# Project Portfolio MCDM Selection

Standard project portfolio selection methods have limited business appeal since they don’t consider all business characteristics. 10 min read.

# The Need for Multiple Project Portfolio Selection Criteria

If only a single project proposal existed project selection would be easy. Similarly, if a set of projects existed which had no limits on money, resourcing or risk then project selection would also be easy. Instead because business constraints exist finding the best valued project portfolio outcome is difficult.

Consider an example in which there are 20 possible projects. A standard project selection method ranks projects by monetary gain. Given the ranked order, projects are funded until the overall budget is reached.

In this way, for a total project budget of \$200k, projects 14, 15, 10, 8, 20, 6 and 18 are selected representing a total gain of \$6,182k for a cost of \$192k. This approach is simple enough when there is only one characteristic but becomes more complicated when multiple criteria need to be considered.

# Converting Project Characteristics to a Common Criteria

During project selection, there are several possible projects, P, each with characteristics, C, such as cost, benefit, customer importance etc. In most practical situations, these characteristics will be contradictory, i.e. minimise cost, maximise benefits, maximise customer importance, etc., which makes it is impossible to find an optimal solution.

To solve this problem, project characteristics are converted to a common scale, for example, money. In this way, the value of a project can be assumed to be the sum of the characteristics allowing an optimal solution to be found. However, pitfalls of this approach include,

1. It might not be possible to assign a common conversion.
2. It might not be possible to simply sum characteristics together.
3. It might not be possible to equally weight converted characteristics.

# Assigned-Weight MCDM Method

The assigned-weight MCDM approach does not convert multiple characteristics into a common attribute but instead combines multiple characteristics into an index. This index is a function of the characteristics whose improvement makes the right trade-off’s so that the right decision is made, represented as,

Index = constant + wt1*attribute1 + wt2*attribute2 + … + wtc*attributec

The weights that determine the index are fitted from observed data using multiple linear regression. If observed data is not available, then the set of weights can be defined in a group discussion.

Referencing the 20 projects above with the three characteristics of cost, benefit and risk whereby gain is maximised, cost is minimised, and risk is minimised. Since there is conflict among these characteristics a way around this is to use, value = risk * (gain/cost) resulting in,

Whereby the calculated value can be used to sort the projects. In this way, for a total project budget of \$200k, projects 14, 20, 10, 8, 6, 18, 13, 7, 17 and 12 are selected representing a total gain of \$5,806k, cost of \$174k and risk per project of 33%.

# Pareto-Optimal MCDM Method

It is often difficult to agree assigned weights because it is hard to define what optimal means for a vector of values. Instead, weights can be generated by applying a Pareto-optimal method by which dominated projects are eliminated, i.e. they are poorer in some other choice of characteristic. A Pareto-Optimal project portfolio depends on which characteristic is selected for ranking, which is made more difficult as the number of characteristics increases.

From our example of 20 projects, comparing project 1 to project 2 it is not clear based on the given characteristics which project dominates because it depends on the characteristic. That is, project 1 dominates project 2 in regard to cost but is dominated by project 2 in regards to gain and risk. Comparison between project 1 and 3 is a little more straightforward, since project 1 dominates project 3 because it is of higher gain, lower cost and lower risk. For this pairwise comparison to be effective, project 1 needs to be compared to all of the remaining projects, then project 2 needs to be compared to all of the remaining projects starting from 3, while project 4 needs to be compared to all the projects starting from 5, and so on. This exercise is no mean feat feat especially when complicated by comparisons like project 1 and 2 exist.

# Dominated Portfolios

Project dominance can also be used at the Portfolio level to determine the optimal portfolio. For each portfolio, the gain, cost and risk can be summed for each project. The number of pairwise comparisons is determined by, Accounting for all possible project portfolios in our 20 possible project example there are 1,048,575 total project portfolios to consider in the search for the optimal portfolio. Checking all pairs of these 1,048,575 portfolios would mean (1,048,575 * 1,048,574)/2 = 549,754,241,025 pairs of project portfolios to be considered. Even allowing for computer programs to handle this large volume, the process can be speed up by pre-sorting to reduce the number of candidates, e.g. only feasible projects selected and only portfolios of a particular size between some minimum and maximum are selected.

# Summary

Project portfolio selection is simple enough if only one characteristic is considered. When additional characteristics are included for consideration the selection process becomes exponentially more complex unless a formula determined either mathematically or in a group session can be used.

While computer programs can be designed to handle Multiple-Criteria Decision-Making projects and portfolios the sheer volumes generated for practical portfolios of 100+ projects make its use problematic and not a great method for finding an optimal solution.

In subsequent, posts we will look to leverage mathematical programming techniques including ‘The Data Envelope Approach’ and ‘Linear Programming’ to optimise project portfolio selection.