# OR-Notes

## J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

#### Network analysis tutorial solution

The network diagram is shown below.

• 16 months
• probability 0.873730

The network diagram is shown below.

• expected time 36.33 days
• probability more than 38 days = 1 - 0.751 = 0.249

The network diagram is shown below.

• project duration using normal times 20 days, critical path B-C-E-G-H

We tabulate below the costs for all durations below 20 days

```        duration         project         penalty         indirect         total
cost            cost            cost             cost
20               6900            600             5000             12,500
19               7100            500             4750             12,350
18               7350            400             4500             12,250
17               7600            300             4250             12,150
16               7900            200             4000             12,100
15               8300            100             3750             12,150
14               8700            -               3500             12,200
13               9100            -               3250             12,350```

Best solution is to crash to 16 days duration by crashing C 1 day, E 2 days, and G 1 day