Modeling price formation in a multi-commodity market - an application in petrochemical industry

Willi Jaeger
Ruprecht-Karls-Universität Heidelberg

The volatile price dynamics for basic resources, especially of oil, poses challenges to operational and strategic planning in particular in chemical industry. Estimating the influence of the prices of raw and basic materials on the pricing of the product portfolio is highly important for the operational and strategic planning in particular in chemical industry. There is an urgent demand for a rational approach to evaluate the price development, including data and process oriented modelling and simulation. The model has to include connection of commodities through their production processes. Important factors like production, price-demand relations, side conditions and contracts, regional structures, transport, storage, general economical development have to be integrated. The huge system size is one of the main challenges. Our team investigated in a frontier project at IWR a system of the petrochemical market. It contained about 140 products connected by more than 300 processes using about 20 different utilities and included several regions (America, Europe/Africa, Asia/Pacific) The lecture gives a summarizing report on the investigation in co-operation with the following partners from analysis, mathematical modelling, optimization and industry:
Lilian Kramer, Sabrina Kellner, Sebastian Sager, Holger Diedam and Simon Jäger.
The following basic concept to determine the dynamics of the product price an optimization model is chosen: The supply side maximizes its total profit taking into account the price-demand relationships for all products and the existing contracts and regulation posing side conditions.
Here the relation between price and demand is playing a decisive role and had to be analysed in a subproject. Due to the high complexity, a mainly deterministic approach was chosen.
The resulting constrained nonlinear optimization problem is in general neither differentiable nor convex. Additional (acceptable) assumptions imply differentiability and convexity. The optimization problem is block-separable, a special structure, which is very useful for a neces-sary further step: The dual optimization problem reflects the separability into sub-problems.
The arising systems may be huge. Already generating realistic full model systems needs in general a special software tool. But more crucial is the problem of collecting the necessary data, which is time consuming and expensive. Therefore the reduction of the optimization problem is a central part of the problem. Here a geometric approach is applied to determine the essential structures of the underlying network of interactions. Sub-problems coupled via linking products are identified and partially lumped in single nodes.
The results obtained for specific petrochemical products are presented. The simulated dynam-ics of the amount and the price of important products in the styrene subsystem are in better agreement with the real data than the predictions of experts.

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