(44b) A Dynamic Game Theoretic Framework for Strategic Production Planning

Chemical industries operate on the competitive edge of their profit margins; production planning algorithms must generate competitively viable plans in order to be useful¹. Production planning methods which do not consider market behaviour and the presence of antagonistic competitors may not generate competitively viable production plans². Game theory provides the tools necessary to model competitive behaviour in production planning problems. We present a dynamic game theoretic framework for production planning. In this framework, prices change dynamically in time based on historical market supply of product; such behaviour is modelled using a modified dynamic Cournot oligopoly model with sticky prices formulated as a dynamic potential game^3,4. The production plans resulting from this framework are obtained for all competitors, and are dynamic Nash equilibrium trajectories, meaning they are optimal in their interpretation as mutual best responses to all other competitors’ plans⁵.

This framework is used to investigate patterns in the petroleum refining industry in Western Canada, namely the persistence of small refineries in the presence of much larger refineries (owned by different parent companies) serving the same markets. The large refiners possess the market power to force the small refiner out of business, thus obtaining larger market shares for themselves^6,7. Yet this does not appear to be the typical outcome, and the small refiner persists through time. We model this scenario as a dynamic game theoretic production planning problem, and present our results and interpretations of this phenomenon, including under what conditions the small refiner should be concerned with the threat of closure, what actions are available to the small refiner to prevent closure (if the threat is legitimate) and why there exist situations in which there is no legitimate threat of closure.

These results have an important impact on organization level planning and the integration of production planning into strategic organizational planning. At the production planning level, we are able to capture market-dependent phenomena, and at the organizational decision level, production capabilities are a driving force of strategy.

1. Sahebi H, Nickel S, Ashayeri J. Strategic and tactical mathematical programming models within the crude oil supply chain context – a review. Comput Chem Eng. 2014; 68: 56-77.
2. Tominac P, Mahalec V. A game theoretic framework for petroleum refinery strategic production planning. AICHE J. 2017; DOI 10.1002/aic/15644.
3. Fershtman C, Kamien MI. Dynamic duopolistic competition with sticky prices. Econometrica. 1987; 55(5): 1151-1164.
4. Monderer D, Shapley L. Potential Games. Game Econ Behav. 1996; 14(1): 124-143.
5. Webb JN. Game Theory: Decisions, Interaction and Evolution. London, UK: Springer London; 2007.
6. Government of Canada, National Energy Board. Feature article: understanding the production, transport, and refining of crude oil in Canada. https://www.neb-one.gc.ca/nrg/ntgrtd/mrkt/prcstrdrtcl/qrtrlprcpdts/ftrrtcl/2016-04-29ndrstndngcrl-eng.html. Updated May 2, 2016. Accessed August 17, 2016.
7. Johnston D. Refining report complexity index indicates refinery capability, value. Oil gas J. 1996; 94(12).