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2. Objective Function —the linear combination of a decision maker’s decision
variables that are to be either minimized or maximized. For example, we may
want to maximize revenue or profit, and we will want to minimize cost or a
deviation from a desired target level. We will refer to the objective function as Z .
3. Constraints —the linear combination of decision variables that represent how
the decision variables can and can not be used. Constraints are often referred to
as the technology of the linear program .
As you can see, the term linear is important throughout the definitions above.
If the conditions of linearity are not met, then you obviously do not have a LP.
Yet, there are techniques for solving non-linear programs, and later we will briefly
discuss the topic. It must be noted that it is far more difficult to solve non-linear
programs, and it may also be very difficult to do so with Solver. There are software
packages available for the specific purpose of solving non-linear programs. Now, let
us consider a problem that can be formulated as a LP.
9.3 Example—York River Archaeology Budgeting
The principles of a thriving, but cash strapped business, York River Archaeology
(YRA), are holding their quarterly budget meeting to decide upon the most criti-
cal budget that they have yet to produce. YRA does archaeological studies of sites
that are to be developed for various uses—family housing, retail sales, public build-
ings, etc. Many cities and states require these studies. They are used to determine
if important historical sites will be disturbed or destroyed due to development, and
are quite similar to environmental impact studies. Thus, their services are in great
demand in regions where significant building activity takes place.
In attendance at the meeting are the three principles, Nick, Matt, and Garrett, all
accomplished Ph.D. archaeologists and historians, and their trusted business advi-
sor, Elizabeth. Nick spoke to the group first—“The importance of this budget cannot
be overstated. In the past 10 years we have not paid much attention to budgets, and it
has gotten us into serious dilemmas with our cash flow. Back then, we could finance
operations from our cash flow only, but now we have grown to the point where we
need a substantial line of credit to keep operations running smoothly and also to
finance our growth. Elizabeth has been telling us for years that it is important to
create realistic budgets and to stick to them, but we haven’t listened. Now, if we
want our bank to provide us a reasonable line of credit, we have no choice but to
do precisely as she has advised, and to show the bank that we can work within a
budget.”
YRA is in the business of managing archeological projects. Just prior to the
beginning of each quarter, the principals and Elizabeth meet to select the projects
they will accept for the forthcoming quarter. From the projects selected and the
resources consumed in the process, they are able to produce a detailed quarterly
budget. YRA has been quite successful, so much so, that they have more requests
for projects than they are capable of accepting. Thus, their resource limitation is
the only factor that restricts them from accepting all the available project contracts.
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