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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
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