where m, is the resource (labor, capital, etc.) requirement for the ith project, and M is the total amount of the resource available for use. The value of x, = 0 or 1 depends on whether or not the ith project is selected.

In essence, the Dean and Nishry approach selects the highest-scoring project candidates from the scoring model, and selects them one after another until the available resources have been depleted. If there are several scarce resources, the selection problem can be recast and solved by dynamic programming methods. There are several other R&D project evaluation/selection models described in this excellent work 116|. Many are adaptable to a wide variety of project types.

Goal Programming with Multiple Objectives Goal programming is a variation of the general linear programming method that can optimize an objective function with multiple objectives. In order to apply this method to project selection, we adopt a linear, 0-1 goal program.

First, establish a set of objectives such as "maximize equipment utilization," "minimize idle labor crews," "maximize profits," and "satisfy investment budget constraints." Alternative sets of projects are adopted or rejected based on their impact on goal achievement. A detailed discussion of goal programming is beyond the scope of this book. The interested reader should consult any modern text on management science, for example, [63, 65].

Because most real-world problems are too large for analytic solutions, heuristic solutions are necessary. Ignizio [ 30, pp. 202—206] has developed a heuristic approach that is easily applied to project selection.

As was the case with profitability models, scoring models have their own characteristic advantages and disadvantages. These are the advantages.

1. These models allow multiple criteria to be used for evaluation and decision, including profit/profitability models and both tangible and intangible criteria.

2. They are structurally simple and therefore easy to understand and use.

3. They are a direct reflection of managerial policy.

4. They are easily altered to accommodate changes in the environment or managerial policy.

5. Weighted scoring models allow for the fact that some criteria are more important than others.

6. These models allow easy sensitivity analysis. The trade-offs between the several criteria are readily observable.

The disadvantages are the following.

1. The output of a scoring model is strictly a relative measure. Project scores do not represent the value or "utility" associated with a project and thus do not directly indicate whether or not the project should be supported.

2. In general, scoring models are linear in form and the elements of such models are assumed to be independent.

3. The ease of use of these models is conducive to the inclusion of a large number of criteria, most of which have such small weights that they have little impact on the total project score.

4. Unweighted scoring models assume all criteria are of equal importance, which is almost certainly contrary to fact.

5. To the extent that profit/profitability is included as an element in the scoring \ model, this element has the advantages and disadvantages noted earlier for the | profitability models themselves. 3

Selecting Projects within a Program

This project selection technique is a special type of weighted scoring model. Let 3 us pose a more complex selection problem. Presume that one of a drug firm's three j R&D laboratories has adopted a research program aimed at the development of a j family of compounds for the treatment of a related set of diseases. An individual | project is created for each compound in the family in order to test the compound's -j efficacy, to test for side effects, to find and install efficient methods for producing ^ the compound in quantity, and to develop marketing strategies for each separate ^ member of the drug family. Assume further that many aspects of the research work s on any one compound both profits from and contributes to the work done on other ' members of the family. In such a case, how does one evaluate a project associated i with any given member of the family? One doesn't! |

To evaluate each project-drug family combination would require a separation 1 of costs and revenues that would be quite impossible except when based on the j most arbitrary allocations. Instead of inviting the political bloodletting that would | inevitably accompany any such approach, let us attempt to evaluate the perfor- j mance of all the projects as well as the laboratory that directed and carried out the . entire program—and that may be conducting other programs at the same time. ¡j B. V. Dean has developed an ingenious technique for accomplishing such an . evaluation |17j. This tool not only helps identify the most desirable projects but , can also be used as a planning tool to identify resource needs, especially for large ( projects. Consider Figure 2-3. R&D Laboratory A is conducting a set of interrelated projects in Program 1. Project i contributes to technology j, one of a set of desirable | technologies that, in turn, makes a contribution to requirement k, one of a desired a set of end requirements with some value Vt, the sum of all values being 1.0. „

Project p.

Program 1

Project p.

Program 1

figure 2-3: Evaluation of a related set of projects for R & D lab A.

Now consider the set of projects, Pif and the technologies, 7}. We can form the transfer matrix

composed of ones and zeros as follows:

_ 1, if Pi contributes to T, " [o, if Pi does not contribute to 7}

Similarly, we form the transfer matrix

composed of ones and zeros as follows:

Now find


The resultant matrix will link Pi directly to Rt, thus indicating which projects contribute to which requirements.*

Now consider the value set Vt. "Normalize" Vk so that k

Each normalized Vk will represent the relative value of Rk in the set (/?*}. The values can be written as a column matrix

Note that a project, Pit that contributes to a requirement, R/,, in cit ways will have a value and that the total value of P, is thus

The column matrix E = |ei| is the set of values for all projects in the laboratory, and the sum of all project values,

where I is a row matrix consisting of ones.

•This step requires the arithmetic process of matrix multiplication. The process is not difficult. An explanation of the methods together with a short example is presented In Appendix D. The method is further illustrated in Case II of this chapter.

Example An R & D program consists of two projects, four technologies, and three requirements. Project 1 contributes to technologies 1 and 4 only but project 2 contributes to technologies 2, 3, and 4. Technology 1 contributes to requirement 2 only and technology 4 contributes to requirement 1 only. Technologies 2 and 3 contribute to requirements 1 and 3 and requirements 1 and 2, respectively. Requirements 1, 2, and 3 have relative values of 0.2, 0.5, and 0.3, respectively. What is the overall value of the program and which project is most important?

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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