(346g) A Multistage Stochastic Program to Evaluate Feedstock/Technology Development for Chemical Process Industry
Top chemical companies are shifting their focus from bulk chemicals to specialty products. For example, BASF expects to increase the share of “customized products, and functionalized materials and solutions” sales to 70% of its total by year 2020. Dow Chemical Company is “carving-out” its chlorine and epoxy assets reducing its commodity chemicals foot-print while it continues to grow in downstream specialty products in integrated plastics, electronics, and agriculture. Bayer recently announced that they will become a “pure Life Science company”, focusing their business entirely on products that enhance human health and nutrition. Dupont continues to focus its product offerings on agriculture and nutrition developed using the latest advancements in biotechnology. These trends suggest that the feedstock and product portfolios along with utilized technologies of chemical process industry (CPI) may grow and be quite different compared to today’s in the near future. As such, there is tremendous opportunity for investigating the impacts of these new technologies/feedstocks/products on chemical process industry.
Incorporation of new feedstocks and technologies into the existing CPI infrastructure may require significant amounts of investment. Determining the investment decisions, i.e., how much to invest, which technologies to invest in, and when to invest in each technology for research and development and for capacity expansion, is a challenging task, as there are often many emerging technologies and the future performance of these technologies is uncertain. In this work, we developed a multistage stochastic programming (MSSP) formulation accounting for both endogenous and exogenous uncertain parameters associated with the new technology investment planning (NTIP) problem.
The NTIP problem is characterized by a set of undeveloped or partially developed feedstock processing technologies and the existing CPI infrastructure system. The objective is to develop an optimal investment strategy that minimizes the total investment cost over a discrete planning horizon. The investment strategy identifies the capacity expansion timing and levels for each of the developing technologies. Each technology is assumed to go through three discrete maturity levels, (1) laboratory, (2) pilot plant, and (3) commercial. Developing technologies are unable to meet production demands unless they have reached the commercial stage. At the time of investment, the yield, the effect of capacity expansion, and the effect of research and development spending on the cost of capacity expansion are not known with certainty. These parameters are endogenous uncertain parameters because the investment decisions affect the realizations of these uncertain parameters. The demand for products is also not known with certainty, and it is represented as an exogenous uncertain parameter. In order to meet demands, the products can be produced from technologies that have been developed to commercial level or the product can be purchased.
The presented formulation models the material flow throughout the technology network using a state-task network where the states are the feedstocks, intermediates, and products, and the tasks are the technologies. Each technology has an initial maturity level. In order to represent the stages of maturity, a stage-gate framework is used. Technologies can move from one stage to the next through capacity expansion. The cost of capacity expansion is modeled using a two-factor learning curve. Capacity expansion costs can be reduced either through capacity expansion or through direct R&D spending. The rate at which each factor affects the capacity expansion cost is uncertain at the time of investment. By expanding capacity and investing in R&D, these factors are revealed. Intermediates and products can be stored, however the amount that can be stored is limited by maximum storage capacities. To incorporate the uncertainty, each uncertain parameter is modeled using a discrete uniform distribution with two possible realizations, a high and a low value. Scenarios are generated using the combinations of realizations for each uncertain parameter. For this formulation, the decisions only impact the realizations (not the distributions) of the endogenous uncertain parameters, which allows for complete enumeration of the realizations of the endogenous parameters a priori.
The MSSP is used to determine the investment-decision plan for the conversion of biomass and naphtha (feedstocks) to ethylene (product) with two intermediates, syngas and ethanol. A total of four different technologies are available, (1) gasification of biomass to syngas, (2) catalytic conversion of syngas to ethanol, (3) catalytic dehydration of ethanol to ethylene, and (4) the cracking of naphtha to ethylene. We assume that technologies (3) and (4) are mature meaning that they are already commercially available, and as such their yields and capacity expansion costs are known. This yields a problem with eight uncertain parameters; six of the uncertain parameters correspond to uncertain parameters relating to each technology, these parameters include the two parameters for the two factor learning curve, and the yield of each technology. Additionally, two parameters represent the demand uncertainty for each product during the planning horizon. The MSSP formulation has 1,376,256 variables and 10,289,152 .
This talk discusses in detail the size of the problem and solution time. The size of this problem grows quickly as the length of the planning horizon increases and the number of undeveloped technologies increases. Based on our preliminary results, linear growth in the number of non-mature technologies caused the size of the problem (number of constraints and variables) grew non-linearly which directly contributes to solution times. The growth in problem size is caused by an increase in the number of possible realizations of uncertain parameters which is multiplicative in nature. Even for the simple presented case, where each parameter has two possible outcomes, the number of scenarios is 256. By increasing the number of non-mature technologies by 1, the number of scenarios in the problem in increased by a factor of 8. This talk will further discuss the impact of extending the planning horizon, the relative ratio of raw material costs, demand, yield, and capacity expansion cost uncertainties on the total cost along with installed and utilized capacity of each technology throughout the planning horizon. Despite the computational challenges associated with implementing the formulation we believe that the formulation provides a flexible approach for the evaluation of developing technologies.