Rockwell Automation Arena OptQuest Users Guide - Manual (Page 26)

A RENA O PT Q UEST U SER ’ S G UIDE
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Elements of an optimization model
Controls
Controls are variables or resources in your model over which you have control, such as
how many pieces of equipment to purchase or whether to outsource certain activities.
Controls are selected from resources and variables defined in an Arena model. The opti-
mization model is formulated in terms of the selected controls. The values of the controls
are changed before each simulation is performed until the best values are found within the
allotted time limit.
Constraints
A constraint defines a relationship among controls and/or responses. For example, if the
total amount of money invested in buying equipment must not exceed $50,000, you can
define this constraint as:
20000*Equipment1 + 10000*Equipment2 <= 50000
Here, we assume that each piece of Equipment1 costs $20,000, while each piece of
Equipment2 costs $10,000. OptQuest only considers combinations of values for the two
equipment purchases whose sum is no greater than $50,000.
Consider the following example. In a service environment, a manager wants to impose a
condition that limits the maximum time spent in queue. This quantity is a response (i.e.,
measured as a simulation output). After selecting appropriate values for the controls,
OptQuest must invoke Arena to run a simulation and determine whether or not the current
trial solution is feasible with respect to the time-in-queue constraint.
OptQuest differentiates between linear constraints and non-linear constraints. Linear
constraints describe a linear relationship among controls. The budget constraint for
purchasing equipment is an example of a linear constraint. A non-linear constraint
contains a non-linear expression or a response. The constraint limiting the time spent in a
queue is a non-linear constraint. OptQuest can evaluate linear constraints without running
an Arena simulation. Non-linear constraints can only be evaluated by running a
simulation. A solution that satisfies all constraints is considered a feasible solution. If one
or more of the constraints is violated, the solution is infeasible.
Not all optimization models need constraints; however, those that do must deal with the
distinction between a feasible and an infeasible solution.
A feasible solution is one that satisfies all constraints. Infeasibility occurs when no
combination of values of the controls can satisfy a set of constraints. Note that a solution
(i.e., a single set of values for the controls) can be infeasible, by failing to satisfy the
problem constraints, and this doesn’t imply that the problem or model itself is infeasible.