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activities/environmental impacts, were obtained from publi-
cations prepared by road/traffic organizations in Sweden and
from discussions with Swedish road authorities. On the basis
of these data it was possible to estimate most of the dimen-
sions of the costs and losses identified here. However, the data
available were inadequate to derive reliable estimates of the
losses associated with both accident-related roadway damages
and inconveniences caused by traffic delays, as well as the costs
due to salt damage to roadways, and these three dimensions
of the expenses have been ignored in this study.
In estimating the total expenses associated with the various
action-event sequences (or branches of the tree), an additive
model of losses and costs has been assumed. That is, the termi-
nal expense assigned to a particular branch of the tree is the
sum of the costs and/or losses associated with the particular
combination of actions and events that define this branch. The
total expenses calculated for the eleven basic terminal
outcomes are listed in the second table.
Outcomes 04, 07, and 011 are associated with action/event
sequences in which the snowstorm event has not yet occurred.
In these cases, expected expenses associated with subsequent
iterations of the snowstorm/road-maintenance DMP have been
added to the basic terminal expense. These expected expenses
vary depending upon the type of snowstorm information used
as a basis for decision making in these iterations. The terminal
expenses given in the table relate to the situation in which
these decisions are based on forecast information.
Snowstorm events and snowstorm forecasts
A typical snowstorm event in this district in south-central
Sweden has a duration of six hours, with snow falling at a rate
of approximately 1cm per hour. In this study, it is assumed that
snowfall is continuous; specifically, a snowstorm event consists
of uninterrupted snowfall for a six-hour period, with a total
accumulation of 6cm. The unknown characteristic of snow-
storms of interest here is their time of initiation. Thus, the
short-range snowstorm forecasts evaluated in this case study
are forecasts of the initiation time of snowfall events.
Three types of snowstorm information are considered in this
study:
• Climatological information based on current weather data
from automatic stations along highways and roads and
weather radar information
• Forecast information
• Perfect information.
of the wake-up decision and pre-salt (S)/don’t pre-salt (S’) in
the case of the pre-salt decision. The weather events are also
assumed to be binary in nature: namely, the occurrence (x =
1) or non-occurrence (x = 0) of a snowstorm in a particular
period.
The timeline identifies the time (in hours) at which the deci-
sions are made. The wake-up decision is taken as the arbitrary
point in time at which this DMP initially arises (t = 0), and the
pre-salt decision is made one hour later (t = 1). This diagram
also defines the time intervals associated with the four periods
of interest; namely, the wake-up period (x1 : 0 ≤ t ≤ 1), the pre-
salt period (x2: 1 ≤ t ≤ 4), maintenance period 1 (x3: 4 ≤ t ≤6),
and maintenance period 2 (x4: 6 ≤t ≤ 12).
Each branch of the decision tree terminates in a node that
represents the outcome of the corresponding sequence of actions
and events. Eleven distinct outcomes (or branches) are identi-
fied, denoted here by 01, 02, …, 011. Outcomes 04, 07, and 011
are associated with sequences of actions/events in which the
snowstorm does not occur during any of the four basic periods.
In these cases it is assumed that road-maintenance authorities
face this same decision-making problem again at a later time.
This assumption leads to an extended version of the basic DMP.
In effect, the basic wakeup/pre-salt decision-making process is
reiterated on these three branches of the decision tree until the
snowstorm occurs, or until the incremental change in the asso-
ciated terminal expense becomes insignificant.
Outcome expenses
The expenses associated with the outcomes are assumed to be
of two basic types:
• Losses due to the snowstorms themselves
• Costs due to maintenance activities.
Each type of expense (the generic term for costs or losses)
contains two categories of loss or cost. In the case of snow-
storms, the expenses are losses due to traffic accidents (La)
and losses due to traffic delays (Ld). In the case of maintenance
activities, the expenses are costs due to maintenance activities
(Cm) and costs due to environmental impacts of maintenance
activities (Ce). In addition, each category of cost or loss
possesses two or more dimensions. The types, categories, and
dimensions of the expenses considered in this snowstorm/road-
maintenance DMP can be seen in the table.
Road and traffic statistics, as well as basic data related to
losses due to accidents/delays and costs due to maintenance
Table 1: Types, categories, and dimensions of
expenses associated with terminal outcomes
Type
Category
Dimension
Snowstorm
Accident losses (L
a
)
Injuries
losses
Deaths
Vehicle damage
Roadway damages
Delay Losses (L
d
)
Loss of work time
Loss of leisure time
Inconvenience
Maintenance
Maintenance costs(C
m
)
Personnel costs
costs
Equipment costs
Material costs
Environmental costs (Ce)
Salt damage to environment
Salt damage to vehicles
Salt damage to roadway
Source: Liljas, E., and Murphy, A.H.
Table 2: Expenses associated with terminal outcomes
in the case of state-of-the-art snowstorm forecasts
Terminal
Expense
Terminal
Expense
outcome
(1,000 SEK)
outcome
(1,000 SEK)
0
1
11,200
0
7
11,206
0
2
9,300
0
8
11,400
0
3
8,500
0
9
1 1,400
0
4
1 1,453
0
10
11,400
0
5
11,100
0
11
11,006
0
6
11,000
Source: Liljas, E., and Murphy, A.H.