Introduction
Units are common
Measurement plays a central role in observations of the real world. Most observed quantities are measured in some unit (e.g. dollar, hour, meter, etc.), and the magnitude of the unit influences the mental picture that you may have of an object (e.g. ounce, kilogram, ton, etc.). When you combine such objects in a numerical relationship, the corresponding units must be commensurable. Without such consistency, the mathematical relationships become meaningless.
Why units in models
There are several good reasons to track units throughout a model. The explicit mentioning of units can enhance the readability of a model, which is especially helpful when others read and/or maintain your model. Units provide the AIMMS compiler with additional checking power to find errors in model formulations. Finally, through the use of units you can let AIMMS perform the job of unit conversion and scaling.
Standard units
The model editor in AIMMS will give you access to a large number of quantities and units, and in particular to those of the International System of Units (referred to as SI from the French “Systeme Internationale”). The SI system is an improved metric system adopted by the Eleventh General Conference of Weights and Measures in 1960. The entire SI system of measurement is constructed from the atomic base units associated with the following nine basic quantities.
Quantity 
Atomic Base Unit 
Text 

length 
m 
meter 
mass 
kg 
kilogram 
time 
s 
second 
temperature 
K 
kelvin 
amount of mass 
mol 
mole 
electric current 
A 
ampere 
luminous intensity 
cd 
candela 
angle 
rad 
radian 
solid angle 
sr 
steradian 
Derived quantities and units
All quantities which are not one of the nine basic SI quantities are
called derived quantities. Each such quantity has a derived base unit
which can be expressed in terms of the atomic base units of the basic SI
quantities. Optionally, a compound unit symbol can be associated with
such a derived base unit, like the symbol N
for the unit
kg*m/s^2
. The following table illustrates some of the more
wellknown derived quantities and their corresponding derived base
units. Note that five of them have an associated compound unit symbol.
Many other derived quantities are available in AIMMS.
Quantity 
Derived Base Unit 
Text 

area 

square meter 
volume 

cubic meter 
force 

newton 
pressure 

pascal 
energy 

joule 
power 

watt 
charge 

coulomb 
density 

kilogram per cubic meter 
velocity 

meter per second 
angular velocity 

radian per second 
Related units
Aside from the base unit that must be associated with every quantity, it
is also possible to specify a number of related units. Related units
are those units that can be expressed in terms of their base unit by
means of a linear relationship. A typical example is the unit km
which is related to the base unit m
by means of the linear
relationship \(x\) km = 1000*x m
. Similarly, the unit degC
(degree Celsius) is related to the base unit K
through the formula
\(x\) degC = (x + 273.15) K
.
Standard unit prefix notation
Frequently, related units are a multiple of their own base unit, which
is reflected through a prefix notation that indicates the level of
scaling. this table shows the standard SI prefix
symbols and their corresponding scaling factor. Familiar examples are
kton
, MHz
, kJ
, etc. Note that any prefix can be applied to
any base unit except the kilogram. The kilogram takes prefixes as if the
base unit were the gram.
Factor 
Name 
Symbol 
Factor 
Name 
Symbol 

\(10^1\) 
deca 
da 
\(10^{1}\) 
deci 
d 
\(10^2\) 
hecto 
h 
\(10^{2}\) 
centi 
c 
\(10^3\) 
kilo 
k 
\(10^{3}\) 
milli 
m 
\(10^6\) 
mega 
M 
\(10^{6}\) 
micro 
mu 
\(10^9\) 
giga 
G 
\(10^{9}\) 
nano 
n 
\(10^{12}\) 
tera 
T 
\(10^{12}\) 
pico 
p 
\(10^{15}\) 
peta 
P 
\(10^{15}\) 
femto 
f 
\(10^{18}\) 
exa 
E 
\(10^{18}\) 
atto 
a 
\(10^{21}\) 
zetta 
Z 
\(10^{21}\) 
zepto 
z 
\(10^{24}\) 
yotta 
Y 
\(10^{24}\) 
yocto 
y 
Flexible specification
To give you maximum freedom to choose your own quantities, units and naming conventions, AIMMS is not exclusively committed to any particular standard. However, you are encouraged to use the standard SI units and prefix symbols to make your model as readable and maintainable as possible.
Summary of terminology
Thus far you have encountered basic quantities (this table) and derived quantities (this table). Each quantity has a base unit. The base unit of a basic quantity is defined through a unit symbol, referred to as an atomic unit. All other base units are derived base units. Such units are defined through an expression in terms of other base units, which can eventually be translated into an expression of atomic base units. You have the option to associate a unit symbol with any derived base unit, which is referred to as a compound unit symbol. Whenever you have associated a unit symbol with the base unit of either a basic or derived quantity, you are also allowed to specify one or more related unit symbols by specifying the corresponding linear relationship.