Journal
OPERATIONS RESEARCH
Volume 58, Issue 2, Pages 289-302Publisher
INFORMS
DOI: 10.1287/opre.1090.0718
Keywords
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Funding
- National Science Foundation [0758061-CMII, 0556106-CMII]
- Singapore-MIT
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0824674] Funding Source: National Science Foundation
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In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition ( in particular a duopoly setting) together with the presence of demand uncertainty. We consider a dynamic setting where multiple products share production capacity. We introduce a demand-based fluid model where the demand is a linear function of the price of the supplier and of her competitor, the inventory and production costs are quadratic, and all coefficients are time dependent. A key part of the model is that no backorders are allowed and the strategy of a supplier depends on her competitor's strategy. First, we reformulate the robust problem as a fluid model of similar form to the deterministic one and show existence of a Nash equilibrium in continuous time. We then discuss issues of uniqueness and address how to compute a particular Nash equilibrium, i.e., the normalized Nash equilibrium.
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