Critical Path Method

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Architectural Associates, Inc. (AA1) specializes in large, industrial, retail, and public projects, including shopping malls, manufacturing complexes, convention centers, and the like. The firm is considered to be one of the region's most effective and creative design studios. Their design facility is located in a large, midwestern city and is housed on the second floor of an old building, originally used for light manufacturing. The offices are at one end of the floor, and about two-thirds of the floor space is occupied by the design staff and technicians. The entire space devoted to design is a single, open area and workstations are laid out in such a way as to encourage communication between individuals working on a common project.

A senior executive of AA1 noticed that, for the past year or two, the chance of bringing design projects in on time and on budget had decreased to the point where the only uncertainty was how late and how much over budget a project would be. Architectural projects, like computer programming and a few other creative processes, seem to be typified by the need to crash projects at the last minute, but even with the usual crash, AAI was still late and, consequently, over budget.

An examination of the workplace disclosed a large, green felt, display board mounted on the wall where it was visible to the entire design staff. The board listed the names of individual designers and technicians vertically, and design contract numbers across the horizontal axis. The times allocated for work on each project by appropriate staff members were shown at the intersections of the rows and columns. The time estimates were made by senior managers, themselves architects, based on their experience. The individuals with direct responsibility for design work generally felt that the time estimates were reasonable.

The work process was studied and the following problem was revealed. If the design of the electrical systems involved in a plan was estimated to take five days, for example, the individual(s) responsible for the work planned it in such a way that it used the five days allowed. If a problem occurred on the first day, the worker(s) simply stayed late or speeded up work the next day in order to get back on schedule. Problems on the second day, and even on the third and fourth days were handled in the same way, by crashing the work. Problems occurring on the fifth day, however, could not be handled so easily and this part of the project would be late. Because most of the different systems (the mechanicals, landscape, etc.) were designed simultaneously and staffed to require about the same number of days (rather than being sequential), and because problems were very likely to arise late in the design process of at least one of the systems, the overall design project, which required all tasks to be completed on time, was almost invariably late.

In an attempt to solve the problem, a simple check-mark to show job assignments was substituted for time allocations on the green board. Additionally, senior management made normal, optimistic, and pessimistic time estimates for each task and calculated "TE," also used to help estimate project cost. These estimates were not given to the design staff who were simply told to do the work involved as efficiently and effectively as they could. The result was that the range of task times increased slightly, but the average time required for the various tasks fell somewhat since they were now designed for efficiency rather than X days. Roughly the same number of tasks were accomplished in less than the expected time as tasks that took more than the expected time.

Consider the data in Table 9-1. First, we compute a cost/time slope for each activity that can be expedited (crashed). Slope is defined as follows:

crash time — normal time that is, the cost per day of crashing a project. The slope is negative, indicating that as the time required for a project or task is decreased, the cost is increased. Not that activity c cannot be expedited. Table 9-2 shows the time/cost slopes for our ex ample.

A clear implication of this calculation is that activities can be crashed in incre ments of one day (or one period). Often, this is not true. A given activity may hav* only two or three technically feasible durations. The "dollars per day" slope of su ' activities is relevant only if the whole crash increment is useful. For example, if an activity can be carried out in either eight days or four days, with no feasible intermediate times, and if an uncrashable parallel path goes critical when the first activity r reduced from eight down to six days, then the last two days (to four days) of tim reduction are useless. (Of course, there are times when the PM may expedite activities that have little or no impact on the network's critical time, such as when the resources used must be made available to another project.)

One must remember that crashing a project results in a change of the technol^ ogy with which something is done. In the language of economics, it is a change in the "production function." At times, crashing may involve a relatively simple decision to increase groups of resources already being used. If the project, for instance, is to dig a ditch of a certain length and depth, we might add units of labor-shovel to shorten the time required. On the other hand, we might replace labor-shovel units with a Ditch Witch. Discontinuities in outcomes usually result. Different amounts o labor-shovel input may result in a job that takes anywhere from one to three day Use of the Ditch Witch may require three hours. There may be no sensible combin" tion of resources that would complete the job in, say, six hours. In some case technology cannot be changed, and task duration is fixed. A 30-day toxicity test for' new drug requires 30 days—no more, no less.

Not only do changes in technology tend to produce discontinuities in ou comes, they also tend to produce discontinuities in cost. As the technology is changed to speed a project, the cost curve relating input costs to time is apt to, jump as we move from less to more sophisticated production systems. Not only is' the curve displaced, it almost certainly will not be parallel to the earlier curve, bu will change at a different rate. (For an extended treatment of this subject, see |37j (chapter 13)).

Table 9-1 An Example of CPM

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