Engineering & Technology
December 2, 2021

The Multi-Objective Portfolio Optimization Tool: Helping the pharmaceutical industry manage its portfolio

The pharmaceutical industry is responsible for developing and providing life-saving drugs, yet this industry, like most others, needs to make a profit to survive. The industry’s dynamic portfolio has many inherent uncertainties, and through complex decision-making they attempt to avoid losses and maintain efficiency. Dr Mahboubeh Farid and Mikael Palmblad, from Captario AB, are leading research to help companies make the right decisions in the face of complex uncertainties, and to produce drugs needed by care providers. The tool being developed by these researchers will help the industry select the best set of existing projects as well as create optimal strategies for the flow of new projects.

Modern medicine vitally depends on drugs: they are commonly the tools used by physicians and care providers to fight sources of disease and infection. The pharmaceutical industry must therefore decide which drugs to develop, so as to cover the needs of the care providers without wasting valuable resources. The development of a drug is a project with a complex, nuanced, and multi-phase process involving long-term planning. Investments are decided at the beginning of each development phase, and the cost of failed projects is imposed upon the companies. Only a very small number of drugs go to market, the majority of projects being terminated for various reasons (these might include technical, regulatory, and commercial issues).

Thus, it is crucial to identify the optimal selection of projects in order to allocate a finite budget and create long-term opportunities for investment. The drug development portfolio involves many existing projects identified by name, and they have a high probability of failure as a result of high uncertainty. In addition, there are numerous important dependencies that affect the outcome. As the named projects fail, the portfolio must be fed over time with new projects that currently don’t exist. These can come from internal research efforts or in-licensing or acquisition. Optimal selection over time must include projects from these streams, projects which are currently unknown as to their name, but have known characteristics. A portfolio that includes named and unnamed projects is called a Dynamic Portfolio. Dr Mahboubeh Farid and Mikael Palmblad, from Captario AB, have developed and tested the Multi-Objective Portfolio Optimization Tool, in order to better manage the portfolios of pharmaceutical companies.

Olivier Le Moal/Shutterstock.com

Traditionally, pharmaceutical portfolio optimization uses a single-objective, deterministic model. For this to work, the uncertainty that is present in time, cost, revenue, and success rates must be possible to collapse to a single value (eg, a mean). This may be possible when the uncertainty can be described with a single-modal distribution, eg, a uniform or a normal distribution. It is not possible with pharmaceutical development projects because their uncertainty follows a multi-modal distribution. Distributions can be categorised by the number of peaks, with a single peak defined as unimodal, two peaks as bimodal and with three or more peaks as multimodal. A sample with multi-modal distribution, could be the result of extreme events, eg, a project failing, or several independent variables. Variables such as time, cost, and revenue have an uncertain nature along with failure probability. An inaccurate model from a single-objective, deterministic optimization approach, therefore, is not reliable and can be misleading.

Data uncertainty and goal programming
A stochastic multi-objective optimization (multi-objective programming) algorithm optimizes several goals simultaneously; it is simple to use and reliable, with a clear path to implementation. This is an extremely useful tool for the project portfolio of a pharmaceutical company, since it can evaluate more than one objective with uncertainties – these objectives might conflict with one another, exacerbating the difficulties of modelling – and it can decide either toward the maximum return or staying within a finite budget, in order to increase portfolio value. Stochastic programming is the framework that models the optimization problem, and is used when there are inherent uncertainties.

Health is the most important asset in life, and the pharmaceutical industry must take sizeable gambles in its attempts to sustain public health.

A common portfolio optimization problem is to maximise a certain parameter, eg, revenue, given one or more constraints, eg, that the total cost does not exceed the budget. In a deterministic setting, the solution to this problem is well known. If we want to simultaneously optimize on more than one objective we can create a multi-objective model that, instead of maximising the single objective, minimises the deviation from some target values of the objectives. For example, the model can find a balance between maximising revenue while minimising cost. This balance between the objectives can be shifted by changing the weights of the respective objectives. A higher weight for one objective means that we can tolerate a larger deviation from the other objective.

A model of the Optimization Tool.

If we wish to add uncertainty to the problem, we can combine multi-objective programming with stochastic optimization and rewrite the constraints so that we do not require strict observance at all times. Instead of strictly enforcing the budget, we can accept a certain risk of ending up over budget. The result is a possibility of finding large increases in value for a small budget overrun.

The first step, called goal programming, was initially proposed by Charnes and Cooper in 1955. Usually, the parameters under uncertainty have a Gaussian (normal) probability distribution or some derivative of this. An algorithm was proposed in the 1960s, also by Charnes and Cooper, which finds a solution to optimisation problems with multi-modal distributions. This is known as chance constrained programming. This method considers the coefficients of the constraints with inherent uncertainties. For the solution, it allows the constraints to change within an acceptable range. For the optimization of project selection, a new model was proposed by Farid, et al, named MICCG (Big-M, Integer, Chance Constrained Goal Programming), which is an extension of the above work.

Optimising the portfolio with uncertain cost and return
Pharmaceutical companies need to allocate their limited budget among numerous projects. The portfolio optimisation is extremely challenging when the duration, the cost, and the return are uncertain. The probability of success when a drug is being developed is low, and the process has multiple phases. The portfolio has a goal revenue and a limited budget, and if a project fails in a phase, it is aborted and the company pays for the losses without compensation.

Modern medicine vitally depends on the production of drugs.Planar/Shutterstock.com

The research undertaken by Farid and Palmblad will help the pharmaceutical industry to remain within their annual budget and to keep the business profitable, by finding the optimal project selection. The method starts by running a Monte Carlo simulation which creates many different scenarios where the variables are random with multi-modal distributions. The Monte Carlo simulations are a class of computational algorithms with a broad range of applications, and the idea is to repeat a random sampling scenario multiple times to derive conclusions. One can solve stochastic problems by utilising randomness, and this is used for calculations when the application of other approaches is difficult or impossible. For the model MICCG, the objectives are twofold: first, to keep the cost within the budget limit; and second, for the total return to be more than the target profit. For both of those objectives the return values are allowed to fluctuate within a defined confidence level.

There is high risk and a good deal of uncertainty inherent in the research phase; every choice has huge real-world consequences.

Pharmaceutical portfolio selection and numerical results
To test this, an experienced analyst constructed the sample dynamic portfolio, with 36 projects in various phases for a time duration of 11 years. Of these projects, 25 are known and 11 unknown. The simulation has 200 random variables and adopts a 20-year planning horizon. Three scenarios with different budget constraints were tested and the algorithm gives a 75–85% success rate through the process of project selection. Overall, there is an 80% chance to stay within the budget limit and 75% of achieving the return goal even in the worst-case scenario. Such results give the drug development companies confidence and help them to be more efficient and productive for the medical community.

Gorodenkoff/Shutterstock.com

Conclusions
Health is the most important asset in life, and the pharmaceutical industry must take sizeable gambles in its attempts to sustain public health. Like all private companies, however, they need to make a profit to continue to exist and to produce good-quality medications. There is high risk and a good deal of uncertainty inherent in the research and development phase, and every choice – from minor to major – has huge real-world consequences. The resources of a pharmaceutical company are limited, and if they invest in projects that fail, then important drugs that can save lives will not have the opportunity to be developed.

Farid and Palmblad are providing crucial help to these companies, enabling them to select the best portfolios through their multi-objective optimization algorithm. They are therefore minimising the bottom-line risk. Their research quantifies a fundamentally qualitative decision-making process, giving numbers to the decisions in pursuit of an optimal choice. Geometry, computer simulation, and algorithms are used to develop portfolio optimization methods. Future research will look to extend these existing algorithms to further enhance the support for portfolio-management decisions.

Personal Response


What work are you currently undertaking to further optimize portfolio management?

So far, the focus has been to answer questions that have been formulated, for example, which projects should we choose for our portfolio. Going forward, we are creating ways to find answers to questions that have not been formalised, for example, should we change the portfolio budget to be able to accommodate more projects.

This feature article was created with the approval of the research team featured. This is a collaborative production, supported by those featured to aid free of charge, global distribution.

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