Develop and solve the knapsack formulation to schedule the project presented in Table 7.10, the resource for which is presented in Table 7.11.

Draw the Gantt chart for the schedule. Use the following notation in your formulation:

\(C_{t}\) is the set of activities eligible for scheduling at time \(t\)

\(\mathrm{CAF}_{i}\) is the relative priority weight for activity \(i\)

\(R_{i t}\) is the units of resource type \(j\) available at time \(t\)

\(\overline{R_{j t}}\) is the units of resource type \(j\) in use at time \(t\)

\(r_{i j}\) is the units of resource type \(j\) required by activity \(i\)

\(x_{i t}\) is the indicator variable for scheduling activity \(i\) at time \(t\)

\(x_{i t}=1\) if activity \(i\) is scheduled at time \(t\)

\(x_{i t}=0\) if activity \(i\) is not scheduled at time \(t\)

There are two resource types. Resource availability varies from day to day based on the schedule as follows:

Table 7.10

Table 7.11

Activity Predecessor Duration (Days) Resource Requirement (Type1, Type 2) Priority Weight ABCDEFGH A, B B C B,F D, E 6524567 2,5 50.1 1,3 57.1 3,1 56.8 2,0 100 1,4 53.2 3,1 51.8 4,3 44.9 2,3 54.9