Multiproject Scheduling Heuristic

To attack this problem, recall the hierarchical approach to project planning we adopted in Chapter 5. A project plan is a nested set of plans, composed of a set of generalized tasks, each of which is decomposed into a more detailed set of work packages that are, in turn, decomposed further. The decomposition is continued until the work packages are simple enough to be considered "elemental." A PERT/CPM diagram of a project might be drawn for any level of task aggregation. A single activity (arrow) at a high level of aggregation would represent an entire network of activities at a lower level (see Figure 9-11). Another level in the planning hierarchy is shown as a Gantt chart in Figure 9-12.

If an entire network is decomposed into subnetworks, we have the equivalent of the multiproject problem where each of the projects (subnetworks) is linked to predecessor and successor projects (other subnetworks). In this case, the

QrQ,

QrQ, figure 9-11: Task a decomposed into a network of subtasks.

predecessor/successor relationships depend on the technology of the parent project. In the true multiproject case, these relationships may still depend on technological relationships—for example, a real estate development project being dependent on the outcome of a land procurement project. The relationships may, however, be determined more or less arbitrarily, as when projects are sequenced on a first-come, first-served basis, or by any other priority-setting rule, or undertaken simultaneously in the hope that some synergistic side effects might occur. Or the relationship among the projects may simply be that they share a common pool of resources.

With this conceptual model, assume we have a set of projects. Each individual

Level 1 plan

Level 1 plan

\ Level 3 plans

Figure 9-12: Hierarchy of Gantt charts. Source: |23|

project is represented by a network of tasks. We can form a single network of these projects by connecting them with dummy activities (no resources, no duration) and/or pseudoactivities (no resources, some duration). Both dummy activities and pseudoactivities represent dependency relationships, but these dependencies, as noted above, may be technological or quite arbitrary.*

As usual, and excepting dummy and pseudoactivities, each task in each network requires time and resources. The amount of time required may or may not vary with the level of resources applied to it. The total amount of resources and/or amounts of individual resources are limited in successive scheduling periods. Our problem is to find a schedule that best satisfies the sequence and resource constraints and minimizes the overall duration of the entire network. The resulting schedule should indicate when to start any activity and at what level of resources it should be maintained while it is active.

Before undertaking the allocation of resources, it is proper to consider the quantity of resources available for allocation. (For the moment, we consider "resources" as an undifferentiated pool of assets that can be used for any purpose.) At the beginning of any period (hour, day, week, month, etc.) we have available any resources in inventory, R,, which is to say, left over as excess from the previous allocation process. Changes in the inventory can be made from within the system of projects or by importing or exporting inventory from the outside. Excluding activities that have been completed in previous periods, every activity planned by the project is in one of four states; ongoing, stopping, waiting and technologically able to start, or waiting and technological unable to start.

Figure 9-13 illustrates these conditions. We label ongoing activities as "resource users." Those stopping are "resource contributors." Those waiting and able to start are "resource demanders." Those waiting and unable to start can be ignored for the present. The amount of resources available for allocation is, therefore, the amount in inventory plus the amount contributed, R, + Ro If the amount demanded is less than this sum, there will be a positive inventory to start the next period. If not, some demanders will go unfunded.

User

Contributor Demander o o

Current Period

Time

Figure 9-13: Sources and uses of resources.

•This exposition is based on Weist's work ]59|, and on Corwin's application of Weist's papers to r source allocation among multiple R&D projects 1111.

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Project Management Made Easy

Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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