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Bayesian Decision Process for Project Management

Amita Kapoor

Amita Kapoor

Uncertainties are an integral part of any project life-cycle. Project managers try their best to avoid these uncertainties, but unfortunately, no one can predict the future. These uncertainties can affect multi-dimensions.

Uncertainties are an integral part of any project life-cycle. Project managers try their best to avoid these uncertainties, but unfortunately, no one can predict the future. These uncertainties can affect multi-dimensions, for example:

  • Impact on project schedule - the uncertainties can delay the project delivery.

  • Impact on project budget -  the estimated budget can go haywire.

  • Implications for project quality - the delivered project may have compromised specifications.

Uncertainties are of four types, each one requiring a different approach.

uncertainty chart

Well, I did say, no one can predict the future - well, almost true - maths tells us that even uncertainties are not that uncertain- they can be modeled with the right tools. One of the favorite tools of statisticians to deal with uncertainty is the Bayesian Decision Process.This blog post will talk about the Bayesian Decision Process and how it can be integrated into the project management task to deal with uncertainties.  

Bayesian Networks

We start with Bayesian Networks (BN). A BN is a directed graph, and it consists of nodes representing random variables and a set of directed links - connecting the pair of nodes. Each node represents a variable with an associated probability (also called conditional probability table). The links tell about the dependence of one node over another.  Their strength lies in the fact that they can be used to model uncertainties combined with expert knowledge and data. They have been employed in diverse fields for their power to do probabilistic and causal reasoning. At the heart of the Bayesian network is the Bayes’ rule, which is used to determine the joint probability of an event given certain conditions. 

The simplest way to understand the BN is that BN can determine the causal relationship between the hypothesis and evidence.  There is some unknown hypothesis H, about which we want to assess the uncertainty and make some decisions. We start with some prior belief about the hypotheses H, and then based on the evidence E, we update our belief about H. And thus using BN, we can answer questions like:

  • Should the company launch a specific new feature in the product?

  • What is the probability that there will be a delay in the next projected upgrade?

  • Does a new-client onboarding system satisfy the prescribed project requirements?

  • Should a completely new algorithm be used to replace the existing one?

  • What is the average life of a product?

  • Is the capital allocation of 10% sufficient to cover operational costs in the project?

Let us see BN in action, consider this scenario: a company producing digital health gadgets wants to implement a new marketing strategy to bring in new clients. Given specific past data, what is the probability that the strategy would be a success?

The first step is to build the BN; building a BN involves two base steps: determining the structure and CPTs. Let us consider some attributes of the client; since the product is a digital gadget for health, we can consider the following attributes:

  • Age group

  • Gender

  • Annual Earnings

  • Education Level

  • Yearly Medical Expense

bayesian network

What you see above is just one hypothesis on how the attributes may be linked. Observe that the nodes in BN can be either discrete or continuous. Once the structure of the network is determined, a probability distribution is assigned to each node. The distributions in the Bayesian can be learned either from the data, or via an expert, or a mixture of both. Every time the BN encounters new data, it can update its prior records. Once the probability distribution is in place, and we have some evidence, variable elimination is used to perform inference. One can use BN even when the data is time-series data or sequences. The networks thus formed are called dynamic Bayesian networks.  

BN has been employed extensively in the literature for vast types of projects in diverse fields. They are used in the aviation industry, construction industry, manufacturing industry, medical diagnosis, and many others to facilitate decision-making under uncertainties.  They can be employed even when data is missing, which is true for most real-world cases.

Project Management and Bayesian Decision Networks

The uncertainty in project cost and project schedule, especially for innovative technology projects, have complex interdependencies. These are complex problems as they depend on various variables and often require dealing with very little information about them. BN can help in identifying, understanding, and quantifying the complex relationships affecting project success. Employing BN requires an analytical mindset; we want the problem at hand to decompose into events and relationships that are granular enough to be meaningful yet not extensively large in numbers that overwhelm the computation process. However, BN alone may not be sufficient to determine the optimal decision pathways in a given situation; we require Bayesian Decision Networks (BDN). In Bayesian networks, all nodes are chance nodes, but in BDN we have decision nodes (Node corresponding to a decision to be made) and utility nodes (the targeted outcome we want to maximize or minimize). There are also present links called information links, entering decision nodes. They indicate that the decision is determined via the information retrieved from the parent nodes. Building a BDN requires expert knowledge. The expert provides information about the decision nodes, the options available and the project manager/decision-maker, and the utilities that we want to maximize or minimize. We can transform a BN into BDN following specific structural rules.

Conclusion

 BN can be used to make informed decisions under the conditions of uncertainties and ambiguities. From project cost, to project schedule, to project success; Bayesian networks have demonstrated that they can handle uncertainties and assist project managers in decision-making and  risk management. There exists a large number of software services that can develop a BN from the data.  However, when we want to build a system for optimized decision-making- BDNs is a better option. At present, building BDNs requires significant manual effort, but the research in this direction is promising.