PROJECT CRASHING ALGORITHM.docVIP

PROJECT CRASHING ALGORITHM The project crashing algorithm described in this section is designed to give the mathematically correct time-cost trade-off curve for small project networks which are to be solved by hand. The algorithm proceeds from a network description of the project and the normal and crash times and durations for the project activities to a set of tables which enable the time-cost trade-off graph to be plotted. The three tables are the project activity marginal cost list with available compression, a path list for the project network, and a breakpoint table for the steps in the project crashing process. These will be developed for an illustrative numerical example after a general statement of the algorithm is given. GENERAL ALGORITHM SPECIFICATION Initialization Steps. Step 1. Each activity is assumed to have a known Normal cost if completed in a Normal time, and a (larger) Crash Cost if completed in a (shorter) Crash time. Compute the marginal crashing costs (i.e. cost per unit time) for each activity according to the following formula: ? Marginal Cost = (change in cost)/(change in time) =? (Crash cost - Normal cost)/(Normal time - Crash time) Place these marginal costs in the first column of the project activity list. Place the number of time periods of crashing availability in the second column of the table. Step 2. Enumerate all the paths through the project network, and list them with their normal time durations in the path list. Identify the critical path(s) as those with longest duration, and mark the critical activities as such in the third column of the project activity list started in Step 1. Step 3. Identify the normal project duration, the normal project cost and the normal critical path in the first row of the breakpoint table, labeled as iteration 0. Iteration Steps. Step 4. Select that subset of critical activities which, when compressed in parallel, enable all current critical paths to become shorter, and do so at the least