Microsoft Office Tutorials and References

In Depth Information

value of 25, thus the
Slack
is approximately 19.7. We can state that 19.7 units of

project type 1 were not utilized in the solution.

How might we use this information? Let us consider Resource A. If more hours

of resource A could be found and added to the RHS, would the objective function

beneﬁt by the addition? Why? Currently you have unused hours of A; the constraint

has
slack
. The addition of a resource that is currently underutilized cannot be of

any value to the objective function. The solution algorithm sees no value to the

objective function by adding an additional unit of A. We are far wiser to acquire

additional hours of resource B, C, and/or D since their constraints are
binding
and

have no
slack
. To demonstrate the point, I will change the formulation to increase

the number of resource B hours by 1 hour. Although this is a very minor change,

it does lead to different decision variable values and to a higher objective function

value as seen in Exhibit 9.8.

The new solution increases the number of project type 1, from 5.3 to 5.4, and

reduces the number of project type 4 from 2.6 to 2.5. All other decision variables

remain the same, including project type 2. Recall it was not at its maximum (30) in

the previous solution and the addition of a single unit of resource B has not caused

it to change. The new value of the objective function is $5,484,656.78, which is

$3,686.44 greater than the previously optimal solution of $5,480,970.34. In essence,

the value of an additional hour of resource B is $3,686.44, and although the changes

in decision variables are minor, the change has been beneﬁcial to the objective func-

tion. We could perform this type of analysis with all our resource hours to determine

the
marginal value
of an additional unit of resource (RHS) for binding constraints.

Exhibit 9.8

Incremental change in resource B to 901

Search JabSto ::

Custom Search