Optimal Decision Making in Product & Process Planning

Design and Scheduling Real Options based Planning

Pharmaceutical R&D Management

The option character of a drug development project is derived from the fact that the project has tremendous upside potential on successful completion with downside risk limited to the amount invested in each stage of R&D.  If an initial investment in lead discovery and pre-clinical research is successful, the company has the right but not the obligation to proceed with each of the three stages of clinical testing followed by an application to gain FDA approval. However, at any point in this sequential process, the company reserves the right to abandon the project due to unfavorable market conditions and/or internal budgetary limitations.

Recognizing this, we addressed the pharmaceutical pipeline management problem by developing a multistage stochastic portfolio optimization model (OptFolio) that views new product development as a series of continuation/abandonment options embedded within the real options framework. The resulting mixed-integer linear programming (MILP) formulation serves as a decision-support tool in selecting the optimal product portfolio from a set of candidate drugs at different stages in the developmental pipeline and subject to varying levels of market and technical uncertainty over the desired planning horizon. In addition, the OptFolio framework provides a roadmap for future decisions by tracking the decision of abandonment over time and calculating the minimum market value above which development is continued under changing resource constraints. Results indicate that the riskier the project is, the larger the minimum market value required for continuing testing in future stages.  Consequently, the value of the abandonment option increases with rising market uncertainty or decreased probability of clinical trial success.  The key result of this real options analysis is the value of gathering information at the beginning stages of drug development to determine whether the investment in later, more expensive stages is justified and using the abandonment option to terminate disappointing candidates. 

To facilitate a sensitivity analysis of model parameters, the Optfolio model was modified to include Monte Carlo simulation to generate the probability distribution of portfolio returns. The results of the sensitivity analysis reveal that simulation-based real options valuations are largely impacted by Phase III and FDA success probabilities, consistent with the desire of pharmaceutical companies to avoid the high late-stage investment costs of risky, marginally profitable products.  The augmented OptFolio framework also provides a risk management strategy for balancing risk versus reward tradeoffs via the construction of an efficient frontier of optimal portfolios that minimize risk for a desired level of return.  A follow-up paper discussed a method for including additional managerial choices into the OptFolio model. These choices could include deferring an R&D investment decision until more information becomes available, expanding or contracting the scale of the investment in response to changing market conditions, accelerating a developmental stage, or conducting indications tests to increase the therapeutic claims of the drug. Inclusion of additional options will lead to a more comprehensive and responsive decision making tool that provides a detailed road-map of current and future managerial decisions.

The OptFolio model framework was next utilized to guide not only internally focused R&D planning decisions but also to evaluate and design external opportunities such as in-/out-licensing of drug development. In today's intensely competitive business environment, pharmaceutical companies are augmenting their product pipelines by in-licensing proprietary compounds or drug discovery-related technologies from smaller biotechnology companies. In view of this, the OptFolio model was extended to evaluate partnership opportunities as real options and determine the optimal timing and investment policy for proposed alliances in the face of technological and market uncertainties and budgetary restrictions. The resulting framework addresses the following research questions:

1. What is the optimal stage for the pharmaceutical company to enter into a licensing deal for a given candidate drug?
2. What is the pharmaceutical company's optimal R&D investment policy under changing market uncertainty and amplification factors?
3. Within a given therapeutic area, what is the optimal portfolio of alliances and their respective timing and investment policies under time varying resource constraints?

Results indicate that early stage alliances become more valuable as market uncertainty and the ability of pharmaceutical companies to enhance the value of the licensed drug increase because of the ability to control downside risk via the abandonment option.  Consideration of additional investment policies allows the pharmaceutical company to creatively allocate its resources, at different times and amounts, to maximize the revenue potential of its alliances. This analysis also suggests the risk management strategy of delaying licensing agreements within a portfolio of alliance deals until early technical hurdles are cleared, but then offering deals containing larger upfront payments to the biotechnology company to negotiate a large percentage of product ownership.

Current research efforts are aimed at providing greater theoretical insights into the real world challenges facing pharmaceutical new product development.  A key aspect of portfolio planning is the recognition that different firms may have different strategic objectives and a firm’s ideal portfolio must reflect its unique planning philosophy. In addition to maximizing the expected value of the portfolio, managers are also concerned with short-term objectives such as generating a billion-dollar blockbuster drug every few years to satisfy investors’ growth expectations. Managers are also concerned with balancing the number of therapeutic areas and the relative strength of each area. These two competing objectives – diversity across therapeutic areas to reduce risk versus focused research within a discovery platform to enhance the probability of success – will be explicitly modeled. In this context, we view the pharmaceutical pipeline as consisting of three planning levels with the following hierarchal decision structure: therapeutic categories (how many and which ones to include), indications within a therapeutic category (how many should be supported for each therapeutic area), and candidates for each indication (how many to support).  Furthermore, resource allocation decisions are viewed not as "all or nothing" as in previous work, but in terms of marginal rates of return to determine the optimal funding level for each therapeutic area, indication, and candidate. These modifications result in a new product development portfolio optimization model that better captures the intricacies of the pharmaceutical industry and allows us to analyze the historical planning decisions of pharmaceutical companies to decipher and compare their respective planning philosophies.

Pollution Abatement Planning

The past decade has witnessed a significant increase in the attention given by both policy-makers and regulators to market-based environmental policy instruments. These policy instruments have emerged as a more cost effective alternative to the conventional "command-and-control" standards that had dominated the previous two decades of environmental law and regulation. In the light of this observation, a model for incorporating market-priced emission permits in the pollution abatement initiative of a company was developed. The basic problem addressed in this work was: Given a set of candidate technologies characterized by their respective emission levels, fixed capital investment and variable production costs, current market price and availability of emission permits and future product demand and emission market forecasts (in terms of permit price and availability), determine the optimal technology-permit portfolio that minimizes total expected pollution abatement costs.

The pollution abatement planning problem was modeled within a multistage stochastic programming framework and led to the development of the EnviroFolio decision making tool. A scenario-based description of uncertainty was used to model the decision-makers ability to react to unfolding uncertainty regarding the product demand and the emissions market. In addition, the impact of the availability of derivative emission contracts, such as options, on the total pollution abatement cost was also investigated. The developed model quantified the benefits of the flexibility offered by these instruments in minimizing total pollution abatement costs and facilitated the estimation of the environmental liability faced by the company both in terms of the probability of meeting compliance requirements in the future and the resulting non-compliance penalties. Management of environmental and financial risks was also addressed by linking the optimization model with basic statistical and probabilistic techniques. In particular, a chance constraint-based approach was utilized to shape the cost distribution in accordance with the risk bearing capacity of the firm. The key features of the modeling framework have been highlighted through several planning case studies (Gupta and Maranas, 2003a,b). Results indicate that significant cost savings and risk reduction can be realized through the inclusion of emission options in the compliance portfolio.

[Rogers et al (2005); Rogers et al (2004); Rogers et al (2003b); Gupta and Maranas (2003a); Rogers et al (2003a); Rogers et al (2002)]

Supply Chain Planning and CPI Design and Scheduling

Planning models can be broadly categorized into three distinct groups based on the time frames they address. Long-range planning or capacity expansion models are "strategic" planning models which aim to identify the optimal timing, location and extent of additional investments in processing networks over a relatively long time horizon (many years). Short-term scheduling models or "operational" planning models constitute the other extreme of the spectrum of planning models. These models are characterized by very short time periods (days) over which the various manufacturing tasks have to be fully sequenced. The third class of models, the midterm planning models are intermediate in nature (months) consolidating features from both the short term and long term planning models. A number of decisions must be made during each one of these time frames. The key challenge here is to provide the necessary theoretical, algorithmic and computational support to aid in optimally making these decisions accounting for future product demand or other parameter variability.

Batch plant design and scheduling under product demand uncertainty

In this work, the multiperiod planning and scheduling of multiproduct plants under demand uncertainty is addressed. The proposed stochastic model involves the maximization of the expected profit subject to the satisfaction of single or multiple product demands with prespecified probability levels (chance-constraints). The stochastic elements of the model are expressed with equivalent deterministic forms eliminating the need for discretization or sampling techniques. This implies that problems with a large number of possibly correlated uncertain product demands can be efficiently handled.

Furthermore, a new method is introduced for optimally designing multiproduct batch plants under the single-product campaign (SPC) production mode. Uncertain future product demands are described with normal probability distributions and more than one processing units of equal size are allowed per stage. At the expense of imposing (i) the normality assumption for product demand uncertainty, and (ii) the SPC production mode, the original two-stage stochastic optimization problem is transformed into a deterministic mixed-integer nonlinear programming (MINLP) problem. Computational results reveal a surprising complexity in the shape and form of the constructed trade-off curves between the probability of meeting all product demands and profit. These curves provided a systematic way for contrasting maximum profitability over demand satisfaction.

Supply chain optimization and midterm planning

Efficient solution techniques are introduced for multisite, multiperiod midterm planning problems based on a Hierarchical Lagrangean Relaxation (HLR) procedure. The basic idea of the procedure is to partition the original supply chain into smaller more tractable pieces. Dual information is utilized to guide the partitioning strategy and subgradient optimization is employed to tighten the lower and upper bounds. Computational results demonstrate that the proposed solution methodology was effective in bracketing the optimal value of the problem in relatively small computational time. The incorporation of the HLR procedure within a cutting plane or branch and bound framework is needed to close the relaxation gap.

The effect of product demand uncertainty is described within a two-stage stochastic programming framework. In this bilevel decision making framework, production decisions are made "here-and-now" prior to the resolution of uncertainty while the supply chain decisions are postponed in a ``wait-and-see'' mode. The challenge associated with the expectation evaluation of the inner optimization problem is resolved by obtaining its closed-form solution using linear programming (LP) duality. The evaluation of the expected second stage costs is achieved by analytical integration yielding an equivalent convex mixed-integer nonlinear problem (MINLP). Efforts at extending the approach to the more general multiperiod and multicustomer problem are under way.

[Gupta and Maranas (2003b); Gupta and Maranas (2001); Gupta et al (2000); Gupta and Maranas (2000); Petkov and Maranas (1998b); Petkov and Maranas (1998a); Petkov and Maranas (1997b)]