a decision-rule based approach as compared to standard design and ROA techniques, very few studies show experimentally their effectiveness in managing flexible engineering systems. This paper presents the results of controlled human-subject experiments involving thirty-two participants evaluating a training procedure in a simulation game environment. The controlled study show that a stochastically optimal flexible strategy combined with an initial policy for the system configuration can improve significantly the expected coverage rate of medical emergencies. These provide insights for further research, development and evaluation of flexible systems design and management strategies for complex engineering systems.

Appendix

List of important parameters and variables

Notation	Value	Unit	Definition
S	10	Year	Number of strategic periods of the system lifecycle
T	40	Quarter	Number of tactical periods of the system lifecycle
N	5	–	Number of scenarios considered
I	10	–	Number of demand grid cells considered
J	10	–	Number of candidate sites for station installation
sc l	2.00, 3.73, 5.38	$, Million	Installation cost for upgradable station with $l ( = 1,2,3)$ capacity
uc l	1.80, 3.36, 4.84	$, Million	Upgrading cost for expanding a station with $l ( = 1,2,3)$ capacity
oc	0.01	$, Million	Operation cost per unit capacity for a station
ac	0.1	$, Million	Unit cost per ambulance
mc	0.01	$, Million	Maintenance cost per ambulance
r s	12 %	–	Annual discount rate
r t	2.87 %	–	Quarterly discount rate
x jtn	[0, 4]	–	The capacity of the station on station j at t under scenario n
w jtn	[0, 4]	–	Number of vehicles allocated on station j at t under scenario n
y ijtn	1 or 0	–	l if grid cell i is assigned to station j at t under scenario n, and 0 otherwise
de j	[1, 8000]	–	Threshold of incident number occurred on grid j for triggering the installation of a new station at $s = 2, \ldots ,S$
d itn	[1, 8000]	–	The number of emergency incidents in location i within tactical period t under scenario n
o jsn	1 or 0	–	1 if total number of incidents occurred on grid j over a strategic period s − 1 is greater than or equal to de j at $s = 2, \ldots ,S$, and 0 otherwise
u jsn	1 or 0	–	1 if the total number of incidents missed in station j over a strategic period s − 1 is greater than or equal to mej at time s = 2,…,S, and 0 otherwise
$op_{j}$	[1, 3]	–	Optimal capacity to be deployed if new station is opened on j at $s = 2, \ldots ,S$. If new station is not opened on j, $op_{j} = 0$
$io_{j}$	[0, 1]	–	$io_{j} = 1$ if new station is opened on j at s = 1
$op\_1_{j}$	[1, 3]	–	Optimal capacity to be deployed if new station is opened on j at beginning of time s = 1.
$oe_{j}$	[1, 3]	–	Optimal amount of capacity to be expanded on j if a station on j is expanded.
me	[1, 3200]	–	Optimal amount of lost incidents in a station to trigger the flexibility of capacity expansion at $s = 2, \ldots ,S$
$\omega_{jtn}$	[1, 8000]	–	The amount of lost incidents at station j within tactical period t under scenario n
M1, M2, M3, M4	100000	–	Constants whose values is large, for optimization purposes
U 0	3200	–	The upper bound for variable me
L 0	0	0	The lower bounds for variable me
$\delta_{1}$	1600	–	The iterative value for searching the optimal value of me